{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"using LinearAlgebra\n",
"using Plots\n",
"import JSON\n",
"# using Quaternions\n",
"using StaticArrays, Rotations\n",
"using Distributed\n",
"using StaticArrays, BenchmarkTools\n",
"using Base.Threads\n",
"using CUDAnative\n",
"using CuArrays,CUDAdrv \n",
"using Test\n",
"import Base: +, * , -, ^"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Todo\n",
"- create struct for material and get for each edge its properties\n",
"- implement getTimestep (done)\n",
"- implement on single voxel (done)\n",
"- get reat E and L (done)\n",
"- compare to Frame3dd"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"struct Vector3\n",
" x::Float64\n",
" y::Float64\n",
" z::Float64\n",
" function Vector3()\n",
" x=0.0\n",
" y=0.0\n",
" z=0.0\n",
" new(x,y,z)\n",
" end\n",
" function Vector3(x,y,z)\n",
" new(x,y,z)\n",
" end\n",
"end\n",
"struct Quaternion\n",
" x::Float64\n",
" y::Float64\n",
" z::Float64\n",
" w::Float64\n",
" function Quaternion()\n",
" x=0.0\n",
" y=0.0\n",
" z=0.0\n",
" w=1.0\n",
" new(x,y,z,w)\n",
" end\n",
" function Quaternion(x,y,z,w)\n",
" new(x,y,z,w)\n",
" end\n",
"end\n",
"struct RotationMatrix\n",
" te1::Float64\n",
" te2::Float64\n",
" te3::Float64\n",
" te4::Float64\n",
" te5::Float64\n",
" te6::Float64\n",
" te7::Float64\n",
" te8::Float64\n",
" te9::Float64\n",
" te10::Float64\n",
" te11::Float64\n",
" te12::Float64\n",
" te13::Float64\n",
" te14::Float64\n",
" te15::Float64\n",
" te16::Float64\n",
" function RotationMatrix()\n",
" te1 =0.0\n",
" te2 =0.0\n",
" te3 =0.0\n",
" te4 =0.0\n",
" te5 =0.0\n",
" te6 =0.0\n",
" te7 =0.0\n",
" te8 =0.0\n",
" te9 =0.0\n",
" te10=0.0\n",
" te11=0.0\n",
" te12=0.0\n",
" te13=0.0\n",
" te14=0.0\n",
" te15=0.0\n",
" te16=0.0\n",
" new(te1,te2,te3,te4,te5,te6,te7,te8,te9,te10,te11,te12,te13,te14,te15,te16)\n",
" end\n",
" function RotationMatrix(te1,te2,te3,te4,te5,te6,te7,te8,te9,te10,te11,te12,te13,te14,te15,te16)\n",
" new(te1,te2,te3,te4,te5,te6,te7,te8,te9,te10,te11,te12,te13,te14,te15,te16)\n",
" end\n",
"end\n",
"\n",
"+(f::Vector3, g::Vector3)=Vector3(f.x+g.x , f.y+g.y,f.z+g.z )\n",
"-(f::Vector3, g::Vector3)=Vector3(f.x-g.x , f.y-g.y,f.z-g.z )\n",
"*(f::Vector3, g::Vector3)=Vector3(f.x*g.x , f.y*g.y,f.z*g.z )\n",
"\n",
"+(f::Vector3, g::Number)=Vector3(f.x+g , f.y+g,f.z+g )\n",
"-(f::Vector3, g::Number)=Vector3(f.x-g , f.y-g,f.z-g )\n",
"*(f::Vector3, g::Number)=Vector3(f.x*g , f.y*g,f.z*g )\n",
"\n",
"+(g::Vector3, f::Number)=Vector3(f.x+g , f.y+g,f.z+g )\n",
"-(g::Vector3, f::Number)=Vector3(g-f.x , g-f.y,g-f.z )\n",
"*(g::Vector3, f::Number)=Vector3(f.x*g , f.y*g,f.z*g )\n",
"\n",
"addX(f::Vector3, g::Number)=Vector3(f.x+g , f.y,f.z)\n",
"addY(f::Vector3, g::Number)=Vector3(f.x , f.y+g,f.z )\n",
"addZ(f::Vector3, g::Number)=Vector3(f.x , f.y,f.z+g )\n",
"\n",
"function normalizeVector3(f::Vector3)\n",
" leng=sqrt((f.x * f.x) + (f.y * f.y) + (f.z * f.z))\n",
" return Vector3(f.x/leng,f.y/leng,f.z/leng)\n",
" \n",
"end\n",
"function normalizeQuaternion(f::Quaternion)\n",
" l = sqrt((f.x * f.x) + (f.y * f.y) + (f.z * f.z)+ (f.w * f.w))\n",
" if l === 0 \n",
" qx = 0\n",
" qy = 0\n",
" qz = 0\n",
" qw = 1\n",
" else \n",
" l = 1 / l\n",
" qx = f.x * l\n",
" qy = f.y * l\n",
" qz = f.z * l\n",
" qw = f.w * l\n",
" end\n",
" return Quaternion(qx,qy,qz,qw)\n",
"end\n",
"\n",
"function normalizeQuaternion1!(fx::Float64,fy::Float64,fz::Float64,fw::Float64)\n",
" l = sqrt((fx * fx) + (fy * fy) + (fz * fz)+ (fw * fw))\n",
" if l === 0 \n",
" qx = 0.0\n",
" qy = 0.0\n",
" qz = 0.0\n",
" qw = 1.0\n",
" else \n",
" l = 1.0 / l\n",
" qx = fx * l\n",
" qy = fy * l\n",
" qz = fz * l\n",
" qw = fw * l\n",
" end\n",
" return qx,qy,qz,qw\n",
"end\n",
"\n",
"\n",
"function dotVector3(f::Vector3, g::Vector3)\n",
" return (f.x * g.x) + (f.y * g.y) + (f.z * g.z)\n",
"end\n",
"\n",
"function Base.show(io::IO, v::Vector3)\n",
" print(io, \"x:$(v.x), y:$(v.y), z:$(v.z)\")\n",
"end\n",
"\n",
"function Base.show(io::IO, v::Quaternion)\n",
" print(io, \"x:$(v.x), y:$(v.y), z:$(v.z), w:$(v.z)\")\n",
"end\n",
"\n",
"Base.Broadcast.broadcastable(q::Vector3) = Ref(q)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"simulateParallel (generic function with 2 methods)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function simulateParallel(numTimeSteps,dt)\n",
" # initialize(setup)\n",
" \n",
" for i in 1:numTimeSteps\n",
" #println(\"Timestep:\",i)\n",
" doTimeStep(dt,i)\n",
" end\n",
"end\n",
"\n",
"function simulateParallel(metavoxel,numTimeSteps,dt)\n",
" # initialize(setup)\n",
" \n",
" for i in 1:numTimeSteps\n",
" #println(\"Timestep:\",i)\n",
" doTimeStep(metavoxel,dt,i)\n",
" end\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"initialize (generic function with 1 method)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function initialize(setup)\n",
" nodes = setup[\"nodes\"]\n",
" edges = setup[\"edges\"]\n",
"\n",
" i=1\n",
" # pre-calculate current position\n",
" for node in nodes\n",
" # element=parse(Int,node[\"id\"][2:end])\n",
" N_position[i]=Vector3(node[\"position\"][\"x\"]*15.0,node[\"position\"][\"y\"]*15.0,node[\"position\"][\"z\"]*15.0)\n",
" N_restrained[i]=node[\"restrained_degrees_of_freedom\"][1] ## todo later consider other degrees of freedom\n",
" N_displacement[i]=Vector3(node[\"displacement\"][\"x\"]*15,node[\"displacement\"][\"y\"]*15,node[\"displacement\"][\"z\"]*15)\n",
" N_angle[i]=Vector3(node[\"angle\"][\"x\"],node[\"angle\"][\"y\"],node[\"angle\"][\"z\"])\n",
" N_force[i]=Vector3(node[\"force\"][\"x\"],node[\"force\"][\"y\"],node[\"force\"][\"z\"])\n",
" N_currPosition[i]=Vector3(node[\"position\"][\"x\"]*15.0,node[\"position\"][\"y\"]*15.0,node[\"position\"][\"z\"]*15.0)\n",
"\n",
" # for dynamic simulations\n",
" # append!(N_posTimeSteps,[[]])\n",
" # append!(N_angTimeSteps,[[]])\n",
"\n",
" i=i+1\n",
" end \n",
"\n",
" i=1\n",
" # pre-calculate the axis\n",
" for edge in edges\n",
" # element=parse(Int,edge[\"id\"][2:end])\n",
"\n",
" # find the nodes that the lements connects\n",
" fromNode = nodes[edge[\"source\"]+1]\n",
" toNode = nodes[edge[\"target\"]+1]\n",
"\n",
"\n",
" node1 = [fromNode[\"position\"][\"x\"]*15.0 fromNode[\"position\"][\"y\"]*15.0 fromNode[\"position\"][\"z\"]*15.0]\n",
" node2 = [toNode[\"position\"][\"x\"]*15.0 toNode[\"position\"][\"y\"]*15.0 toNode[\"position\"][\"z\"]*15.0]\n",
"\n",
" length=norm(node2-node1)\n",
" axis=normalize(collect(Iterators.flatten(node2-node1)))\n",
"\n",
" E_source[i]=edge[\"source\"]+1\n",
" E_target[i]=edge[\"target\"]+1\n",
" E_area[i]=edge[\"area\"]\n",
" E_density[i]=edge[\"density\"]\n",
" E_stiffness[i]=edge[\"stiffness\"]\n",
" E_axis[i]=Vector3(axis[1],axis[2],axis[3])\n",
" E_currentRestLength[i]=length #?????????? todo change\n",
"# E_currentRestLength[i]=75/sqrt(2)\n",
"\n",
" N_edgeID[E_source[i],N_currEdge[E_source[i]]]=i\n",
" N_edgeFirst[E_source[i],N_currEdge[E_source[i]]]=true\n",
" N_currEdge[E_source[i]]+=1\n",
"\n",
" N_edgeID[E_target[i],N_currEdge[E_target[i]]]=i\n",
" N_edgeFirst[E_target[i],N_currEdge[E_target[i]]]=false\n",
" N_currEdge[E_target[i]]+=1\n",
"\n",
"\n",
" # for dynamic simulations\n",
" # append!(E_stressTimeSteps,[[]])\n",
"\n",
" i=i+1\n",
" end \n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"doTimeStep! (generic function with 1 method)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function doTimeStep(dt,currentTimeStep)\n",
" # update forces: go through edges, get currentposition from nodes, calc pos2 and update stresses and interior forces of nodes\n",
" run_updateEdges!(\n",
" E_sourceGPU, \n",
" E_targetGPU,\n",
" E_areaGPU,\n",
" E_densityGPU,\n",
" E_stiffnessGPU,\n",
" E_stressGPU,\n",
" E_axisGPU,\n",
" E_currentRestLengthGPU,\n",
" E_pos2GPU,\n",
" E_angle1vGPU,\n",
" E_angle2vGPU,\n",
" E_angle1GPU,\n",
" E_angle2GPU,\n",
" E_intForce1GPU,\n",
" E_intMoment1GPU,\n",
" E_intForce2GPU,\n",
" E_intMoment2GPU,\n",
" E_dampGPU,\n",
" N_currPositionGPU,\n",
" N_orientGPU)\n",
" \n",
" # update forces: go through nodes and update interior force (according to int forces from edges), integrate and update currpos\n",
" run_updateNodes!(dt,currentTimeStep,\n",
" N_positionGPU, \n",
" N_restrainedGPU,\n",
" N_displacementGPU,\n",
" N_angleGPU,\n",
" N_currPositionGPU,\n",
" N_linMomGPU,\n",
" N_angMomGPU,\n",
" N_intForceGPU,\n",
" N_intMomentGPU,\n",
" N_forceGPU,\n",
" N_momentGPU,\n",
" N_orientGPU,\n",
" N_edgeIDGPU, \n",
" N_edgeFirstGPU, \n",
" E_intForce1GPU,\n",
" E_intMoment1GPU,\n",
" E_intForce2GPU,\n",
" E_intMoment2GPU)\n",
" \n",
"end\n",
"\n",
"function doTimeStep!(metavoxel,dt,currentTimeStep)\n",
" # update forces: go through edges, get currentposition from nodes, calc pos2 and update stresses and interior forces of nodes\n",
" run_updateEdges!(\n",
" metavoxel[\"E_sourceGPU\"], \n",
" metavoxel[\"E_targetGPU\"],\n",
" metavoxel[\"E_areaGPU\"],\n",
" metavoxel[\"E_densityGPU\"],\n",
" metavoxel[\"E_stiffnessGPU\"],\n",
" metavoxel[\"E_stressGPU\"],\n",
" metavoxel[\"E_axisGPU\"],\n",
" metavoxel[\"E_currentRestLengthGPU\"],\n",
" metavoxel[\"E_pos2GPU\"],\n",
" metavoxel[\"E_angle1vGPU\"],\n",
" metavoxel[\"E_angle2vGPU\"],\n",
" metavoxel[\"E_angle1GPU\"],\n",
" metavoxel[\"E_angle2GPU\"],\n",
" metavoxel[\"E_intForce1GPU\"],\n",
" metavoxel[\"E_intMoment1GPU\"],\n",
" metavoxel[\"E_intForce2GPU\"],\n",
" metavoxel[\"E_intMoment2GPU\"],\n",
" metavoxel[\"E_dampGPU\"],\n",
" metavoxel[\"N_currPositionGPU\"],\n",
" metavoxel[\"N_orientGPU\"])\n",
" \n",
" # update forces: go through nodes and update interior force (according to int forces from edges), integrate and update currpos\n",
" run_updateNodes!(dt,currentTimeStep,\n",
" metavoxel[\"N_positionGPU\"], \n",
" metavoxel[\"N_restrainedGPU\"],\n",
" metavoxel[\"N_displacementGPU\"],\n",
" metavoxel[\"N_angleGPU\"],\n",
" metavoxel[\"N_currPositionGPU\"],\n",
" metavoxel[\"N_linMomGPU\"],\n",
" metavoxel[\"N_angMomGPU\"],\n",
" metavoxel[\"N_intForceGPU\"],\n",
" metavoxel[\"N_intMomentGPU\"],\n",
" metavoxel[\"N_forceGPU\"],\n",
" metavoxel[\"N_momentGPU\"],\n",
" metavoxel[\"N_orientGPU\"],\n",
" metavoxel[\"N_edgeIDGPU\"], \n",
" metavoxel[\"N_edgeFirstGPU\"], \n",
" metavoxel[\"E_intForce1GPU\"],\n",
" metavoxel[\"E_intMoment1GPU\"],\n",
" metavoxel[\"E_intForce2GPU\"],\n",
" metavoxel[\"E_intMoment2GPU\"])\n",
" \n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"run_updateEdges! (generic function with 1 method)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function updateEdges!(E_source,E_target,E_area,E_density,E_stiffness,E_stress,E_axis,\n",
" E_currentRestLength,E_pos2,E_angle1v,E_angle2v,\n",
" E_angle1,E_angle2,E_intForce1,E_intMoment1,E_intForce2,E_intMoment2,E_damp,\n",
" N_currPosition,N_orient)\n",
"\n",
" index = (blockIdx().x - 1) * blockDim().x + threadIdx().x\n",
" stride = blockDim().x * gridDim().x\n",
" ## @cuprintln(\"thread $index, block $stride\")\n",
" N=length(E_source)\n",
" for i = index:stride:N\n",
" \n",
" @inbounds pVNeg=N_currPosition[E_source[i]]\n",
" @inbounds pVPos=N_currPosition[E_target[i]]\n",
" \n",
" @inbounds oVNeg=N_orient[E_source[i]]\n",
" @inbounds oVPos=N_orient[E_target[i]]\n",
" \n",
" @inbounds oldPos2=Vector3(E_pos2[i].x,E_pos2[i].y,E_pos2[i].z) #?copy?\n",
" @inbounds oldAngle1v = Vector3(E_angle1v[i].x,E_angle1v[i].y,E_angle1v[i].z)\n",
" @inbounds oldAngle2v = Vector3(E_angle2v[i].x,E_angle2v[i].y,E_angle2v[i].z)# remember the positions/angles from last timestep to calculate velocity\n",
" \n",
" \n",
" @inbounds E_pos2[i],E_angle1v[i],E_angle2v[i],E_angle1[i],E_angle2[i],totalRot= orientLink!(E_currentRestLength[i],pVNeg,pVPos,oVNeg,oVPos,E_axis[i])\n",
" \n",
" @inbounds dPos2 = Vector3(0.5,0.5,0.5) * (E_pos2[i]-oldPos2) #deltas for local damping. velocity at center is half the total velocity\n",
" @inbounds dAngle1 = Vector3(0.5,0.5,0.5) *(E_angle1v[i]-oldAngle1v)\n",
" @inbounds dAngle2 = Vector3(0.5,0.5,0.5) *(E_angle2v[i]-oldAngle2v)\n",
" \n",
" \n",
" @inbounds strain=(E_pos2[i].x/E_currentRestLength[i])\n",
" \n",
" positiveEnd=true\n",
" if axialStrain( positiveEnd,strain)>100.0\n",
" diverged=true\n",
" @cuprintln(\"DIVERGED!!!!!!!!!!\")\n",
" return \n",
" end\n",
" \n",
" @inbounds E = E_stiffness[i]\n",
" \n",
" \n",
" \n",
" @inbounds l = E_currentRestLength[i]\n",
" \n",
" \n",
" nu=0\n",
"# L = 5.0 #?? change!!!!!!\n",
" L=l\n",
" a1 = E*L # EA/L : Units of N/m\n",
" a2 = E * L*L*L / (12.0*(1+nu)) # GJ/L : Units of N-m\n",
" b1 = E*L # 12EI/L^3 : Units of N/m\n",
" b2 = E*L*L/2.0 # 6EI/L^2 : Units of N (or N-m/m: torque related to linear distance)\n",
" b3 = E*L*L*L/6.0 # 2EI/L : Units of N-m\n",
" \n",
" nu=0.35\n",
" W = 75\n",
"# L = W/sqrt(2)\n",
" l=L\n",
" n_min = 1\n",
" n_max = 7\n",
" # Cross Section inputs, must be floats\n",
" mass=125000 #before for voxel\n",
" mass=10\n",
" E = 2000 # MPa\n",
" G = E * 1 / 3 # MPa\n",
" h = 2.38 # mm\n",
" b = 2.38 # mm\n",
" rho = 7.85e-9 / 3 # kg/mm^3\n",
" S = h * b\n",
" Sy = (S * (6 + 12 * nu + 6 * nu^2)/ (7 + 12 * nu + 4 * nu^2))\n",
" # For solid rectangular cross section (width=b, depth=d & ( b < d )):\n",
" Q = 1 / 3 - 0.2244 / (min(h / b, b / h) + 0.1607)\n",
" Jxx = Q * min(h * b^3, b * h^3)\n",
" s=b\n",
" \n",
" MaxFreq2=E*s/mass\n",
" dt= 1/(6.283185*sqrt(MaxFreq2))\n",
"\n",
"\n",
" ##if voxels\n",
" #nu=0\n",
" #L=l\n",
" #a1 = E*L # EA/L : Units of N/m\n",
" #a2 = E * L*L*L / (12.0*(1+nu)) # GJ/L : Units of N-m\n",
" #b1 = E*L # 12EI/L^3 : Units of N/m\n",
" #b2 = E*L*L/2.0 # 6EI/L^2 : Units of N (or N-m/m: torque related to linear distance)\n",
" #b3 = E*L*L*L/6.0 # 2EI/L : Units of N-m\n",
"\n",
" I= b*h^3/12\n",
" J=b*h*(b*b+h*h)/12\n",
" a1=E*b*h/L\n",
" a2=G*J/L\n",
" b1=12*E*I/(L^3)\n",
" b2=6*E*I/(L^2)\n",
" b3=2*E*I/(L)\n",
" \n",
" \n",
"\n",
" \n",
" #inbounds currentTransverseArea=25.0 #?? change!!!!!! E_area[i]\n",
" @inbounds currentTransverseArea= b*h\n",
" @inbounds _stress=updateStrain(strain,E)\n",
" \n",
" #@inbounds currentTransverseArea= E_area[i]\n",
" #@inbounds _stress=updateStrain(strain,E_stiffness[i])\n",
" \n",
" @inbounds E_stress[i]=_stress\n",
" \n",
" #@cuprintln(\"_stress $_stress\")\n",
" x=(_stress*currentTransverseArea)\n",
" @inbounds y=(b1*E_pos2[i].y-b2*(E_angle1v[i].z + E_angle2v[i].z))\n",
" @inbounds z=(b1*E_pos2[i].z + b2*(E_angle1v[i].y + E_angle2v[i].y))\n",
" \n",
" x=convert(Float64,x)\n",
" y=convert(Float64,y)\n",
" z=convert(Float64,z)\n",
" \n",
" # Use Curstress instead of -a1*Pos2.x to account for non-linear deformation \n",
" forceNeg = Vector3(x,y,z)\n",
" \n",
" forcePos = Vector3(-x,-y,-z)\n",
" \n",
" @inbounds x= (a2*(E_angle2v[i].x-E_angle1v[i].x))\n",
" @inbounds y= (-b2*E_pos2[i].z-b3*(2.0*E_angle1v[i].y+E_angle2v[i].y))\n",
" @inbounds z=(b2*E_pos2[i].y - b3*(2.0*E_angle1v[i].z + E_angle2v[i].z)) \n",
" x=convert(Float64,x)\n",
" y=convert(Float64,y)\n",
" z=convert(Float64,z)\n",
" momentNeg = Vector3(x,y,z)\n",
" \n",
"\n",
" @inbounds x= (a2*(E_angle1v[i].x-E_angle2v[i].x))\n",
" @inbounds y= (-b2*E_pos2[i].z- b3*(E_angle1v[i].y+2.0*E_angle2v[i].y))\n",
" @inbounds z=(b2*E_pos2[i].y - b3*(E_angle1v[i].z + 2.0*E_angle2v[i].z))\n",
" x=convert(Float64,x)\n",
" y=convert(Float64,y)\n",
" z=convert(Float64,z)\n",
" momentPos = Vector3(x,y,z)\n",
" \n",
" \n",
" ### damping\n",
" @inbounds if E_damp[i] #first pass no damping\n",
" sqA1=CUDAnative.sqrt(a1) \n",
" sqA2xIp=CUDAnative.sqrt(a2*L*L/6.0) \n",
" sqB1=CUDAnative.sqrt(b1) \n",
" sqB2xFMp=CUDAnative.sqrt(b2*L/2) \n",
" sqB3xIp=CUDAnative.sqrt(b3*L*L/6.0)\n",
" \n",
" dampingMultiplier=Vector3(28099.3,28099.3,28099.3) # 2*mat->_sqrtMass*mat->zetaInternal/previousDt;?? todo link to material\n",
" \n",
" zeta=1\n",
" dampingM= 2*sqrt(mass)*zeta/dt\n",
" dampingMultiplier=Vector3(dampingM,dampingM,dampingM)\n",
" \n",
" posCalc=Vector3(sqA1*dPos2.x, sqB1*dPos2.y - sqB2xFMp*(dAngle1.z+dAngle2.z),sqB1*dPos2.z + sqB2xFMp*(dAngle1.y+dAngle2.y))\n",
" \n",
" \n",
" forceNeg =forceNeg + (dampingMultiplier*posCalc);\n",
" forcePos =forcePos - (dampingMultiplier*posCalc);\n",
"\n",
" momentNeg -= Vector3(0.5,0.5,0.5)*dampingMultiplier*Vector3(-sqA2xIp*(dAngle2.x - dAngle1.x),\n",
" sqB2xFMp*dPos2.z + sqB3xIp*(2*dAngle1.y + dAngle2.y),\n",
" -sqB2xFMp*dPos2.y + sqB3xIp*(2*dAngle1.z + dAngle2.z));\n",
" momentPos -= Vector3(0.5,0.5,0.5)*dampingMultiplier*Vector3(sqA2xIp*(dAngle2.x - dAngle1.x),\n",
" sqB2xFMp*dPos2.z + sqB3xIp*(dAngle1.y + 2*dAngle2.y),\n",
" -sqB2xFMp*dPos2.y + sqB3xIp*(dAngle1.z + 2*dAngle2.z));\n",
"\n",
" else\n",
" @inbounds E_damp[i]=true \n",
" end\n",
"\n",
" smallAngle=true\n",
" if !smallAngle # ?? check\n",
" @inbounds forceNeg = RotateVec3DInv(E_angle1[i],forceNeg)\n",
" @inbounds momentNeg = RotateVec3DInv(E_angle1[i],momentNeg)\n",
" end\n",
" \n",
" @inbounds forcePos = RotateVec3DInv(E_angle2[i],forcePos)\n",
" @inbounds momentPos = RotateVec3DInv(E_angle2[i],momentPos)\n",
"\n",
" @inbounds forceNeg =toAxisOriginalVector3(forceNeg,E_axis[i])\n",
" @inbounds forcePos =toAxisOriginalVector3(forcePos,E_axis[i])\n",
"\n",
" @inbounds momentNeg=toAxisOriginalQuat(momentNeg,E_axis[i])# TODOO CHECKKKKKK\n",
" @inbounds momentPos=toAxisOriginalQuat(momentPos,E_axis[i])\n",
"\n",
"\n",
" @inbounds E_intForce1[i] =forceNeg\n",
" @inbounds E_intForce2[i] =forcePos\n",
" \n",
"\n",
"\n",
" @inbounds x= momentNeg.x\n",
" @inbounds y= momentNeg.y\n",
" @inbounds z= momentNeg.z \n",
" x=convert(Float64,x)\n",
" y=convert(Float64,y)\n",
" z=convert(Float64,z)\n",
" \n",
" @inbounds E_intMoment1[i]=Vector3(x,y,z)\n",
"\n",
" @inbounds x= momentNeg.x\n",
" @inbounds y= momentNeg.y\n",
" @inbounds z= momentNeg.z\n",
" x=convert(Float64,x)\n",
" y=convert(Float64,y)\n",
" z=convert(Float64,z)\n",
" \n",
" @inbounds E_intMoment2[i]=Vector3(x,y,z)\n",
" \n",
" #x=E_pos2[i].x*10000000000\n",
" #y=E_pos2[i].y*10000000000\n",
" #z=E_pos2[i].z*10000000000\n",
" #@cuprintln(\"pos2 x $x, y $y, z $z \")\n",
" ##x=E_intMoment2[i].x*10000000000\n",
" #y=E_intMoment2[i].y*10000000000\n",
" #z=E_intMoment2[i].z*10000000000\n",
" #@cuprintln(\"E_intMoment2 x $x, y $y, z $z \")\n",
"\n",
" \n",
" \n",
" end\n",
" return\n",
"end\n",
"\n",
"function run_updateEdges!(E_source,E_target,E_area,E_density,E_stiffness,\n",
" E_stress,E_axis,E_currentRestLength,E_pos2,E_angle1v,E_angle2v,\n",
" E_angle1,E_angle2,E_intForce1,E_intMoment1,E_intForce2,E_intMoment2,\n",
" E_damp,N_currPosition,N_orient)\n",
" N=length(E_source)\n",
" numblocks = ceil(Int, N/256)\n",
" CuArrays.@sync begin\n",
" @cuda threads=256 blocks=numblocks updateEdges!(E_source,E_target,E_area,E_density,\n",
" E_stiffness,E_stress,E_axis,E_currentRestLength,E_pos2,E_angle1v,\n",
" E_angle2v,E_angle1,E_angle2,E_intForce1,E_intMoment1,E_intForce2,\n",
" E_intMoment2,E_damp,N_currPosition,N_orient)\n",
" end\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"run_updateNodes! (generic function with 1 method)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function updateNodes!(dt,currentTimeStep,N_position, N_restrained,N_displacement,N_angle,N_currPosition,N_linMom,N_angMom,N_intForce,N_intMoment,N_force,N_moment,N_orient,N_edgeID,N_edgeFirst,E_intForce1,E_intMoment1,E_intForce2,E_intMoment2)\n",
"\n",
" index = (blockIdx().x - 1) * blockDim().x + threadIdx().x\n",
" stride = blockDim().x * gridDim().x\n",
" ## @cuprintln(\"thread $index, block $stride\")\n",
" N,M=size(N_edgeID)\n",
" for i = index:stride:N\n",
" @inbounds if N_restrained[i]\n",
" return\n",
" else\n",
" for j in 1:M\n",
" temp=N_edgeID[i,j]\n",
" @inbounds if (N_edgeID[i,j]!=-1)\n",
" #@cuprintln(\"i $i, j $j, N_edgeID[i,j] $temp\")\n",
" @inbounds N_intForce[i]=ifelse(N_edgeFirst[i,j], N_intForce[i]+E_intForce1[N_edgeID[i,j]], N_intForce[i]+E_intForce2[N_edgeID[i,j]] )\n",
" @inbounds N_intMoment[i]=ifelse(N_edgeFirst[i,j], N_intMoment[i]+E_intMoment1[N_edgeID[i,j]], N_intMoment[i]+E_intMoment2[N_edgeID[i,j]] )\n",
" end\n",
" end\n",
" @inbounds curForce = force(N_intForce[i],N_orient[i],N_force[i],true,currentTimeStep)\n",
" \n",
" #@inbounds N_force[i]=Vector3(0,0,0) ##????\n",
" \n",
" @inbounds N_intForce[i]=Vector3(0,0,0)\n",
" \n",
" #x=curForce.x\n",
" #y=curForce.y\n",
" #z=curForce.z\n",
" #@cuprintln(\"curForce x $x, y $y, z $z \")\n",
" \n",
" #x=N_linMom[i].x*10000000000\n",
" #y=N_linMom[i].y*10000000000\n",
" #z=N_linMom[i].z*10000000000\n",
" #@cuprintln(\"N_linMom[i] x $x, y $y, z $z \")\n",
" \n",
" \n",
" @inbounds N_linMom[i]=N_linMom[i]+curForce*Vector3(dt,dt,dt) #todo make sure right\n",
" massInverse=8e-6 # todo ?? later change //8e-6\n",
" mass=10\n",
" massInverse=1.0/mass #\n",
" @inbounds translate=N_linMom[i]*Vector3((dt*massInverse),(dt*massInverse),(dt*massInverse)) # ??massInverse\n",
" \n",
" #x=translate.x*10000000000\n",
" #y=translate.y*10000000000\n",
" #z=translate.z*10000000000\n",
" #@cuprintln(\"translate x $x, y $y, z $z \")\n",
" \n",
" @inbounds N_currPosition[i]=N_currPosition[i]+translate\n",
" @inbounds N_displacement[i]=N_displacement[i]+translate\n",
" \n",
" \n",
" \n",
" # Rotation\n",
" @inbounds curMoment = moment(N_intMoment[i],N_orient[i],N_moment[i]) \n",
" \n",
" \n",
" \n",
" @inbounds N_intMoment[i]=Vector3(0,0,0) # do i really need it?\n",
" \n",
" @inbounds N_angMom[i]=N_angMom[i]+curMoment*Vector3(dt,dt,dt)\n",
" \n",
" \n",
" \n",
" \n",
" momentInertiaInverse=1.92e-6 # todo ?? later change 1/Inertia (1/(kg*m^2))\n",
" \n",
" \n",
" @inbounds temp=FromRotationVector(N_angMom[i]*Vector3((dt*momentInertiaInverse),(dt*momentInertiaInverse),(dt*momentInertiaInverse)))\n",
" \n",
" \n",
" #x=temp.x*10000000000\n",
" #y=temp.y*10000000000\n",
" #z=temp.z*10000000000\n",
" #@cuprintln(\"temp x $x, y $y, z $z \")\n",
" \n",
" @inbounds N_orient[i]=multiplyQuaternions(temp,N_orient[i])\n",
" \n",
" #@inbounds x= N_orient[i].x*temp.x\n",
" #@inbounds y= N_orient[i].y*temp.y\n",
" #@inbounds z= N_orient[i].z*temp.z\n",
" #@inbounds w= N_orient[i].w*temp.w\n",
" #x=convert(Float64,x)\n",
" #y=convert(Float64,y)\n",
" #z=convert(Float64,z)\n",
" #w=convert(Float64,w)\n",
" \n",
" #@inbounds N_orient[i]=Quaternion(x,y,z,w)\n",
" \n",
" #x=N_orient[i].x*10000000000\n",
" #y=N_orient[i].y*10000000000\n",
" #z=N_orient[i].z*10000000000\n",
" #w=N_orient[i].w\n",
" #@cuprintln(\"N_orient x $x, y $y, z $z, w $w \")\n",
" \n",
" \n",
" end\n",
" end\n",
" return\n",
"end\n",
"\n",
"\n",
"function run_updateNodes!(dt,currentTimeStep,N_position, N_restrained,N_displacement, N_angle,N_currPosition,N_linMom,N_angMom,N_intForce,N_intMoment,N_force,N_moment,N_orient,N_edgeID,N_edgeFirst,E_intForce1,E_intMoment1,E_intForce2,E_intMoment2)\n",
" N=length(N_intForce)\n",
" numblocks = ceil(Int, N/256)\n",
" CuArrays.@sync begin\n",
" @cuda threads=256 blocks=numblocks updateNodes!(dt,currentTimeStep,N_position, N_restrained,N_displacement, N_angle,N_currPosition,N_linMom,N_angMom,N_intForce,N_intMoment,N_force,N_moment,N_orient,N_edgeID,N_edgeFirst,E_intForce1,E_intMoment1,E_intForce2,E_intMoment2)\n",
" end\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"orientLink! (generic function with 1 method)"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function orientLink!(currentRestLength,pVNeg,pVPos,oVNeg,oVPos,axis) # updates pos2, angle1, angle2, and smallAngle //Quat3D<double> /*double restLength*/\n",
" \n",
" pos2 = toAxisXVector3(pVPos-pVNeg,axis) # digit truncation happens here...\n",
" angle1 = toAxisXQuat(oVNeg,axis)\n",
" angle2 = toAxisXQuat(oVPos,axis)\n",
" \n",
" #x=pos2.x*10000000000\n",
" #y=pos2.y*10000000000\n",
" #z=pos2.z*10000000000\n",
" #@cuprintln(\"pos2 x $x, y $y, z $z \")\n",
" \n",
" #x=angle1.x*10000000000\n",
" #y=angle1.y*10000000000\n",
" #z=angle1.z*10000000000\n",
" #@cuprintln(\"angle1 x $x, y $y, z $z \")\n",
" #x=oVNeg.x*10000000000\n",
" #y=oVNeg.y*10000000000\n",
" #z=oVNeg.z*10000000000\n",
" #@cuprintln(\"oVNeg x $x, y $y, z $z \")\n",
" \n",
" \n",
" \n",
" totalRot = conjugate(angle1) #keep track of the total rotation of this bond (after toAxisX()) # Quat3D<double>\n",
" pos2 = RotateVec3D(totalRot,pos2)\n",
" \n",
" #x=pos2.x*10000000000\n",
" #y=pos2.y*10000000000\n",
" #z=pos2.z*10000000000\n",
" #@cuprintln(\"pos2 2 x $x, y $y, z $z \")\n",
" \n",
" \n",
" #x=totalRot.x*10000000000\n",
" #y=totalRot.y*10000000000\n",
" #z=totalRot.z*10000000000\n",
" #@cuprintln(\"totalRot x $x, y $y, z $z \")\n",
" \n",
" \n",
"# x=pos2.x*10000000000\n",
"# y=pos2.y*10000000000\n",
"# z=pos2.z*10000000000\n",
"# @cuprintln(\"pos2 x $x, y $y, z $z \")\n",
" \n",
" angle2 = Quaternion(angle2.x*totalRot.x,angle2.y*totalRot.y,angle2.z*totalRot.z,angle2.w*totalRot.w)\n",
" angle1 = Quaternion(0.0,0.0,0.0,1.0)#new THREE.Quaternion() #zero for now...\n",
"\n",
" smallAngle=true #todo later remove\n",
" \n",
" \n",
" if (smallAngle)\t #Align so Angle1 is all zeros\n",
" #pos2[1] =pos2[1]- currentRestLength #only valid for small angles\n",
" pos2=Vector3(pos2.x-currentRestLength,pos2.y,pos2.z)\n",
" else #Large angle. Align so that Pos2.y, Pos2.z are zero.\n",
" # FromAngleToPosX(angle1,pos2) #get the angle to align Pos2 with the X axis\n",
" # totalRot = angle1.clone().multiply(totalRot) #update our total rotation to reflect this\n",
" # angle2 = angle1.clone().multiply( angle2) #rotate angle2\n",
" # pos2 = new THREE.Vector3(pos2.length() - currentRestLength, 0, 0);\n",
" end\n",
" \n",
" angle1v = ToRotationVector(angle1)\n",
" angle2v = ToRotationVector(angle2)\n",
" \n",
" \n",
" \n",
" \n",
"# pos2,angle1v,angle2v,angle1,angle2,\n",
" return pos2,angle1v,angle2v,angle1,angle2,totalRot\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"toAxisOriginalQuat (generic function with 1 method)"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function toAxisXVector3(pV::Vector3,axis::Vector3) #TODO CHANGE\n",
"\n",
" xaxis=Vector3(1.0,0.0,0.0)\n",
"\n",
" vector=normalizeVector3(axis)\n",
" q=setFromUnitVectors(vector,xaxis)\n",
" \n",
" \n",
" \n",
"# rot=setFromRotationMatrix(quatToMatrix( q ))\n",
" \n",
" \n",
"# v= applyQuaternion1( pV ,setQuaternionFromEuler(rot) )\n",
" v=applyQuaternion1( pV ,q )\n",
" \n",
" #d=15\n",
" #vx=round(v.x, digits=d)\n",
" #vy=round(v.y, digits=d)\n",
" #vz=round(v.z, digits=d)\n",
" \n",
" \n",
" return Vector3(v.x,v.y,v.z)\n",
"end\n",
"\n",
"function toAxisOriginalVector3(pV::Vector3,axis::Vector3)\n",
" \n",
" xaxis=Vector3(1.0,0.0,0.0)\n",
"\n",
" vector=normalizeVector3(axis)\n",
"\n",
" q=setFromUnitVectors(xaxis,vector)\n",
" \n",
"\n",
"# rot=setFromRotationMatrix(quatToMatrix( q ))\n",
"\n",
"# v= applyQuaternion1( pV ,setQuaternionFromEuler(rot) )\n",
" v=applyQuaternion1( pV ,q )\n",
" \n",
" #d=15\n",
" #vx=round(v.x, digits=d)\n",
" #vy=round(v.y, digits=d)\n",
" #vz=round(v.z, digits=d)\n",
" \n",
" \n",
" return Vector3(v.x,v.y,v.z)\n",
"end\n",
"\n",
"function toAxisXQuat(pQ::Quaternion,axis::Vector3)\n",
" \n",
" xaxis=Vector3(1.0,0.0,0.0)\n",
"\n",
" vector=normalizeVector3(axis)\n",
"\n",
"\n",
" q=setFromUnitVectors(vector,xaxis)\n",
" \n",
" #d=17\n",
" #qw=round(q[1], digits=d)\n",
" #qx=round(q[2], digits=d)\n",
" #qy=round(q[3], digits=d)\n",
" #qz=round(q[4], digits=d)\n",
" #\n",
"\n",
"# rot=setFromRotationMatrix(quatToMatrix( q ))\n",
" \n",
" pV=Vector3(pQ.x,pQ.y,pQ.z)\n",
" \n",
"# v=applyQuaternion1( pV ,setQuaternionFromEuler(rot) )\n",
" v=applyQuaternion1( pV ,q )\n",
" \n",
" #d=15\n",
" #vx=round(v.x, digits=d)\n",
" #vy=round(v.y, digits=d)\n",
" #vz=round(v.z, digits=d)\n",
" \n",
" return Quaternion(v.x,v.y,v.z,1.0)\n",
" \n",
" # return [1.0 v[1] v[2] v[3]]\n",
"end\n",
"\n",
"function toAxisOriginalQuat(pQ::Vector3,axis::Vector3)\n",
" xaxis=Vector3(1.0,0.0,0.0)\n",
"\n",
" vector=normalizeVector3(axis)\n",
" \n",
" q=setFromUnitVectors(xaxis,vector)\n",
" \n",
"\n",
"# rot=setFromRotationMatrix(quatToMatrix( q ))\n",
" \n",
" pV=Vector3(pQ.x,pQ.y,pQ.z)\n",
"# v=applyQuaternion1( pV ,setQuaternionFromEuler(rot) )\n",
" v=applyQuaternion1( pV ,q )\n",
" \n",
" #d=15\n",
" #vx=round(v.x, digits=d)\n",
" #vy=round(v.y, digits=d)\n",
" #vz=round(v.z, digits=d)\n",
" \n",
" return Quaternion(v.x,v.y,v.z,1.0)\n",
" \n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"applyQuaternion1 (generic function with 1 method)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function setFromUnitVectors(vFrom::Vector3, vTo::Vector3)\n",
" # assumes direction vectors vFrom and vTo are normalized\n",
" EPS = 0.000000001;\n",
" r= dotVector3(vFrom,vTo)+1.0\n",
" # r = dot(vFrom,vTo)+1\n",
"\n",
" if r < EPS\n",
" r = 0;\n",
" if abs( vFrom.x ) > abs( vFrom.z ) \n",
" qx = - vFrom.y\n",
" qy = vFrom.x\n",
" qz = 0.0\n",
" qw = r\n",
" else \n",
" qx = 0.0\n",
" qy = -(vFrom.z)\n",
" qz = vFrom.y\n",
" qw = r\n",
" end\n",
" else \n",
" # crossVectors( vFrom, vTo ); // inlined to avoid cyclic dependency on Vector3\n",
" qx = vFrom.y * vTo.z - vFrom.z * vTo.y\n",
" qy = vFrom.z * vTo.x - vFrom.x * vTo.z\n",
" qz = vFrom.x * vTo.y - vFrom.y * vTo.x\n",
" qw = r\n",
"\n",
" end\n",
" qx= (qx==-0.0) ? 0.0 : qx\n",
" qy= (qy==-0.0) ? 0.0 : qy\n",
" qz= (qz==-0.0) ? 0.0 : qz\n",
" qw= (qw==-0.0) ? 0.0 : qw\n",
" \n",
" \n",
" mx=qx*qx\n",
" my=qy*qy\n",
" mz=qz*qz\n",
" mw=qw*qw\n",
" mm=mx+my\n",
" mm=mm+mz\n",
" mm=mm+mw\n",
" mm=convert(Float64,mm)#??????????????????? todo check later\n",
" \n",
" l=CUDAnative.sqrt(mm)\n",
" \n",
" #l = sqrt((qx * qx) + (qy * qy) + (qz * qz)+ (qw * qw))\n",
" if l === 0 \n",
" qx = 0.0\n",
" qy = 0.0\n",
" qz = 0.0\n",
" qw = 1.0\n",
" else \n",
" l = 1.0 / l\n",
" qx = qx * l\n",
" qy = qy * l\n",
" qz = qz * l\n",
" qw = qw * l\n",
" end\n",
" \n",
" \n",
"\n",
" # return qx,qy,qz,qw\n",
" return Quaternion(qx,qy,qz,qw)\n",
" \n",
" # return normalizeQ(Quat(qw,qx,qy,qz))\n",
" # return Quat(nn[1], nn[2], nn[3], nn[4])\n",
"\n",
"end\n",
"\n",
"function quatToMatrix( quaternion::Quaternion)\n",
"\n",
" #te = RotationMatrix()\n",
" \n",
" x = quaternion.x\n",
" y = quaternion.y\n",
" z = quaternion.z\n",
" w = quaternion.w\n",
" \n",
" x2 = x + x\n",
" y2 = y + y\n",
" z2 = z + z\n",
" xx = x * x2\n",
" xy = x * y2\n",
" xz = x * z2\n",
" yy = y * y2\n",
" yz = y * z2\n",
" zz = z * z2\n",
" wx = w * x2\n",
" wy = w * y2\n",
" wz = w * z2\n",
"\n",
" sx = 1.0\n",
" sy = 1.0\n",
" sz = 1.0\n",
"\n",
" te1 = ( 1.0 - ( yy + zz ) ) * sx\n",
" te2 = ( xy + wz ) * sx\n",
" te3 = ( xz - wy ) * sx\n",
" te4 = 0.0\n",
"\n",
" te5 = ( xy - wz ) * sy\n",
" te6 = ( 1.0 - ( xx + zz ) ) * sy\n",
" te7 = ( yz + wx ) * sy\n",
" te8 = 0.0\n",
"\n",
" te9 = ( xz + wy ) * sz\n",
" te10 = ( yz - wx ) * sz\n",
" te11 = ( 1.0 - ( xx + yy ) ) * sz\n",
" te12 = 0.0\n",
"\n",
" te13 = 0.0 #position.x;\n",
" te14 = 0.0 #position.y;\n",
" te15 = 0.0 #position.z;\n",
" te16 = 1.0\n",
" \n",
" \n",
" te= RotationMatrix(te1,te2,te3,te4,te5,te6,te7,te8,te9,te10,te11,te12,te13,te14,te15,te16)\n",
"\n",
" return te\n",
"\n",
"end\n",
"\n",
"function setFromRotationMatrix(m::RotationMatrix)\n",
" #te = m\n",
" #m11 = (te[ 1 ]== -0.0) ? 0.0 : te[ 1 ]\n",
" #m12 = (te[ 5 ]== -0.0) ? 0.0 : te[ 5 ]\n",
" #m13 = (te[ 9 ]== -0.0) ? 0.0 : te[ 9 ]\n",
" #m21 = (te[ 2 ]== -0.0) ? 0.0 : te[ 2 ]\n",
" #m22 = (te[ 6 ]== -0.0) ? 0.0 : te[ 6 ]\n",
" #m23 = (te[ 10]== -0.0) ? 0.0 : te[ 10]\n",
" #m31 = (te[ 3 ]== -0.0) ? 0.0 : te[ 3 ]\n",
" #m32 = (te[ 7 ]== -0.0) ? 0.0 : te[ 7 ]\n",
" #m33 = (te[ 11]== -0.0) ? 0.0 : te[ 11]\n",
"\n",
" m11 = convert(Float64,m.te1 )\n",
" m12 = convert(Float64,m.te5 )\n",
" m13 = convert(Float64,m.te9 )\n",
" m21 = convert(Float64,m.te2 )\n",
" m22 = convert(Float64,m.te6 )\n",
" m23 = convert(Float64,m.te10)\n",
" m31 = convert(Float64,m.te3 )\n",
" m32 = convert(Float64,m.te7 )\n",
" m33 = convert(Float64,m.te11)\n",
" \n",
"\n",
" y = CUDAnative.asin( clamp( m13, -1.0, 1.0 ) ) ##check if has to be changed to cuda\n",
"\n",
" if ( abs( m13 ) < 0.9999999999 ) \n",
" \n",
" x = CUDAnative.atan2( - m23, m33 )\n",
" z = CUDAnative.atan2( - m12, m11 )#-m12, m11\n",
" # if(m23==0.0)\n",
" # x = atan( m23, m33 )\n",
" # end\n",
" # if(m12==0.0)\n",
" # z = atan( m12, m11 )\n",
" # end\n",
"\n",
" else\n",
"\n",
" x = CUDAnative.atan2( m32, m22 )\n",
" z = 0.0;\n",
"\n",
" end\n",
" \n",
" \n",
" return Vector3(x,y,z)\n",
" \n",
"end\n",
"\n",
"function setQuaternionFromEuler(euler::Vector3)\n",
" x=euler.x\n",
" y=euler.y\n",
" z=euler.z\n",
" \n",
" \n",
" c1 = CUDAnative.cos( x / 2.0 )\n",
" c2 = CUDAnative.cos( y / 2.0 )\n",
" c3 = CUDAnative.cos( z / 2.0 )\n",
"\n",
" s1 = CUDAnative.sin( x / 2.0 )\n",
" s2 = CUDAnative.sin( y / 2.0 )\n",
" s3 = CUDAnative.sin( z / 2.0 )\n",
" \n",
" \n",
" x = s1 * c2 * c3 + c1 * s2 * s3\n",
" y = c1 * s2 * c3 - s1 * c2 * s3\n",
" z = c1 * c2 * s3 + s1 * s2 * c3\n",
" w = c1 * c2 * c3 - s1 * s2 * s3\n",
" \n",
" return Quaternion(x,y,z,w)\n",
"end\n",
"\n",
"function applyQuaternion1(e::Vector3,q2::Quaternion)\n",
" x = e.x\n",
" y = e.y\n",
" z = e.z\n",
"\n",
" qx = q2.x\n",
" qy = q2.y\n",
" qz = q2.z\n",
" qw = q2.w\n",
"\n",
" # calculate quat * vector\n",
"\n",
" ix = qw * x + qy * z - qz * y\n",
" iy = qw * y + qz * x - qx * z\n",
" iz = qw * z + qx * y - qy * x\n",
" iw = - qx * x - qy * y - qz * z\n",
"\n",
" # calculate result * inverse quat\n",
"\n",
" xx = ix * qw + iw * - qx + iy * - qz - iz * - qy\n",
" yy = iy * qw + iw * - qy + iz * - qx - ix * - qz\n",
" zz = iz * qw + iw * - qz + ix * - qy - iy * - qx\n",
" \n",
" d=15\n",
"\n",
" return Vector3(xx,yy,zz)\n",
"end\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"multiplyQuaternions (generic function with 1 method)"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function conjugate(q::Quaternion)\n",
" x= (-q.x==-0) ? 0.0 : -q.x\n",
" y= (-q.y==-0) ? 0.0 : -q.y\n",
" z= (-q.z==-0) ? 0.0 : -q.z\n",
" w=q.w\n",
" x=convert(Float64,x)\n",
" y=convert(Float64,y)\n",
" z=convert(Float64,z)\n",
" w=convert(Float64,w)\n",
" return Quaternion(x,y,z,w)\n",
"end\n",
"\n",
"function RotateVec3D(a::Quaternion, f::Vector3) \n",
" fx= (f.x==-0) ? 0 : f.x\n",
" fy= (f.y==-0) ? 0 : f.y\n",
" fz= (f.z==-0) ? 0 : f.z\n",
" # fx= f.x\n",
" # fy= f.y\n",
" # fz= f.z\n",
" tw = fx*a.x + fy*a.y + fz*a.z\n",
" tx = fx*a.w - fy*a.z + fz*a.y\n",
" ty = fx*a.z + fy*a.w - fz*a.x\n",
" tz = -fx*a.y + fy*a.x + fz*a.w\n",
"\n",
" return Vector3((a.w*tx+a.x*tw+a.y*tz-a.z*ty),(a.w*ty-a.x*tz+a.y*tw+a.z*tx),(a.w*tz+a.x*ty-a.y*tx+a.z*tw))\n",
"end\n",
"#!< Returns a vector representing the specified vector \"f\" rotated by this quaternion. @param[in] f The vector to transform.\n",
"\n",
"function RotateVec3DInv(a::Quaternion, f::Vector3) \n",
" fx=f.x\n",
" fy=f.y\n",
" fz=f.z\n",
" tw = a.x*fx + a.y*fy + a.z*fz\n",
" tx = a.w*fx - a.y*fz + a.z*fy\n",
" ty = a.w*fy + a.x*fz - a.z*fx\n",
" tz = a.w*fz - a.x*fy + a.y*fx\n",
" return Vector3((tw*a.x + tx*a.w + ty*a.z - tz*a.y),(tw*a.y - tx*a.z + ty*a.w + tz*a.x),(tw*a.z + tx*a.y - ty*a.x + tz*a.w))\n",
"end\n",
"#!< Returns a vector representing the specified vector \"f\" rotated by the inverse of this quaternion. This is the opposite of RotateVec3D. @param[in] f The vector to transform.\n",
"\n",
"function ToRotationVector(a::Quaternion) \n",
" if (a.w >= 1.0 || a.w <= -1.0) \n",
" return Vector3(0.0,0.0,0.0)\n",
" end\n",
" squareLength = 1.0-a.w*a.w; # because x*x + y*y + z*z + w*w = 1.0, but more susceptible to w noise (when \n",
" SLTHRESH_ACOS2SQRT= 2.4e-3; # SquareLength threshhold for when we can use square root optimization for acos. From SquareLength = 1-w*w. (calculate according to 1.0-W_THRESH_ACOS2SQRT*W_THRESH_ACOS2SQRT\n",
"\n",
" if (squareLength < SLTHRESH_ACOS2SQRT) # ???????\n",
" x=a.x*(2.0*CUDAnative.sqrt((2-2*a.w)/squareLength))\n",
" y=a.y*(2.0*CUDAnative.sqrt((2-2*a.w)/squareLength))\n",
" z=a.z*(2.0*CUDAnative.sqrt((2-2*a.w)/squareLength))\n",
" x=convert(Float64,x)\n",
" y=convert(Float64,y)\n",
" z=convert(Float64,z)\n",
" \n",
" return Vector3(x,y,z) ; # acos(w) = sqrt(2*(1-x)) for w close to 1. for w=0.001, error is 1.317e-6\n",
" else \n",
" x=a.x*(2.0*CUDAnative.acos(a.w)/CUDAnative.sqrt(squareLength))\n",
" y=a.y*(2.0*CUDAnative.acos(a.w)/CUDAnative.sqrt(squareLength))\n",
" z=a.z*(2.0*CUDAnative.acos(a.w)/CUDAnative.sqrt(squareLength))\n",
" x=convert(Float64,x)\n",
" y=convert(Float64,y)\n",
" z=convert(Float64,z)\n",
"\n",
" return Vector3(x,y,z)\n",
" end \n",
"end \n",
"# !< Returns a rotation vector representing this quaternion rotation. Adapted from http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToAngle/\n",
"\n",
"function FromRotationVector(VecIn::Vector3)\n",
" theta=VecIn*Vector3(0.5,0.5,0.5)\n",
" ntheta=CUDAnative.sqrt((theta.x * theta.x) + (theta.y * theta.y) + (theta.z * theta.z))\n",
" thetaMag2=ntheta*ntheta\n",
" \n",
" DBL_EPSILONx24 =5.328e-15\n",
" if thetaMag2*thetaMag2 < DBL_EPSILONx24\n",
" qw=1.0 - 0.5*thetaMag2\n",
"\t\ts=1.0 - thetaMag2 / 6.0\n",
" else\n",
" thetaMag = CUDAnative.sqrt(thetaMag2)\n",
"\t\tqw=CUDAnative.cos(thetaMag)\n",
"\t\ts=CUDAnative.sin(thetaMag) / thetaMag\n",
" end\n",
" qx=theta.x*s\n",
" qy=theta.y*s\n",
" qz=theta.z*s\n",
" \n",
" qx=convert(Float64,qx)\n",
" qy=convert(Float64,qy)\n",
" qz=convert(Float64,qz)\n",
" qw=convert(Float64,qw)\n",
" \n",
" return Quaternion(qx,qy,qz,qw)\n",
"end\n",
"\n",
"function multiplyQuaternions(q::Quaternion,f::Quaternion)\n",
" x=q.x\n",
" y=q.y\n",
" z=q.z\n",
" w=q.w\n",
" x1=w*f.x + x*f.w + y*f.z - z*f.y \n",
" y1=w*f.y - x*f.z + y*f.w + z*f.x\n",
" z1=w*f.z + x*f.y - y*f.x + z*f.w\n",
" w1=w*f.w - x*f.x - y*f.y - z*f.z\n",
"# x1=convert(Float64,x1)\n",
"# y1=convert(Float64,y1)\n",
"# z1=convert(Float64,z1)\n",
"# w1=convert(Float64,w1)\n",
"\treturn Quaternion(x1,y1,z1,w1 ); #!< overload quaternion multiplication.\n",
"end\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"axialStrain (generic function with 1 method)"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function updateStrain( axialStrain,E) # ?from where strain\n",
" strain = axialStrain # redundant?\n",
" currentTransverseStrainSum=0.0 # ??? todo\n",
" linear=true\n",
" maxStrain=1000000000000000;# ?? todo later change\n",
" if linear\n",
" if axialStrain > maxStrain\n",
" maxStrain = axialStrain # remember this maximum for easy reference\n",
" end\n",
" return stress(axialStrain,E)\n",
" else \n",
" if (axialStrain > maxStrain) # if new territory on the stress/strain curve\n",
" maxStrain = axialStrain # remember this maximum for easy reference\n",
" returnStress = stress(axialStrain,E) # ??currentTransverseStrainSum\n",
" if (nu != 0.0) \n",
" strainOffset = maxStrain-stress(axialStrain,E)/(_eHat*(1.0-nu)) # precalculate strain offset for when we back off\n",
" else \n",
" strainOffset = maxStrain-returnStress/E # precalculate strain offset for when we back off\n",
" end\n",
" else # backed off a non-linear material, therefore in linear region.\n",
" relativeStrain = axialStrain-strainOffset # treat the material as linear with a strain offset according to the maximum plastic deformation\n",
" if (nu != 0.0) \n",
" returnStress = stress(relativeStrain,E)\n",
" else \n",
" returnStress = E*relativeStrain\n",
" end\n",
" end\n",
" return returnStress\n",
" end\n",
"end\n",
"\n",
"function stress( strain , E ) #end,transverseStrainSum, forceLinear){\n",
" # reference: http://www.colorado.edu/engineering/CAS/courses.d/Structures.d/IAST.Lect05.d/IAST.Lect05.pdf page 10\n",
" # if (isFailed(strain)) return 0.0f; //if a failure point is set and exceeded, we've broken!\n",
" # var E =setup.edges[0].stiffness; //todo change later to material ??\n",
" # var E=1000000;//todo change later to material ??\n",
" # var scaleFactor=1;\n",
" return E*strain;\n",
"\n",
" # # if (strain <= strainData[1] || linear || forceLinear){ //for compression/first segment and linear materials (forced or otherwise), simple calculation\n",
"\n",
" # if (nu==0.0) return E*strain;\n",
" # else return _eHat*((1-nu)*strain + nu*transverseStrainSum); \n",
" # else return eHat()*((1-nu)*strain + nu*transverseStrainSum); \n",
" # # }\n",
"\n",
" #//the non-linear feature with non-zero poissons ratio is currently experimental\n",
" #int DataCount = modelDataPoints();\n",
" #for (int i=2; i<DataCount; i++){ //go through each segment in the material model (skipping the first segment because it has already been handled.\n",
" # if (strain <= strainData[i] || i==DataCount-1){ //if in the segment ending with this point (or if this is the last point extrapolate out) \n",
" # float Perc = (strain-strainData[i-1])/(strainData[i]-strainData[i-1]);\n",
" # float basicStress = stressData[i-1] + Perc*(stressData[i]-stressData[i-1]);\n",
" # if (nu==0.0f) return basicStress;\n",
" # else { //accounting for volumetric effects\n",
" # float modulus = (stressData[i]-stressData[i-1])/(strainData[i]-strainData[i-1]);\n",
" # float modulusHat = modulus/((1-2*nu)*(1+nu));\n",
" # float effectiveStrain = basicStress/modulus; //this is the strain at which a simple linear stress strain line would hit this point at the definied modulus\n",
" # float effectiveTransverseStrainSum = transverseStrainSum*(effectiveStrain/strain);\n",
" # return modulusHat*((1-nu)*effectiveStrain + nu*effectiveTransverseStrainSum);\n",
" # }\n",
" # }\n",
" #}\n",
"\n",
" # assert(false); //should never reach this point\n",
" # return 0.0f;\n",
"end \n",
"\n",
"function axialStrain( positiveEnd,strain)\n",
"\t#strainRatio = pVPos->material()->E/pVNeg->material()->E;\n",
"\tstrainRatio=1.0;\n",
"\treturn positiveEnd ? 2.0 *strain*strainRatio/(1.0+strainRatio) : 2.0*strain/(1.0+strainRatio)\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"moment (generic function with 1 method)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function force(N_intForce,N_orient,N_force,static,currentTimeStep) \n",
" # forces from internal bonds\n",
" totalForce=Vector3(0,0,0)\n",
" # new THREE.Vector3(node.force.x,node.force.y,node.force.z);\n",
" # todo \n",
"\n",
"\n",
" totalForce=totalForce+N_intForce\n",
"\n",
" # for (int i=0; i<6; i++){ \n",
" # \tif (links[i]) totalForce += links[i]->force(isNegative((linkDirection)i)); # total force in LCS\n",
" # }\n",
" totalForce = RotateVec3D(N_orient,totalForce); # from local to global coordinates\n",
"\n",
"\n",
" # assert(!(totalForce.x != totalForce.x) || !(totalForce.y != totalForce.y) || !(totalForce.z != totalForce.z)); //assert non QNAN\n",
"\n",
" # other forces\n",
" if(static)\n",
" totalForce=totalForce+N_force\n",
" # }else if(currentTimeStep<50){\n",
" # \ttotalForce.add(new THREE.Vector3(node.force.x,node.force.y,node.force.z));\n",
" else\n",
" # var ex=0.1;\n",
" # if(node.force.y!=0){\n",
" # \tvar f=400*Math.sin(currentTimeStep*ex);\n",
" # \ttotalForce.add(new THREE.Vector3(0,f,0));\n",
"\n",
" # }\n",
" #x=N_position[node][3]\n",
" #t=currentTimeStep\n",
" #wave=getForce(x,t)\n",
" #totalForce=totalForce+[0 wave 0]\n",
" end\n",
"\n",
"\n",
" # if (externalExists()) totalForce += external()->force(); //external forces\n",
" # totalForce -= velocity()*mat->globalDampingTranslateC(); //global damping f-cv\n",
" # totalForce.z += mat->gravityForce(); //gravity, according to f=mg\n",
"\n",
" # if (isCollisionsEnabled()){\n",
" # \tfor (std::vector<CVX_Collision*>::iterator it=colWatch->begin(); it!=colWatch->end(); it++){\n",
" # \t\ttotalForce -= (*it)->contactForce(this);\n",
" # \t}\n",
" # }\n",
" # todo make internal forces 0 again\n",
" # N_intForce[node]=[0 0 0] # do i really need it?\n",
"\n",
" # node.force.x=0;\n",
" # node.force.y=0;\n",
" # node.force.z=0;\n",
"\n",
"\n",
" return totalForce\n",
"end\n",
"\n",
"\n",
"function moment(intMoment,orient,moment) \n",
" #moments from internal bonds\n",
" totalMoment=Vector3(0,0,0)\n",
" # for (int i=0; i<6; i++){ \n",
" # \tif (links[i]) totalMoment += links[i]->moment(isNegative((linkDirection)i)); //total force in LCS\n",
" # }\n",
"\n",
" totalMoment=totalMoment+intMoment\n",
" \n",
" \n",
"\n",
" totalMoment = RotateVec3D(orient,totalMoment);\n",
" \n",
" \n",
"\n",
" totalMoment=totalMoment+moment\n",
"\n",
"\n",
" #other moments\n",
" # if (externalExists()) totalMoment += external()->moment(); //external moments\n",
" # totalMoment -= angularVelocity()*mat->globalDampingRotateC(); //global damping\n",
"\n",
" return totalMoment\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"updateDataAndSaveFEA! (generic function with 1 method)"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function updateDataAndSaveFEA!(setup,fileName)\n",
"# nodes = setup[\"nodes\"]\n",
"# edges = setup[\"edges\"]\n",
" \n",
"# setup[\"animation\"][\"showDisplacement\"]=false\n",
"# voxCount=size(nodes)[1]\n",
"# linkCount=size(edges)[1]\n",
" \n",
"# N_displacement=Array(metavoxel[\"N_displacementGPU\"])\n",
"# N_angle=Array(metavoxel[\"N_angleGPU\"])\n",
"# E_stress=Array(metavoxel[\"E_stressGPU\"])\n",
" \n",
"# setup[\"viz\"][\"maxStress\"]=maximum(E_stress)\n",
"# setup[\"viz\"][\"minStress\"]=minimum(E_stress) \n",
"\n",
"\n",
"# i=1\n",
"# \tfor edge in edges\n",
"# edge[\"stress\"]=E_stress[i]\n",
"# i=i+1\n",
"\n",
"# end\n",
" \n",
" \n",
"# i=1 \n",
"# \tfor node in nodes\n",
"# node[\"displacement\"][\"x\"]=N_displacement[i].x*100\n",
"# node[\"displacement\"][\"y\"]=N_displacement[i].y*100\n",
"# node[\"displacement\"][\"z\"]=N_displacement[i].z*100\n",
" \n",
"# node[\"angle\"][\"x\"]=N_angle[i].x\n",
"# node[\"angle\"][\"y\"]=N_angle[i].y\n",
"# node[\"angle\"][\"z\"]=N_angle[i].z\n",
"# i=i+1\n",
"\n",
"# end\n",
" \n",
" # pass data as a json string (how it shall be displayed in a file)\n",
" stringdata = JSON.json(setup)\n",
"\n",
" # write the file with the stringdata variable information\n",
" open(fileName, \"w\") do f\n",
" write(f, stringdata)\n",
" end\n",
" \n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"updateDataAndSave! (generic function with 1 method)"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function updateDataAndSave!(metavoxel,setup,fileName)\n",
" nodes = setup[\"nodes\"]\n",
" edges = setup[\"edges\"]\n",
" \n",
" setup[\"animation\"][\"showDisplacement\"]=true\n",
" voxCount=size(nodes)[1]\n",
" linkCount=size(edges)[1]\n",
" \n",
" N_displacement=Array(metavoxel[\"N_displacementGPU\"])\n",
" N_angle=Array(metavoxel[\"N_angleGPU\"])\n",
" E_stress=Array(metavoxel[\"E_stressGPU\"])\n",
" \n",
" setup[\"viz\"][\"maxStress\"]=maximum(E_stress)\n",
" setup[\"viz\"][\"minStress\"]=minimum(E_stress) \n",
"\n",
"\n",
" i=1\n",
"\tfor edge in edges\n",
" edge[\"stress\"]=E_stress[i]\n",
" i=i+1\n",
"\n",
" end\n",
" \n",
" \n",
" i=1 \n",
"\tfor node in nodes\n",
" node[\"displacement\"][\"x\"]=N_displacement[i].x/15\n",
" node[\"displacement\"][\"y\"]=N_displacement[i].y/15\n",
" node[\"displacement\"][\"z\"]=N_displacement[i].z/15\n",
" \n",
" node[\"angle\"][\"x\"]=N_angle[i].x\n",
" node[\"angle\"][\"y\"]=N_angle[i].y\n",
" node[\"angle\"][\"z\"]=N_angle[i].z\n",
" i=i+1\n",
"\n",
" end\n",
" \n",
" # pass data as a json string (how it shall be displayed in a file)\n",
" stringdata = JSON.json(setup)\n",
"\n",
" # write the file with the stringdata variable information\n",
" open(fileName, \"w\") do f\n",
" write(f, stringdata)\n",
" end\n",
" \n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"runMetavoxelGPU! (generic function with 1 method)"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function runMetavoxelGPU!(setup,numTimeSteps,latticeSize,displacements,returnEvery,save)\n",
" function initialize!(setup)\n",
" nodes = setup[\"nodes\"]\n",
" edges = setup[\"edges\"]\n",
"\n",
" i=1\n",
" # pre-calculate current position\n",
" for node in nodes\n",
" # element=parse(Int,node[\"id\"][2:end])\n",
" N_position[i]=Vector3(node[\"position\"][\"x\"]*15.0,node[\"position\"][\"y\"]*15.0,node[\"position\"][\"z\"]*15.0)\n",
" N_restrained[i]=node[\"restrained_degrees_of_freedom\"][1] ## todo later consider other degrees of freedom\n",
" N_displacement[i]=Vector3(node[\"displacement\"][\"x\"]*15,node[\"displacement\"][\"y\"]*15,node[\"displacement\"][\"z\"]*15)\n",
" N_angle[i]=Vector3(node[\"angle\"][\"x\"],node[\"angle\"][\"y\"],node[\"angle\"][\"z\"])\n",
" N_force[i]=Vector3(node[\"force\"][\"x\"],node[\"force\"][\"y\"],node[\"force\"][\"z\"])\n",
" N_currPosition[i]=Vector3(node[\"position\"][\"x\"]*15.0,node[\"position\"][\"y\"]*15.0,node[\"position\"][\"z\"]*15.0)\n",
"\n",
" # for dynamic simulations\n",
" # append!(N_posTimeSteps,[[]])\n",
" # append!(N_angTimeSteps,[[]])\n",
"\n",
" i=i+1\n",
" end \n",
"\n",
" i=1\n",
" # pre-calculate the axis\n",
" for edge in edges\n",
" # element=parse(Int,edge[\"id\"][2:end])\n",
"\n",
" # find the nodes that the lements connects\n",
" fromNode = nodes[edge[\"source\"]+1]\n",
" toNode = nodes[edge[\"target\"]+1]\n",
"\n",
"\n",
" node1 = [fromNode[\"position\"][\"x\"]*15.0 fromNode[\"position\"][\"y\"]*15.0 fromNode[\"position\"][\"z\"]*15.0]\n",
" node2 = [toNode[\"position\"][\"x\"]*15.0 toNode[\"position\"][\"y\"]*15.0 toNode[\"position\"][\"z\"]*15.0]\n",
"\n",
" length=norm(node2-node1)\n",
" axis=normalize(collect(Iterators.flatten(node2-node1)))\n",
"\n",
" E_source[i]=edge[\"source\"]+1\n",
" E_target[i]=edge[\"target\"]+1\n",
" E_area[i]=edge[\"area\"]\n",
" E_density[i]=edge[\"density\"]\n",
" E_stiffness[i]=edge[\"stiffness\"]\n",
" E_axis[i]=Vector3(axis[1],axis[2],axis[3])\n",
" E_currentRestLength[i]=length #?????? todo change\n",
"# E_currentRestLength[i]=75/sqrt(2)\n",
" \n",
"\n",
" N_edgeID[E_source[i],N_currEdge[E_source[i]]]=i\n",
" N_edgeFirst[E_source[i],N_currEdge[E_source[i]]]=true\n",
" N_currEdge[E_source[i]]+=1\n",
"\n",
" N_edgeID[E_target[i],N_currEdge[E_target[i]]]=i\n",
" N_edgeFirst[E_target[i],N_currEdge[E_target[i]]]=false\n",
" N_currEdge[E_target[i]]+=1\n",
"\n",
"\n",
" # for dynamic simulations\n",
" # append!(E_stressTimeSteps,[[]])\n",
"\n",
" i=i+1\n",
" end \n",
" end\n",
" function simulateParallel!(metavoxel,numTimeSteps,dt,returnEvery)\n",
" # initialize(setup)\n",
"\n",
" for i in 1:numTimeSteps\n",
" #println(\"Timestep:\",i)\n",
" doTimeStep!(metavoxel,dt,i)\n",
" if(mod(i,returnEvery)==0)\n",
" append!(displacements,[Array(metavoxel[\"N_displacementGPU\"])])\n",
" end\n",
" end\n",
" end\n",
" \n",
" ########\n",
" voxCount=0\n",
" linkCount=0\n",
" nodes = setup[\"nodes\"]\n",
" edges = setup[\"edges\"]\n",
" voxCount=size(nodes)[1]\n",
" linkCount=size(edges)[1]\n",
" strain =0 #todooo moveeee\n",
" maxNumEdges=10\n",
"\n",
" ########\n",
" voxCount=0\n",
" linkCount=0\n",
" nodes = setup[\"nodes\"]\n",
" edges = setup[\"edges\"]\n",
" voxCount=size(nodes)[1]\n",
" linkCount=size(edges)[1]\n",
" strain =0 #todooo moveeee\n",
"\n",
" ############# nodes\n",
" N_position=fill(Vector3(),voxCount)\n",
" N_restrained=zeros(Bool, voxCount)\n",
" N_displacement=fill(Vector3(),voxCount)\n",
" N_angle=fill(Vector3(),voxCount)\n",
" N_currPosition=fill(Vector3(),voxCount)\n",
" N_linMom=fill(Vector3(),voxCount)\n",
" N_angMom=fill(Vector3(),voxCount)\n",
" N_intForce=fill(Vector3(),voxCount)\n",
" N_intMoment=fill(Vector3(),voxCount)\n",
" N_moment=fill(Vector3(),voxCount)\n",
" # N_posTimeSteps=[]\n",
" # N_angTimeSteps=[]\n",
" N_force=fill(Vector3(),voxCount)\n",
" N_orient=fill(Quaternion(),voxCount)\n",
" N_edgeID=fill(-1,(voxCount,maxNumEdges))\n",
" N_edgeFirst=fill(true,(voxCount,maxNumEdges))\n",
" N_currEdge=fill(1,voxCount)\n",
"\n",
" ############# edges\n",
" E_source=fill(0,linkCount)\n",
" E_target=fill(0,linkCount)\n",
" E_area=fill(0.0f0,linkCount)\n",
" E_density=fill(0.0f0,linkCount)\n",
" E_stiffness=fill(0.0f0,linkCount)\n",
" E_stress=fill(0.0f0,linkCount)\n",
" E_axis=fill(Vector3(1.0,0.0,0.0),linkCount)\n",
" E_currentRestLength=fill(0.0f0,linkCount)\n",
" E_pos2=fill(Vector3(),linkCount)\n",
" E_angle1v=fill(Vector3(),linkCount)\n",
" E_angle2v=fill(Vector3(),linkCount)\n",
" E_angle1=fill(Quaternion(),linkCount)\n",
" E_angle2=fill(Quaternion(),linkCount)\n",
"\n",
" E_intForce1=fill(Vector3(),linkCount)\n",
" E_intMoment1=fill(Vector3(),linkCount) \n",
"\n",
" E_intForce2=fill(Vector3(),linkCount)\n",
" E_intMoment2=fill(Vector3(),linkCount)\n",
" E_damp=fill(false,linkCount)\n",
"\n",
" E_currentTransverseStrainSum=fill(0.0f0,linkCount)# TODO remove ot incorporate\n",
" # E_stressTimeSteps=[]\n",
"\n",
"\n",
" #################################################################\n",
" initialize!(setup)\n",
" #################################################################\n",
"\n",
" ########################## turn to cuda arrays\n",
" ############# nodes\n",
" N_positionGPU= CuArray(N_position) \n",
" N_restrainedGPU= CuArray(N_restrained) \n",
" N_displacementGPU=CuArray(N_displacement) \n",
" N_angleGPU= CuArray(N_angle) \n",
" N_currPositionGPU=CuArray(N_currPosition) \n",
" N_linMomGPU= CuArray(N_linMom) \n",
" N_angMomGPU= CuArray(N_angMom) \n",
" N_intForceGPU= CuArray(N_intForce) \n",
" N_intMomentGPU= CuArray(N_intMoment) \n",
" N_momentGPU= CuArray(N_moment) \n",
" N_forceGPU= CuArray(N_force) \n",
" N_orientGPU= CuArray(N_orient) \n",
" N_edgeIDGPU= CuArray(N_edgeID) \n",
" N_edgeFirstGPU= CuArray(N_edgeFirst) \n",
"\n",
"\n",
" ############# edges\n",
" E_sourceGPU= CuArray(E_source) \n",
" E_targetGPU= CuArray(E_target)\n",
" E_areaGPU= CuArray(E_area) \n",
" E_densityGPU= CuArray(E_density)\n",
" E_stiffnessGPU= CuArray(E_stiffness)\n",
" E_stressGPU= CuArray(E_stress)\n",
" E_axisGPU= CuArray(E_axis) \n",
" E_currentRestLengthGPU= CuArray(E_currentRestLength)\n",
" E_pos2GPU= CuArray(E_pos2)\n",
" E_angle1vGPU= CuArray(E_angle1v)\n",
" E_angle2vGPU= CuArray(E_angle2v)\n",
" E_angle1GPU= CuArray(E_angle1)\n",
" E_angle2GPU= CuArray(E_angle2)\n",
" E_currentTransverseStrainSumGPU=CuArray(E_currentTransverseStrainSum)\n",
" E_intForce1GPU= CuArray(E_intForce1) \n",
" E_intMoment1GPU= CuArray(E_intMoment1) \n",
" E_intForce2GPU= CuArray(E_intForce2) \n",
" E_intMoment2GPU= CuArray(E_intMoment2)\n",
" E_dampGPU= CuArray(E_damp) \n",
" # E_stressTimeSteps=[]\n",
"\n",
"\n",
" #########################################\n",
" metavoxel = Dict(\n",
" \"N_positionGPU\" => N_positionGPU, \n",
" \"N_restrainedGPU\" => N_restrainedGPU, \n",
" \"N_displacementGPU\" => N_displacementGPU,\n",
" \"N_angleGPU\" => N_angleGPU, \n",
" \"N_currPositionGPU\" => N_currPositionGPU,\n",
" \"N_linMomGPU\" => N_linMomGPU, \n",
" \"N_angMomGPU\" => N_angMomGPU, \n",
" \"N_intForceGPU\" => N_intForceGPU, \n",
" \"N_intMomentGPU\" => N_intMomentGPU, \n",
" \"N_momentGPU\" => N_momentGPU, \n",
" \"N_forceGPU\" => N_forceGPU, \n",
" \"N_orientGPU\" => N_orientGPU, \n",
" \"N_edgeIDGPU\" => N_edgeIDGPU, \n",
" \"N_edgeFirstGPU\" => N_edgeFirstGPU,\n",
" \"E_sourceGPU\" =>E_sourceGPU, \n",
" \"E_targetGPU\" =>E_targetGPU, \n",
" \"E_areaGPU\" =>E_areaGPU, \n",
" \"E_densityGPU\" =>E_densityGPU, \n",
" \"E_stiffnessGPU\" =>E_stiffnessGPU, \n",
" \"E_stressGPU\" =>E_stressGPU, \n",
" \"E_axisGPU\" =>E_axisGPU, \n",
" \"E_currentRestLengthGPU\" =>E_currentRestLengthGPU, \n",
" \"E_pos2GPU\" =>E_pos2GPU, \n",
" \"E_angle1vGPU\" =>E_angle1vGPU, \n",
" \"E_angle2vGPU\" =>E_angle2vGPU, \n",
" \"E_angle1GPU\" =>E_angle1GPU, \n",
" \"E_angle2GPU\" =>E_angle2GPU, \n",
" \"E_currentTransverseStrainSumGPU\" =>E_currentTransverseStrainSumGPU,\n",
" \"E_intForce1GPU\" =>E_intForce1GPU, \n",
" \"E_intMoment1GPU\" =>E_intMoment1GPU, \n",
" \"E_intForce2GPU\" =>E_intForce2GPU, \n",
" \"E_intMoment2GPU\" =>E_intMoment2GPU, \n",
" \"E_dampGPU\" =>E_dampGPU \n",
" )\n",
"\n",
" #########################################\n",
" \n",
"\n",
" dt=0.0251646\n",
" E = 2000 # MPa\n",
" s=2.38\n",
" mass=10 \n",
" \n",
" \n",
" \n",
" MaxFreq2=E*s/mass\n",
" dt= 1/(6.283185*sqrt(MaxFreq2))\n",
"# dt=0.0001646\n",
" println(\"dt: $dt\")\n",
" \n",
" append!(displacements,[Array(metavoxel[\"N_displacementGPU\"])])\n",
" \n",
" t=@timed doTimeStep!(metavoxel,dt,0)\n",
" append!(displacements,[Array(metavoxel[\"N_displacementGPU\"])])\n",
" time=t[2]\n",
" println(\"first timestep took $time seconds\")\n",
" t=@timed simulateParallel!(metavoxel,numTimeSteps-1,dt,returnEvery)\n",
" time=t[2]\n",
" \n",
" if save\n",
" updateDataAndSave!(metavoxel,setup,\"../json/trialJuliaParallelGPU.json\")\n",
" end\n",
" println(\"ran latticeSize $latticeSize with $voxCount voxels and $linkCount edges for $numTimeSteps time steps took $time seconds\")\n",
" return\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"fea (generic function with 1 method)"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function fea(setup)\n",
" #######################################################\n",
" function points(element, properties)\n",
" elements = properties[\"elements\"]\n",
" nodes = properties[\"nodes\"]\n",
" degrees_of_freedom = properties[\"degrees_of_freedom\"]\n",
"\n",
" # find the nodes that the lements connects\n",
" fromNode = elements[element][1]\n",
" toNode = elements[element][2]\n",
"\n",
" # the coordinates for each node\n",
" fromPoint = nodes[fromNode]\n",
" toPoint = nodes[toNode]\n",
"\n",
" # find the degrees of freedom for each node\n",
" dofs = degrees_of_freedom[fromNode]\n",
" dofs=vcat(dofs,degrees_of_freedom[toNode])\n",
"\n",
" return fromPoint, toPoint, dofs\n",
" end\n",
"\n",
" function direction_cosine(vec1, vec2)\n",
" return dot(vec1,vec2) / (norm(vec1) * norm(vec2))\n",
" end\n",
"\n",
" function rotation_matrix(element_vector, x_axis, y_axis,z_axis)\n",
" # find the direction cosines\n",
" x_proj = direction_cosine(element_vector, x_axis)\n",
" y_proj = direction_cosine(element_vector, y_axis)\n",
" z_proj = direction_cosine(element_vector, z_axis);\n",
" return [[x_proj y_proj z_proj 0 0 0];[0 0 0 x_proj y_proj z_proj]]\n",
" end\n",
"\n",
" function rotation_matrix(element_vector, x_axis, y_axis,z_axis)\n",
" # find the direction cosines\n",
" L=norm(element_vector)\n",
" l = (element_vector[1])/L\n",
" m = (element_vector[2])/L\n",
" n = (element_vector[3])/L\n",
" D = ( l^2+ m^2+n^2)^0.5\n",
"\n",
" transMatrix=[[l m n 0 0 0 0 0 0 0 0 0];[-m/D l/D 0 0 0 0 0 0 0 0 0 0];[ -l*n/D -m*n/D D 0 0 0 0 0 0 0 0 0];[ 0 0 0 l m n 0 0 0 0 0 0];[ 0 0 0 -m/D l/D 0 0 0 0 0 0 0];[ 0 0 0 -l*n/D -m*n/D D 0 0 0 0 0 0];[ 0 0 0 0 0 0 l m n 0 0 0];[ 0 0 0 0 0 0 -m/D l/D 0 0 0 0];[ 0 0 0 0 0 0 -l*n/D -m*n/D D 0 0 0];[ 0 0 0 0 0 0 0 0 0 l m n];[ 0 0 0 0 0 0 0 0 0 -m/D l/D 0];[ 0 0 0 0 0 0 0 0 0 -l*n/D -m*n/D D]]\n",
"\n",
" return transMatrix\n",
" end\n",
" \n",
" #######################################################\n",
" function get_matrices(setup)\n",
"\n",
" nodes = setup[\"nodes\"]\n",
" edges = setup[\"edges\"]\n",
" ndofs = length(nodes)*6\n",
"\n",
" x_axis = [1 0 0]\n",
" y_axis = [0 1 0]\n",
" z_axis = [0 0 1]\n",
"\n",
" M = zeros((ndofs,ndofs))\n",
" K = zeros((ndofs,ndofs))\n",
" \n",
" \n",
" for edge in edges\n",
" #degrees_of_freedom = properties[\"degrees_of_freedom\"]\n",
"\n",
" element=parse(Int,edge[\"id\"][2:end])\n",
"\n",
" # find the nodes that the lements connects\n",
" fromNode = nodes[edge[\"source\"]+1]\n",
" toNode = nodes[edge[\"target\"]+1]\n",
" \n",
"\n",
" # the coordinates for each node\n",
" fromPoint = [fromNode[\"position\"][\"x\"]*15.0 fromNode[\"position\"][\"y\"]*15.0 fromNode[\"position\"][\"z\"]*15.0]\n",
" toPoint = [toNode[\"position\"][\"x\"]*15.0 toNode[\"position\"][\"y\"]*15.0 toNode[\"position\"][\"z\"]*15.0]\n",
"\n",
" # find the degrees of freedom for each node\n",
" dofs = convert(Array{Int}, fromNode[\"degrees_of_freedom\"])\n",
" dofs=vcat(dofs,convert(Array{Int}, toNode[\"degrees_of_freedom\"]))\n",
"\n",
" element_vector=toPoint-fromPoint\n",
"\n",
" # find element mass and stifness matrices\n",
" length = norm(element_vector)\n",
" rho = edge[\"density\"]\n",
" area = edge[\"area\"]\n",
" E = edge[\"stiffness\"]# youngs modulus\n",
"\n",
" A = edge[\"area\"]\n",
" G=1.0#todo shear_modulus\n",
" ixx = 1.0#todo section ixx\n",
" iyy = 1.0#todo section.iyy#\n",
" l0=length\n",
" j=1.0;#todo check\n",
" l02 = l0 * l0\n",
" l03 = l0 * l0 * l0\n",
" \n",
" # find element mass and stifness matrices\n",
" length = norm(element_vector)\n",
" rho = edge[\"density\"]\n",
" area = edge[\"area\"]\n",
" E = edge[\"stiffness\"]# youngs modulus\n",
" \n",
" \n",
" \n",
" A = edge[\"area\"]\n",
" G=1.0#todo shear_modulus\n",
" ixx = 1.0#todo section ixx\n",
" iyy = 1.0#todo section.iyy#\n",
" j=1.0;#todo check\n",
" \n",
" \n",
" h = 2.38 # mm\n",
" b = 2.38 # mm\n",
" E = 2000 # MPa\n",
" rho = 7.85e-9 / 3 # kg/mm^3\n",
" G = E * 1 / 3 # MPa\n",
" A=h*b\n",
" Q = 1 / 3 - 0.2244 / (min(h / b, b / h) + 0.1607)\n",
" J = Q * min(h * b^3, b * h^3)\n",
" I= b*h^3/12\n",
" ixx=I\n",
" iyy=I\n",
" j=J\n",
" \n",
" l0=length\n",
" l02 = l0 * l0\n",
" l03 = l0 * l0 * l0\n",
"\n",
" # Cm = rho * area * length /6.0\n",
" # Ck= E * area / length \n",
"\n",
" # m = [[2 1];[1 2]]\n",
" # k = [[1 -1];[-1 1]]\n",
"\n",
" k = [[E*A/l0 0 0 0 0 0 -E*A/l0 0 0 0 0 0];[0 12*E*ixx/l03 0 0 0 6*E*ixx/l02 0 -12*E*ixx/l03 0 0 0 6*E*ixx/l02];[0 0 12*E*iyy/l03 0 -6*E*iyy/l02 0 0 0 -12*E*iyy/l03 0 -6*E*iyy/l02 0];[0 0 0 G*j/l0 0 0 0 0 0 -G*j/l0 0 0];[0 0 -6*E*iyy/l02 0 4*E*iyy/l0 0 0 0 6*E*iyy/l02 0 2*E*iyy/l0 0];[0 6*E*ixx/l02 0 0 0 4*E*ixx/l0 0 -6*E*ixx/l02 0 0 0 2*E*ixx/l0];[-E*A/l0 0 0 0 0 0 E*A/l0 0 0 0 0 0];[0 -12*E*ixx/l03 0 0 0 -6*E*ixx/l02 0 12*E*ixx/l03 0 0 0 -6*E*ixx/l02];[0 0 -12*E*iyy/l03 0 6*E*iyy/l02 0 0 0 12*E*iyy/l03 0 6*E*iyy/l02 0];[0 0 0 -G*j/l0 0 0 0 0 0 G*j/l0 0 0];[0 0 -6*E*iyy/l02 0 2*E*iyy/l0 0 0 0 6*E*iyy/l02 0 4*E*iyy/l0 0];[0 6*E*ixx/l02 0 0 0 2*E*ixx/l0 0 -6*E*ixx/l02 0 0 0 4*E*ixx/l0]]\n",
"\n",
" \n",
" ################################\n",
"# mass=10\n",
"# nu=0.35\n",
"# W = 75\n",
"# L = W/sqrt(2)\n",
"# L=length\n",
"# n_min = 1\n",
"# n_max = 7\n",
"# # Cross Section inputs, must be floats\n",
"# E = 2000 # MPa\n",
"# G = E * 1 / 3 # MPa\n",
"# h = 2.38 # mm\n",
"# b = 2.38 # mm\n",
"# rho = 7.85e-9 / 3 # kg/mm^3\n",
"# S = h * b\n",
"# Sy = (S * (6 + 12 * nu + 6 * nu^2)/ (7 + 12 * nu + 4 * nu^2))\n",
"# # For solid rectangular cross section (width=b, depth=d & ( b < d )):\n",
"# Q = 1 / 3 - 0.2244 / (min(h / b, b / h) + 0.1607)\n",
"# J = Q * min(h * b^3, b * h^3)\n",
" \n",
" \n",
"# ##if voxels\n",
"# #nu=0\n",
"# #L=l\n",
"# #a1 = E*L # EA/L : Units of N/m\n",
"# #a2 = E * L*L*L / (12.0*(1+nu)) # GJ/L : Units of N-m\n",
"# #b1 = E*L # 12EI/L^3 : Units of N/m\n",
"# #b2 = E*L*L/2.0 # 6EI/L^2 : Units of N (or N-m/m: torque related to linear distance)\n",
"# #b3 = E*L*L*L/6.0 # 2EI/L : Units of N-m\n",
" \n",
"# I= b*h^3/12\n",
"# # J=b*h*(b*b+h*h)/12\n",
"# a1=E*b*h/L\n",
"# a2=G*J/L\n",
"# b1=12*E*I/(L^3)\n",
"# b2=6*E*I/(L^2)\n",
"# b3=2*E*I/(L)\n",
"\n",
" \n",
"\n",
"# k = [[E*A/l0 0 0 0 0 0 -E*A/l0 0 0 0 0 0];[0 12*E*ixx/l03 0 0 0 6*E*ixx/l02 0 -12*E*ixx/l03 0 0 0 6*E*ixx/l02];[0 0 12*E*iyy/l03 0 -6*E*iyy/l02 0 0 0 -12*E*iyy/l03 0 -6*E*iyy/l02 0];[0 0 0 G*j/l0 0 0 0 0 0 -G*j/l0 0 0];[0 0 -6*E*iyy/l02 0 4*E*iyy/l0 0 0 0 6*E*iyy/l02 0 2*E*iyy/l0 0];[0 6*E*ixx/l02 0 0 0 4*E*ixx/l0 0 -6*E*ixx/l02 0 0 0 2*E*ixx/l0];[-E*A/l0 0 0 0 0 0 E*A/l0 0 0 0 0 0];[0 -12*E*ixx/l03 0 0 0 -6*E*ixx/l02 0 12*E*ixx/l03 0 0 0 -6*E*ixx/l02];[0 0 -12*E*iyy/l03 0 6*E*iyy/l02 0 0 0 12*E*iyy/l03 0 6*E*iyy/l02 0];[0 0 0 -G*j/l0 0 0 0 0 0 G*j/l0 0 0];[0 0 -6*E*iyy/l02 0 2*E*iyy/l0 0 0 0 6*E*iyy/l02 0 4*E*iyy/l0 0];[0 6*E*ixx/l02 0 0 0 2*E*ixx/l0 0 -6*E*ixx/l02 0 0 0 4*E*ixx/l0]]\n",
"# k= [[ a1 0 0 0 0 0 -a1 0 0 0 0 0 ];\n",
"# [ 0 b1 0 0 0 b2 0 -b1 0 0 0 b2 ];\n",
"# [ 0 0 b1 0 -b2 0 0 0 -b1 0 -b2 0 ];\n",
"# [ 0 0 0 a2 0 0 0 0 0 -a2 0 0 ];\n",
"# [ 0 0 0 0 2b3 0 0 0 b2 0 b3 0 ];\n",
"# [ 0 0 0 0 0 2b3 0 -b2 0 0 0 b3 ];\n",
"# [ 0 0 0 0 0 0 a1 0 0 0 0 0 ];\n",
"# [ 0 0 0 0 0 0 0 b1 0 0 0 -b2 ];\n",
"# [ 0 0 0 0 0 0 0 0 b1 0 b2 0 ];\n",
"# [ 0 0 0 0 0 0 0 0 0 a2 0 0 ];\n",
"# [ 0 0 0 0 0 0 0 0 0 0 2b3 0 ];\n",
"# [ 0 0 0 0 0 0 0 0 0 0 0 2b3 ]]\n",
" # find rotated mass and stifness matrices\n",
" tau = rotation_matrix(element_vector, x_axis,y_axis,z_axis)\n",
"\n",
" # m_r=transpose(tau)*m*tau\n",
" k_r=transpose(tau)*k*tau\n",
"\n",
" # change from element to global coordinate\n",
" index= dofs.+1\n",
"\n",
" B=zeros((12,ndofs))\n",
" for i in 1:12\n",
" B[i,index[i]]=1.0\n",
" end\n",
"\n",
"\n",
" # M_rG= transpose(B)*m_r*B\n",
" K_rG= transpose(B)*k_r*B\n",
"\n",
" # M += Cm .* M_rG\n",
" # K += Ck .* K_rG\n",
" K += K_rG\n",
"\n",
" end\n",
" \n",
" \n",
" # construct the force vector\n",
" F=zeros(ndofs)\n",
" remove_indices=[];\n",
" for node in nodes\n",
" #insert!(F,i, value);\n",
" #F=vcat(F,value)\n",
" \n",
" \n",
" i=parse(Int,node[\"id\"][2:end])\n",
" f=node[\"force\"]\n",
" \n",
" # println(f)\n",
" F[(i)*6+1]+=f[\"x\"]\n",
" F[(i)*6+2]+=f[\"y\"]\n",
" F[(i)*6+3]+=f[\"z\"]\n",
" F[(i)*6+4]+=0\n",
" F[(i)*6+5]+=0\n",
" F[(i)*6+6]+=0\n",
" Load+=f[\"y\"]\n",
" if (F[(i)*6+2]!=0)\n",
" append!(topNodesIndices,i+1)\n",
" end\n",
" \n",
" dofs = convert(Array{Int}, node[\"degrees_of_freedom\"]).+1\n",
" restrained_dofs=node[\"restrained_degrees_of_freedom\"]\n",
" for (index, value) in enumerate(dofs)\n",
" if restrained_dofs[index]\n",
" append!( remove_indices, value)\n",
" end\n",
" end\n",
" \n",
" end\n",
"\n",
" #println(remove_indices)\n",
" #print(K)\n",
" #print(F)\n",
" \n",
"\n",
" #M = M[setdiff(1:end, remove_indices), :]\n",
" K = K[setdiff(1:end, remove_indices), :]\n",
"\n",
" #M = M[:,setdiff(1:end, remove_indices)]\n",
" K = K[:,setdiff(1:end, remove_indices)]\n",
"\n",
" F = F[setdiff(1:end, remove_indices)]\n",
" \n",
" U=zeros(ndofs)\n",
" \n",
" return M,K,F,U,remove_indices\n",
" end\n",
"\n",
" \n",
" function updateDisplacement(setup, X)\n",
" nodes= setup[\"nodes\"]\n",
" i=0\n",
" for node in nodes\n",
" \n",
"# if !node[\"restrained_degrees_of_freedom\"][2]\n",
" #i=parse(Int,node[\"id\"][2:end])\n",
" node[\"displacement\"][\"x\"]=X[(i)*6+1]/15\n",
" node[\"displacement\"][\"y\"]=X[(i)*6+2]/15\n",
" node[\"displacement\"][\"z\"]=X[(i)*6+3]/15\n",
" node[\"angle\"][\"x\"]=X[(i)*6+4]\n",
" node[\"angle\"][\"y\"]=X[(i)*6+5]\n",
" node[\"angle\"][\"z\"]=X[(i)*6+6]\n",
" append!(displacementFEA,[Vector3(X[(i)*6+1],X[(i)*6+2],X[(i)*6+3])])\n",
" i=i+1\n",
"# else\n",
"# append!(displacementFEA,[Vector3(0,0,0)])\n",
"# end\n",
" end\n",
" end\n",
" \n",
" #######################################################\n",
"\n",
" function get_stresses(setup)\n",
" nodes = setup[\"nodes\"]\n",
" edges = setup[\"edges\"]\n",
" ndofs = length(nodes)*6\n",
"\n",
" x_axis = [1 0 0]\n",
" y_axis = [0 1 0]\n",
" z_axis = [0 0 1]\n",
"\n",
" # find the stresses in each member\n",
" stresses=zeros(length(edges))\n",
" max11=-10e6\n",
" min11=10e6\n",
" for edge in edges\n",
" #degrees_of_freedom = properties[\"degrees_of_freedom\"]\n",
"\n",
" element=parse(Int,edge[\"id\"][2:end])\n",
"\n",
" # find the nodes that the lements connects\n",
" fromNode = nodes[edge[\"source\"]+1]\n",
" toNode = nodes[edge[\"target\"]+1]\n",
"\n",
" # the coordinates for each node\n",
" fromPoint = [fromNode[\"position\"][\"x\"]*15.0 fromNode[\"position\"][\"y\"]*15.0 fromNode[\"position\"][\"z\"]*15.0]\n",
" toPoint = [toNode[\"position\"][\"x\"]*15.0 toNode[\"position\"][\"y\"]*15.0 toNode[\"position\"][\"z\"]*15.0]\n",
"\n",
" # find the degrees of freedom for each node\n",
" dofs = convert(Array{Int}, fromNode[\"degrees_of_freedom\"])\n",
" dofs=vcat(dofs,convert(Array{Int}, toNode[\"degrees_of_freedom\"]))\n",
"\n",
" element_vector=toPoint-fromPoint\n",
"\n",
"\n",
" # find rotated mass and stifness matrices\n",
" tau = rotation_matrix(element_vector, x_axis,y_axis,z_axis)\n",
"\n",
" # i1=parse(Int,fromNode[\"id\"][2:end])\n",
" # i2=parse(Int,toNode[\"id\"][2:end])\n",
"\n",
" # global_displacements=[X[(i1)*6+1] X[(i1)*6+2] X[(i1)*6+3] X[(i1)*6+4] X[(i1)*6+5] X[(i1)*6+6] X[(i2)*6+1] X[(i2)*6+2] X[(i2)*6+3] X[(i2)*6+4] X[(i2)*6+5] X[(i2)*6+6]] # todo change\n",
" global_displacements=[fromNode[\"displacement\"][\"x\"]*15 fromNode[\"displacement\"][\"y\"]*15 fromNode[\"displacement\"][\"z\"]*15 fromNode[\"angle\"][\"x\"] fromNode[\"angle\"][\"y\"] fromNode[\"angle\"][\"z\"] toNode[\"displacement\"][\"x\"]*15 toNode[\"displacement\"][\"y\"]*15 toNode[\"displacement\"][\"z\"]*15 toNode[\"angle\"][\"x\"] toNode[\"angle\"][\"y\"] toNode[\"angle\"][\"z\"]] # todo change\n",
"\n",
" # nodal displacement\n",
"\n",
" q=tau*transpose(global_displacements)\n",
" # println(q)\n",
" # calculate the strain and stresses\n",
" strain =(q[7]-q[1])/norm(element_vector)\n",
" E = edge[\"stiffness\"]# youngs modulus\n",
" E=2000\n",
" stress=E.*strain\n",
" edge[\"stress\"]=stress\n",
" if stress>max11\n",
" max11=stress\n",
" end\n",
" if stress<min11\n",
" min11=stress\n",
" end\n",
" # println(element)\n",
" # println(stress)\n",
" end\n",
"\n",
"\n",
"\n",
" setup[\"viz\"][\"minStress\"]=min11\n",
" setup[\"viz\"][\"maxStress\"]=max11\n",
" return stresses\n",
" end\n",
" \n",
" function initialize(setup)\n",
" nodes = setup[\"nodes\"]\n",
" ndofs = length(nodes)*6\n",
" \n",
" i=0\n",
" for node in nodes\n",
" dg=[]\n",
" for ii in 0:5\n",
" append!(dg,i+ii) \n",
" end\n",
" i+=6\n",
" node[\"degrees_of_freedom\"]=dg\n",
" end\n",
" end\n",
"\n",
" #######################################################\n",
" function solveFea(setup)\n",
" // # determine the global matrices\n",
" initialize(setup)\n",
" \n",
" M,K,F,U,ind=get_matrices(setup)\n",
" \n",
" #println(M)\n",
" #println(K)\n",
" #println(F)\n",
"\n",
" #evals=eigvals(K,M)\n",
" #evecs=eigvecs(K,M)\n",
" #frequencies=sqrt.(evals)\n",
" X=inv(K)*F\n",
" U[setdiff(1:end, ind)]=X\n",
"\n",
" updateDisplacement(setup, U)\n",
"\n",
" # determine the stresses in each element\n",
" stresses=get_stresses(setup)\n",
" end\n",
" #######################################################\n",
" displacementFEA=[]\n",
" Load=0\n",
" topNodesIndices=[]\n",
" solveFea(setup)\n",
" return displacementFEA,Load,topNodesIndices\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"getYoungsModulus (generic function with 1 method)"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function getYoungsModulus(latticeSize,voxelSize,disp,Load,topNodesIndices)\n",
" F=-Load\n",
" l0=voxelSize*latticeSize\n",
" A=l0*l0\n",
"\n",
" δl1=-mean( x.y for x in disp[topNodesIndices])\n",
" \n",
" stresses=F/A\n",
" strain=δl1/l0\n",
" println(\"Load=$Load\")\n",
" println(\"stress=$stresses\")\n",
"\n",
" E=stresses/strain \n",
"\n",
" return E\n",
"end\n"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"getSetup (generic function with 1 method)"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function getSetup(latticeSize)\n",
" setup = Dict()\n",
" name=string(\"../json/setupTestUni$latticeSize\",\".json\")\n",
" name=string(\"../json/canteliver\",\".json\")\n",
" \n",
"# open(\"../json/setupValid2.json\", \"r\") do f\n",
"# open(\"../json/setupTest.json\", \"r\") do f\n",
" # open(\"../json/trialJulia.json\", \"r\") do f\n",
"# open(\"../json/setupTestUni4.json\", \"r\") do f\n",
" # open(\"../json/setupChiral.json\", \"r\") do f\n",
"# open(\"../json/setupTestCubeUni10.json\", \"r\") do f\n",
" open(name, \"r\") do f\n",
"# global setup\n",
" dicttxt = String(read(f)) # file information to string\n",
" setup=JSON.parse(dicttxt) # parse and transform data\n",
" end\n",
"\n",
" setup=setup[\"setup\"]\n",
" return setup\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"36\n"
]
},
{
"data": {
"text/plain": [
"84"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"latticeSize=1\n",
"setup=getSetup(latticeSize)\n",
"displacementFEA,Load,topNodesIndices=fea(setup)\n",
"topNodesIndices\n",
"println(length(setup[\"nodes\"]))\n",
"length(setup[\"edges\"])"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"5-element Array{Float64,1}:\n",
" 0.0\n",
" 0.0\n",
" 0.0\n",
" 0.0\n",
" 0.0"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"DDisplacements=[[],[],[],[],[]]\n",
"DDisplacementsFEA=[[],[],[],[],[]]\n",
"Loads=[0.0,0,0,0,0]\n",
"EsFEA=[0.0,0,0,0,0]\n",
"Es=[0.0,0,0,0,0]"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Dict{String,Any} with 8 entries:\n",
" \"nodes\" => Any[Dict{String,Any}(\"degrees_of_freedom\"=>Any[0, 1, 2, 3, …\n",
" \"voxelSize\" => 5\n",
" \"numTimeSteps\" => 100\n",
" \"hierarchical\" => false\n",
" \"animation\" => Dict{String,Any}(\"speed\"=>3,\"exaggeration\"=>2.0,\"showDisplac…\n",
" \"viz\" => Dict{String,Any}(\"colorMap\"=>0,\"colorMaps\"=>Any[Any[Any[0, …\n",
" \"edges\" => Any[Dict{String,Any}(\"source\"=>0,\"area\"=>1,\"density\"=>0.028…\n",
" \"ndofs\" => 216"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"setup"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"71521"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"latticeSize=1\n",
"setup=getSetup(latticeSize)\n",
"displacementFEA,Load,topNodesIndices=fea(setup)\n",
"# displacementFEA,Load,topNodesIndices=feaDisplacement(setup,latticeSize)\n",
"updateDataAndSaveFEA!(setup,\"../json/trialJuliaParallelGPU.json\")\n"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"dt: 0.007294855212986816\n",
"first timestep took 0.0004967 seconds\n",
"ran latticeSize 1 with 36 voxels and 84 edges for 2000 time steps took 0.6889823 seconds\n",
"Load=-60\n",
"stress=0.010666666666666666\n",
"Load=-60\n",
"stress=0.010666666666666666\n",
"EsFEA:[0.006574508319567247, 0.0, 0.0, 0.0, 0.0]\n",
"Es:[0.022776269378094814, 0.0, 0.0, 0.0, 0.0]\n",
"FEA displacement= -143.1011794080455,converged displacement= -41.97987125835496\n"
]
},
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},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\n",
"setup=getSetup(latticeSize)\n",
"numTimeSteps=2000\n",
"displacements=[]\n",
"save=true\n",
"returnEvery=10\n",
"runMetavoxelGPU!(setup,numTimeSteps,latticeSize,displacements,returnEvery,true)\n",
"\n",
"numTimeStepsRecorded=length(displacements)\n",
"d=[]\n",
"dFEA=[]\n",
"j=length(displacements[end])\n",
"step=100\n",
"for i in 1:step:numTimeStepsRecorded\n",
" append!(d,displacements[i][j].y)\n",
" append!(dFEA,displacementFEA[j].y)\n",
"end\n",
"Loads[latticeSize]=Load\n",
"DDisplacements[latticeSize]=d\n",
"DDisplacementsFEA[latticeSize]=dFEA\n",
"\n",
"E1=getYoungsModulus(latticeSize,75,displacementFEA,Load,topNodesIndices)\n",
"E2=getYoungsModulus(latticeSize,75,displacements[end],Load,topNodesIndices)\n",
"\n",
"EsFEA[latticeSize]=E1\n",
"Es[latticeSize]=E2\n",
"\n",
"print(\"EsFEA:\" )\n",
"println(EsFEA)\n",
"print(\"Es:\" )\n",
"println(Es)\n",
"\n",
"println(\"FEA displacement= $(displacementFEA[j].y),converged displacement= $(displacements[numTimeStepsRecorded][j].y)\")\n",
"plot(1:step:numTimeStepsRecorded,d,label=\"Dynamic\",xlabel=\"timestep\",ylabel=\"displacement\",title=\"$latticeSize Voxel Convergence Study\")\n",
"plot!(1:step:numTimeStepsRecorded,dFEA,label=\"FEA\")\n",
"# savefig(\"4_voxel_convergence\")\n"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
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],
"source": [
"n=[]\n",
"nFEA=[]\n",
"j=length(displacements[end])\n",
"for i in 1:j\n",
" append!(n,displacements[end][i].y)\n",
" append!(nFEA,displacementFEA[i].y)\n",
"end\n",
"scatter(1:j,n,label=\"Dyanmic\",xlabel=\"Node ID\",ylabel=\"displacement\",title=\"Node Displacement\")\n",
"scatter!(1:j,nFEA,label=\"FEA\")\n",
"# savefig(\"node_displacement_four_voxel\")"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"scrolled": true
},
"outputs": [
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},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Es[1]=EsFEA[1]\n",
"plot(1:5,Es,label=\"Dyanmic\",xlabel=\"lattice size\",ylabel=\"E\",title=\"Young's Modulus\")\n",
"plot!(1:5,EsFEA,label=\"FEA\")\n",
"scatter!(1:5,Es,color=\"black\",label=\"\")\n",
"scatter!(1:5,EsFEA,color=\"black\",label=\"\")\n",
"# savefig(\"youngs_modulus1\")"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"ename": "BoundsError",
"evalue": "BoundsError: attempt to access 0-element Array{Float64,1} at index [1:201]",
"output_type": "error",
"traceback": [
"BoundsError: attempt to access 0-element Array{Float64,1} at index [1:201]",
"",
"Stacktrace:",
" [1] throw_boundserror(::Array{Float64,1}, ::Tuple{UnitRange{Int64}}) at .\\abstractarray.jl:538",
" [2] checkbounds at .\\abstractarray.jl:503 [inlined]",
" [3] getindex(::Array{Float64,1}, ::UnitRange{Int64}) at .\\array.jl:734",
" [4] gr_display(::Plots.Subplot{Plots.GRBackend}, ::Measures.Length{:mm,Float64}, ::Measures.Length{:mm,Float64}, ::Array{Float64,1}) at C:\\Users\\amira\\.julia\\packages\\Plots\\cc8wh\\src\\backends\\gr.jl:1597",
" [5] gr_display(::Plots.Plot{Plots.GRBackend}, ::String) at C:\\Users\\amira\\.julia\\packages\\Plots\\cc8wh\\src\\backends\\gr.jl:716",
" [6] _show(::Base.GenericIOBuffer{Array{UInt8,1}}, ::MIME{Symbol(\"image/svg+xml\")}, ::Plots.Plot{Plots.GRBackend}) at C:\\Users\\amira\\.julia\\packages\\Plots\\cc8wh\\src\\backends\\gr.jl:1922",
" [7] show(::Base.GenericIOBuffer{Array{UInt8,1}}, ::MIME{Symbol(\"image/svg+xml\")}, ::Plots.Plot{Plots.GRBackend}) at C:\\Users\\amira\\.julia\\packages\\Plots\\cc8wh\\src\\output.jl:216",
" [8] #sprint#342(::Nothing, ::Int64, ::typeof(sprint), ::Function, ::MIME{Symbol(\"image/svg+xml\")}, ::Vararg{Any,N} where N) at .\\strings\\io.jl:107",
" [9] sprint(::Function, ::MIME{Symbol(\"image/svg+xml\")}, ::Vararg{Any,N} where N) at .\\strings\\io.jl:103",
" [10] _ijulia_display_dict(::Plots.Plot{Plots.GRBackend}) at C:\\Users\\amira\\.julia\\packages\\Plots\\cc8wh\\src\\ijulia.jl:53",
" [11] display_dict(::Plots.Plot{Plots.GRBackend}) at C:\\Users\\amira\\.julia\\packages\\Plots\\cc8wh\\src\\init.jl:83",
" [12] #invokelatest#1 at .\\essentials.jl:790 [inlined]",
" [13] invokelatest at .\\essentials.jl:789 [inlined]",
" [14] execute_request(::ZMQ.Socket, ::IJulia.Msg) at C:\\Users\\amira\\.julia\\packages\\IJulia\\DrVMH\\src\\execute_request.jl:112",
" [15] #invokelatest#1 at .\\essentials.jl:790 [inlined]",
" [16] invokelatest at .\\essentials.jl:789 [inlined]",
" [17] eventloop(::ZMQ.Socket) at C:\\Users\\amira\\.julia\\packages\\IJulia\\DrVMH\\src\\eventloop.jl:8",
" [18] (::getfield(IJulia, Symbol(\"##15#18\")))() at .\\task.jl:268"
]
}
],
"source": [
"plot()\n",
"for i in 2:5\n",
" plot!(1:step:numTimeStepsRecorded,DDisplacements[i],label=\"$i x dynamic\",xlabel=\"timestep\",ylabel=\"displacement\",title=\"Dynamic Model Convergence\")\n",
" plot!(1:step:numTimeStepsRecorded,DDisplacementsFEA[i],label=\"$i x fea\",xlabel=\"timestep\",ylabel=\"displacement\",title=\"Dynamic Model Convergence\")\n",
"\n",
"end\n",
"plot!()\n",
"# savefig(\"total_convergence1\")"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
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},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Emeasured = [0.4500, 1.6959, 2.3031, 3.6480]\n",
"voxFrameSingle=[0.06,1.36,1.49,1.68,1.73]#,1.80,1.83]\n",
"println(EsFEA)\n",
"plot(1:5,EsFEA,label=\"metavoxel (single)\",xlabel=\"lattice size\",ylabel=\"E\")\n",
"scatter!(1:5,EsFEA,color=\"black\",label=\"\")\n",
"plot!(1:4,Emeasured,label=\"measured (double)\")\n",
"scatter!(1:4,Emeasured,color=\"black\",label=\"\")\n",
"plot!(1:5,voxFrameSingle,label=\"voxframe (single)\")\n",
"scatter!(1:5,voxFrameSingle,color=\"black\",label=\"\")\n",
"# savefig(\"youngs_fea_comparison\")"
]
},
{
"cell_type": "code",
"execution_count": 284,
"metadata": {},
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"source": [
"gpu=[5.668E-02,1.534E-01,3.000E-01,4.000E-01,8.000E-01]\n",
"csolver=[1.010E-03,2.483E-03,5.534E-02,5.949E-01,2.438E+01]\n",
"X=[1,8,64,512,4096]\n",
"plot(X,gpu,label=\"dynamic gpu\",xlabel=\"number of voxels\",ylabel=\"Time(s)\")\n",
"scatter!(X,gpu,color=\"black\",label=\"\")\n",
"plot!(X,csolver,label=\"c solver\")\n",
"scatter!(X,csolver,color=\"black\",label=\"\")\n"
]
},
{
"cell_type": "code",
"execution_count": 279,
"metadata": {},
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"metadata": {},
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],
"source": [
"plot()\n",
"for i in 1:5\n",
" l0=75*i\n",
" A=l0*l0\n",
"# plot!(1:step:numTimeStepsRecorded,DDisplacements[i]/A,label=\"$i x dynamic\",xlabel=\"timestep\",ylabel=\"strain\",title=\"Dynamic Model Convergence\")\n",
" plot!(1:step:numTimeStepsRecorded,-DDisplacementsFEA[i]/l0,label=\"$i x fea\",xlabel=\"timestep\",ylabel=\"strain\",title=\"Dynamic Model Convergence\")\n",
"\n",
"end\n",
"plot!()\n",
"# savefig(\"total_convergence\")"
]
},
{
"cell_type": "code",
"execution_count": 280,
"metadata": {},
"outputs": [
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},
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"metadata": {},
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],
"source": [
"strains=[-DDisplacementsFEA[1][1],-DDisplacementsFEA[2][1],-DDisplacementsFEA[3][1],-DDisplacementsFEA[4][1],-DDisplacementsFEA[5][1]]\n",
"plot(strains,-Loads,label=\"fea\",xlabel=\"displacement\",ylabel=\"load\",title=\"load vs displacement\")\n",
"scatter!(strains,-Loads,label=\"fea\",xlabel=\"displacement\",ylabel=\"load\",title=\"load vs displacement\")\n"
]
},
{
"cell_type": "code",
"execution_count": 281,
"metadata": {},
"outputs": [
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},
"execution_count": 281,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot()\n",
"stresss=[]\n",
"strainn=[]\n",
"for i in 1:5\n",
" l0=75*i\n",
" A=l0*l0\n",
" append!(stresss,400000000)\n",
"# append!(stresss,-Loads[i]/A)\n",
" append!(strainn,-DDisplacementsFEA[i][1]/l0)\n",
" scatter!([-DDisplacementsFEA[i][1]/l0],[400000000],label=\"$i\",xlabel=\"strain\",ylabel=\"stess\",title=\"stress vs strain\")\n",
"\n",
"end\n",
"plot!()\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 282,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"dt: 0.007294855212986816\n",
"first timestep took 0.001470699 seconds\n",
"ran latticeSize 5 with 540 voxels and 1800 edges for 20000 time steps took 9.3035085 seconds\n"
]
}
],
"source": [
"setup=getSetup(latticeSize)\n",
"numTimeSteps=20000\n",
"displacements=[]\n",
"save=true\n",
"returnEvery=1\n",
"runMetavoxelGPU!(setup,numTimeSteps,latticeSize,displacements,returnEvery,false)\n"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"feaDisplacement (generic function with 1 method)"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function feaDisplacement(setup,latticeSize)\n",
" #######################################################\n",
" function points(element, properties)\n",
" elements = properties[\"elements\"]\n",
" nodes = properties[\"nodes\"]\n",
" degrees_of_freedom = properties[\"degrees_of_freedom\"]\n",
"\n",
" # find the nodes that the lements connects\n",
" fromNode = elements[element][1]\n",
" toNode = elements[element][2]\n",
"\n",
" # the coordinates for each node\n",
" fromPoint = nodes[fromNode]\n",
" toPoint = nodes[toNode]\n",
"\n",
" # find the degrees of freedom for each node\n",
" dofs = degrees_of_freedom[fromNode]\n",
" dofs=vcat(dofs,degrees_of_freedom[toNode])\n",
"\n",
" return fromPoint, toPoint, dofs\n",
" end\n",
"\n",
" function direction_cosine(vec1, vec2)\n",
" return dot(vec1,vec2) / (norm(vec1) * norm(vec2))\n",
" end\n",
"\n",
" function rotation_matrix(element_vector, x_axis, y_axis,z_axis)\n",
" # find the direction cosines\n",
" x_proj = direction_cosine(element_vector, x_axis)\n",
" y_proj = direction_cosine(element_vector, y_axis)\n",
" z_proj = direction_cosine(element_vector, z_axis);\n",
" return [[x_proj y_proj z_proj 0 0 0];[0 0 0 x_proj y_proj z_proj]]\n",
" end\n",
"\n",
" function rotation_matrix(element_vector, x_axis, y_axis,z_axis)\n",
" # find the direction cosines\n",
" L=norm(element_vector)\n",
" l = (element_vector[1])/L\n",
" m = (element_vector[2])/L\n",
" n = (element_vector[3])/L\n",
" D = ( l^2+ m^2+n^2)^0.5\n",
"\n",
" transMatrix=[[l m n 0 0 0 0 0 0 0 0 0];[-m/D l/D 0 0 0 0 0 0 0 0 0 0];[ -l*n/D -m*n/D D 0 0 0 0 0 0 0 0 0];[ 0 0 0 l m n 0 0 0 0 0 0];[ 0 0 0 -m/D l/D 0 0 0 0 0 0 0];[ 0 0 0 -l*n/D -m*n/D D 0 0 0 0 0 0];[ 0 0 0 0 0 0 l m n 0 0 0];[ 0 0 0 0 0 0 -m/D l/D 0 0 0 0];[ 0 0 0 0 0 0 -l*n/D -m*n/D D 0 0 0];[ 0 0 0 0 0 0 0 0 0 l m n];[ 0 0 0 0 0 0 0 0 0 -m/D l/D 0];[ 0 0 0 0 0 0 0 0 0 -l*n/D -m*n/D D]]\n",
"\n",
" return transMatrix\n",
" end\n",
" \n",
" #######################################################\n",
" function get_matrices(setup)\n",
"\n",
" nodes = setup[\"nodes\"]\n",
" edges = setup[\"edges\"]\n",
" ndofs = length(nodes)*6\n",
"\n",
" x_axis = [1 0 0]\n",
" y_axis = [0 1 0]\n",
" z_axis = [0 0 1]\n",
"\n",
" M = zeros((ndofs,ndofs))\n",
" K = zeros((ndofs,ndofs))\n",
" \n",
" \n",
" for edge in edges\n",
" #degrees_of_freedom = properties[\"degrees_of_freedom\"]\n",
"\n",
" element=parse(Int,edge[\"id\"][2:end])\n",
"\n",
" # find the nodes that the lements connects\n",
" fromNode = nodes[edge[\"source\"]+1]\n",
" toNode = nodes[edge[\"target\"]+1]\n",
" \n",
"\n",
" # the coordinates for each node\n",
" fromPoint = [fromNode[\"position\"][\"x\"]*15.0 fromNode[\"position\"][\"y\"]*15.0 fromNode[\"position\"][\"z\"]*15.0]\n",
" toPoint = [toNode[\"position\"][\"x\"]*15.0 toNode[\"position\"][\"y\"]*15.0 toNode[\"position\"][\"z\"]*15.0]\n",
"\n",
" # find the degrees of freedom for each node\n",
" dofs = convert(Array{Int}, fromNode[\"degrees_of_freedom\"])\n",
" dofs=vcat(dofs,convert(Array{Int}, toNode[\"degrees_of_freedom\"]))\n",
"\n",
" element_vector=toPoint-fromPoint\n",
"\n",
" # find element mass and stifness matrices\n",
" length = norm(element_vector)\n",
" rho = edge[\"density\"]\n",
" area = edge[\"area\"]\n",
" E = edge[\"stiffness\"]# youngs modulus\n",
"\n",
" A = edge[\"area\"]\n",
" G=1.0#todo shear_modulus\n",
" ixx = 1.0#todo section ixx\n",
" iyy = 1.0#todo section.iyy#\n",
" l0=length\n",
" j=1.0;#todo check\n",
" l02 = l0 * l0\n",
" l03 = l0 * l0 * l0\n",
" \n",
" # find element mass and stifness matrices\n",
" length = norm(element_vector)\n",
" rho = edge[\"density\"]\n",
" area = edge[\"area\"]\n",
" E = edge[\"stiffness\"]# youngs modulus\n",
" \n",
" \n",
" \n",
" A = edge[\"area\"]\n",
" G=1.0#todo shear_modulus\n",
" ixx = 1.0#todo section ixx\n",
" iyy = 1.0#todo section.iyy#\n",
" j=1.0;#todo check\n",
" \n",
" \n",
" h = 2.38 # mm\n",
" b = 2.38 # mm\n",
" E = 2000 # MPa\n",
" rho = 7.85e-9 / 3 # kg/mm^3\n",
" G = E * 1 / 3 # MPa\n",
" A=h*b\n",
" Q = 1 / 3 - 0.2244 / (min(h / b, b / h) + 0.1607)\n",
" J = Q * min(h * b^3, b * h^3)\n",
" I= b*h^3/12\n",
" ixx=I\n",
" iyy=I\n",
" j=J\n",
" \n",
" l0=length\n",
" l02 = l0 * l0\n",
" l03 = l0 * l0 * l0\n",
"\n",
"\n",
" k = [[E*A/l0 0 0 0 0 0 -E*A/l0 0 0 0 0 0];[0 12*E*ixx/l03 0 0 0 6*E*ixx/l02 0 -12*E*ixx/l03 0 0 0 6*E*ixx/l02];[0 0 12*E*iyy/l03 0 -6*E*iyy/l02 0 0 0 -12*E*iyy/l03 0 -6*E*iyy/l02 0];[0 0 0 G*j/l0 0 0 0 0 0 -G*j/l0 0 0];[0 0 -6*E*iyy/l02 0 4*E*iyy/l0 0 0 0 6*E*iyy/l02 0 2*E*iyy/l0 0];[0 6*E*ixx/l02 0 0 0 4*E*ixx/l0 0 -6*E*ixx/l02 0 0 0 2*E*ixx/l0];[-E*A/l0 0 0 0 0 0 E*A/l0 0 0 0 0 0];[0 -12*E*ixx/l03 0 0 0 -6*E*ixx/l02 0 12*E*ixx/l03 0 0 0 -6*E*ixx/l02];[0 0 -12*E*iyy/l03 0 6*E*iyy/l02 0 0 0 12*E*iyy/l03 0 6*E*iyy/l02 0];[0 0 0 -G*j/l0 0 0 0 0 0 G*j/l0 0 0];[0 0 -6*E*iyy/l02 0 2*E*iyy/l0 0 0 0 6*E*iyy/l02 0 4*E*iyy/l0 0];[0 6*E*ixx/l02 0 0 0 2*E*ixx/l0 0 -6*E*ixx/l02 0 0 0 4*E*ixx/l0]]\n",
"\n",
"\n",
" # find rotated mass and stifness matrices\n",
" tau = rotation_matrix(element_vector, x_axis,y_axis,z_axis)\n",
"\n",
" # m_r=transpose(tau)*m*tau\n",
" k_r=transpose(tau)*k*tau\n",
"\n",
" # change from element to global coordinate\n",
" index= dofs.+1\n",
"\n",
" B=zeros((12,ndofs))\n",
" for i in 1:12\n",
" B[i,index[i]]=1.0\n",
" end\n",
"\n",
"\n",
" # M_rG= transpose(B)*m_r*B\n",
" K_rG= transpose(B)*k_r*B\n",
"\n",
" # M += Cm .* M_rG\n",
" # K += Ck .* K_rG\n",
" K += K_rG\n",
"\n",
" end\n",
" \n",
" \n",
" # construct the force vector\n",
" F=zeros(ndofs)\n",
" U=zeros(ndofs)\n",
" remove_indices=[];\n",
" for node in nodes\n",
" #insert!(F,i, value);\n",
" #F=vcat(F,value)\n",
" \n",
" \n",
" \n",
" \n",
" i=parse(Int,node[\"id\"][2:end])\n",
" f=node[\"force\"]\n",
" \n",
" # println(f)\n",
" U[(i)*6+1]=0\n",
" U[(i)*6+2]=-0.01*(node[\"position\"][\"y\"]+2.5)*15.0 *((node[\"position\"][\"y\"]+2.5)/(5*latticeSize))\n",
" U[(i)*6+3]=0\n",
" U[(i)*6+4]=0\n",
" U[(i)*6+5]=0\n",
" U[(i)*6+6]=0\n",
" \n",
" # println(f)\n",
" F[(i)*6+1]+=f[\"x\"]\n",
" F[(i)*6+2]+=f[\"y\"]\n",
" F[(i)*6+3]+=f[\"z\"]\n",
" F[(i)*6+4]+=0\n",
" F[(i)*6+5]+=0\n",
" F[(i)*6+6]+=0\n",
" Load+=f[\"y\"]\n",
" if (F[(i)*6+2]!=0)\n",
" append!(topNodesIndices,i+1)\n",
" end\n",
" \n",
" dofs = convert(Array{Int}, node[\"degrees_of_freedom\"]).+1\n",
" restrained_dofs=node[\"restrained_degrees_of_freedom\"]\n",
" for (index, value) in enumerate(dofs)\n",
" if restrained_dofs[index]\n",
" append!( remove_indices, value)\n",
" end\n",
" end\n",
" \n",
" end\n",
"\n",
" #println(remove_indices)\n",
" #print(K)\n",
" #print(F)\n",
" \n",
"\n",
" #M = M[setdiff(1:end, remove_indices), :]\n",
" K = K[setdiff(1:end, remove_indices), :]\n",
"\n",
" #M = M[:,setdiff(1:end, remove_indices)]\n",
" K = K[:,setdiff(1:end, remove_indices)]\n",
"\n",
" F = F[setdiff(1:end, remove_indices)]\n",
" X = U[setdiff(1:end, remove_indices)]\n",
" \n",
" return M,K,F,U,remove_indices,X\n",
" end\n",
"\n",
" \n",
" function updateDisplacement(setup, X)\n",
" nodes= setup[\"nodes\"]\n",
" i=0\n",
" for node in nodes\n",
" \n",
"# if !node[\"restrained_degrees_of_freedom\"][2]\n",
" #i=parse(Int,node[\"id\"][2:end])\n",
" node[\"displacement\"][\"x\"]=X[(i)*6+1]\n",
" node[\"displacement\"][\"y\"]=X[(i)*6+2]\n",
" node[\"displacement\"][\"z\"]=X[(i)*6+3]\n",
" node[\"angle\"][\"x\"]=X[(i)*6+4]\n",
" node[\"angle\"][\"y\"]=X[(i)*6+5]\n",
" node[\"angle\"][\"z\"]=X[(i)*6+6]\n",
" append!(displacementFEA,[Vector3(X[(i)*6+1],X[(i)*6+2],X[(i)*6+3])])\n",
" i=i+1\n",
"# else\n",
"# append!(displacementFEA,[Vector3(0,0,0)])\n",
"# end\n",
" end\n",
" end\n",
" \n",
" #######################################################\n",
"\n",
" function get_stresses(setup)\n",
" nodes = setup[\"nodes\"]\n",
" edges = setup[\"edges\"]\n",
" ndofs = length(nodes)*6\n",
"\n",
" x_axis = [1 0 0]\n",
" y_axis = [0 1 0]\n",
" z_axis = [0 0 1]\n",
"\n",
" # find the stresses in each member\n",
" stresses=zeros(length(edges))\n",
" max11=-10e6\n",
" min11=10e6\n",
" for edge in edges\n",
" #degrees_of_freedom = properties[\"degrees_of_freedom\"]\n",
"\n",
" element=parse(Int,edge[\"id\"][2:end])\n",
"\n",
" # find the nodes that the lements connects\n",
" fromNode = nodes[edge[\"source\"]+1]\n",
" toNode = nodes[edge[\"target\"]+1]\n",
"\n",
" # the coordinates for each node\n",
" fromPoint = [fromNode[\"position\"][\"x\"]*15 fromNode[\"position\"][\"y\"]*15 fromNode[\"position\"][\"z\"]*15]\n",
" toPoint = [toNode[\"position\"][\"x\"]*15 toNode[\"position\"][\"y\"]*15 toNode[\"position\"][\"z\"]*15]\n",
"\n",
" # find the degrees of freedom for each node\n",
" dofs = convert(Array{Int}, fromNode[\"degrees_of_freedom\"])\n",
" dofs=vcat(dofs,convert(Array{Int}, toNode[\"degrees_of_freedom\"]))\n",
"\n",
" element_vector=toPoint-fromPoint\n",
"\n",
"\n",
" # find rotated mass and stifness matrices\n",
" tau = rotation_matrix(element_vector, x_axis,y_axis,z_axis)\n",
"\n",
" # i1=parse(Int,fromNode[\"id\"][2:end])\n",
" # i2=parse(Int,toNode[\"id\"][2:end])\n",
"\n",
" # global_displacements=[X[(i1)*6+1] X[(i1)*6+2] X[(i1)*6+3] X[(i1)*6+4] X[(i1)*6+5] X[(i1)*6+6] X[(i2)*6+1] X[(i2)*6+2] X[(i2)*6+3] X[(i2)*6+4] X[(i2)*6+5] X[(i2)*6+6]] # todo change\n",
" global_displacements=[fromNode[\"displacement\"][\"x\"]*15 fromNode[\"displacement\"][\"y\"]*15 fromNode[\"displacement\"][\"z\"]*15 fromNode[\"angle\"][\"x\"] fromNode[\"angle\"][\"y\"] fromNode[\"angle\"][\"z\"] toNode[\"displacement\"][\"x\"]*15 toNode[\"displacement\"][\"y\"]*15 toNode[\"displacement\"][\"z\"]*15 toNode[\"angle\"][\"x\"] toNode[\"angle\"][\"y\"] toNode[\"angle\"][\"z\"]] # todo change\n",
"\n",
" # nodal displacement\n",
"\n",
" q=tau*transpose(global_displacements)\n",
" # println(q)\n",
" # calculate the strain and stresses\n",
" strain =(q[7]-q[1])/norm(element_vector)\n",
" E = edge[\"stiffness\"]# youngs modulus\n",
" E=2000\n",
" stress=E.*strain\n",
" edge[\"stress\"]=stress\n",
" if stress>max11\n",
" max11=stress\n",
" end\n",
" if stress<min11\n",
" min11=stress\n",
" end\n",
" # println(element)\n",
" # println(stress)\n",
" end\n",
"\n",
"\n",
"\n",
" setup[\"viz\"][\"minStress\"]=min11\n",
" setup[\"viz\"][\"maxStress\"]=max11\n",
" return stresses\n",
" end\n",
" \n",
" function initialize(setup)\n",
" nodes = setup[\"nodes\"]\n",
" ndofs = length(nodes)*6\n",
" \n",
" i=0\n",
" for node in nodes\n",
" dg=[]\n",
" for ii in 0:5\n",
" append!(dg,i+ii) \n",
" end\n",
" i+=6\n",
" node[\"degrees_of_freedom\"]=dg\n",
" end\n",
" end\n",
" \n",
"\n",
" #######################################################\n",
" function solveFea(setup)\n",
" // # determine the global matrices\n",
" initialize(setup)\n",
" \n",
" M,K,F,U,ind,X=get_matrices(setup)\n",
" \n",
" #println(M)\n",
" #println(K)\n",
" #println(F)\n",
" \n",
"# X = deepcopy(F)\n",
" iiind=F.!=0\n",
" \n",
"# X[X.!=0] .= -0.01*5/100*latticeSize\n",
"# print(\"displacementtt: \")\n",
"# println(X)\n",
"\n",
"# X=inv(K)*F\n",
" F=inv(K)*X\n",
" \n",
" Load=sum(F[iiind])\n",
"# print(\"load: \")\n",
"# println(F)\n",
" \n",
"# X=inv(K)*F\n",
" \n",
"# U[setdiff(1:end, ind)]=X\n",
"\n",
" updateDisplacement(setup, U)\n",
"\n",
" # determine the stresses in each element\n",
" stresses=get_stresses(setup)\n",
" end\n",
" #######################################################\n",
" displacementFEA=[]\n",
" Load=0\n",
" topNodesIndices=[]\n",
" solveFea(setup)\n",
" return displacementFEA,Load,topNodesIndices\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 621,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"5-element Array{Int64,1}:\n",
" 1\n",
" 2\n",
" 3\n",
" 5\n",
" 7"
]
},
"execution_count": 621,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A=[1,2,3,0,0,5,7,0]\n",
"iiind=A.!=0\n",
"A[iiind]"
]
}
],
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