Metavoxel GPU Validation 4.ipynb

    "\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",
    "    \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": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "getYoungsModulus (generic function with 1 method)"
      ]
     },
     "execution_count": 138,
     "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": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "getSetup (generic function with 1 method)"
      ]
     },
     "execution_count": 139,
     "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": 140,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "54\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "144"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "latticeSize=2\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": 141,
   "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": 141,
     "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": 142,
   "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}(\"exaggeration\"=>2000,\"speed\"=>3,\"showDispl…\n",
       "  \"viz\"          => Dict{String,Any}(\"colorMap\"=>0,\"exaggeration\"=>10000,\"color…\n",
       "  \"edges\"        => Any[Dict{String,Any}(\"source\"=>0,\"area\"=>1,\"density\"=>0.028…\n",
       "  \"ndofs\"        => 324"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "145396"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "latticeSize=3\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": 146,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dt: 0.007294855212986816\n",
      "first timestep took 0.000645101 seconds\n",
      "ran latticeSize 3 with 144 voxels and 432 edges for 6000 time steps took 2.0397974 seconds\n",
      "Load=-900.0\n",
      "stress=0.017777777777777778\n",
      "Load=-900.0\n",
      "stress=0.017777777777777778\n",
      "EsFEA:[0.0, 1.3631163779051199, 1.4928557096014121, 0.0, 0.0]\n",
      "Es:[0.0, 1.3636389591522067, 1.4821324986526747, 0.0, 0.0]\n",
      "FEA displacement= -3.161875031059339,converged displacement= -3.199251807603066\n"
     ]
    },
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       "<g clip-path=\"url(#clip3900)\">\n",
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       "<g clip-path=\"url(#clip3900)\">\n",
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      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "setup=getSetup(latticeSize)\n",
    "numTimeSteps=6000\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": 147,
   "metadata": {},
   "outputs": [
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