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// Amira Abdel-Rahman
// (c) Massachusetts Institute of Technology 2019
////////////3D bar-truss fea/////////////////////
function solveFea(){
// # determine the global matrices
var M,K,F;
var t0 = performance.now();
[M,K,F]=getMatrices(setup);
var t1 = performance.now();
console.log("Call to getMatrices " + (t1 - t0) + " milliseconds.");
// M.print();
// K.print();
// F.print();
// M, K, F = get_matrices(properties)
// [Q,R]=tf.linalg.qr(K);
t0 = performance.now();
var displacements=lusolve(K.arraySync(), F.arraySync(),false);
t1 = performance.now();
console.log("Call to invert " + (t1 - t0) + " milliseconds.");
// console.log(displacements);
updateDisplacement(displacements);
var X= tf.tensor(displacements);//change later to more effecient solver
console.log("Displacements:");
X.print();
// # determine the stresses in each element
var stresses = get_stresses(setup, displacements);
updateStresses(stresses.arraySync());
console.log("Stresses:");
stresses.print();
// console.log(setup);
// console.log(setup);
//TODO CHECK SINGULARITY AND DOFSC
}
function getMatrices(setup){
var M = tf.zeros([setup.ndofs,setup.ndofs]);
var K = tf.zeros([setup.ndofs,setup.ndofs]);
for(var ii=0;ii<setup.edges.length;ii++){
var element=setup.edges[ii];
var fromPoint= toTf3D(setup.nodes[element.source].position);
var toPoint= toTf3D(setup.nodes[element.target].position);
var dofs=[];
dofs.push(...setup.nodes[element.source].degrees_of_freedom);
dofs.push(...setup.nodes[element.target].degrees_of_freedom);
var element_vector=tf.sub (toPoint,fromPoint);
var length = element_vector.norm();
var rho = tf.scalar(element.density);
var A = element.area;
var E = element.stiffness;// youngs modulus
var G=1.0;//todo shear_modulus
var ixx = 1.0;//todo section ixx
var iyy = 1.0;//todo section.iyy//
var l0=length.dataSync();
var j=1.0;//todo check
var l02 = l0 * l0;
var l03 = l0 * l0 * l0;
// var Cm = tf.div(tf.mul(rho,tf.mul(area,length)),tf.scalar(6.0));//rho * area * length /6.0
// var Ck= tf.div(tf.mul(E,area),length);//E * area / length
// Cm.print();
// var m = tf.tensor ([[2,1],[1,2]]) ;
// var k = tf.tensor([[1,-1],[-1,1]]);
k = tf.tensor([
[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]
]);
var x_axis=tf.tensor ([1,0,0]);
var y_axis=tf.tensor ([0,1,0]);
var z_axis=tf.tensor ([0,0,1]);
// # find rotated mass and stifness matrices
var tau = rotation_matrix(element_vector, x_axis,y_axis,z_axis);
// var m_r=tf.matMul(tau,tf.matMul(m,tau) ,true ,false) //tau.T.dot(m).dot(tau)
var k_r=tf.matMul(tau,tf.matMul(k,tau) ,true ,false) //tau.T.dot(k).dot(tau)
// # change from element to global coordinate
// var B=tf.zeros([12,setup.ndofs]);
var B=[];
for(var i=0;i<12;i++){
B.push([]);
for(var j=0;j<setup.ndofs;j++){
B[i].push(0.0);
}
}
for(var i=0;i<12;i++){
B[i][dofs[i]]=1.0;
}
B=tf.tensor(B);
// B.print();
// var M_rG=tf.matMul(B,tf.matMul(m_r,B) ,true ,false) //B.T.dot(m_r).dot(B)
var K_rG=tf.matMul(B,tf.matMul(k_r,B) ,true ,false) //B.T.dot(k_r).dot(B)
// M=tf.add(M,tf.mul(Cm, M_rG)); //+= Cm * M_rG
// K=tf.add(K,tf.mul(Ck, K_rG)); //+= Ck * K_rG
K=tf.add(K, K_rG); //+= Ck * K_rG
}
// # construct the force vector
var F=[];
for(var i=0;i<setup.nodes.length;i++){
F.push(setup.nodes[i].force.x);
F.push(setup.nodes[i].force.y);
F.push(setup.nodes[i].force.z);
F.push(0.0);
F.push(0.0);
F.push(0.0);
}
F=tf.tensor(F);
// # remove the restrained dofs
var remove_indices=[];
for(var i=0;i<setup.nodes.length;i++){
for(var j=0;j<setup.nodes[i].degrees_of_freedom.length;j++){
if(setup.nodes[i].restrained_degrees_of_freedom[j]){
remove_indices.push(setup.nodes[i].degrees_of_freedom[j]);
}
}
}
// M.print();
// K.print();
// F.print();
for(var i=0;i<2;i++){
M=tf_delete(M,remove_indices,i);
K=tf_delete(K,remove_indices,i);
}
F=tf_delete(F,remove_indices,0);
// M.print()
// K.print()
// F.print()
return [ M,K,F ];
}
function get_stresses(setup,X){
// # find the stresses in each member
var stresses=[];
for(var ii=0;ii<setup.edges.length;ii++){
var element=setup.edges[ii];
// # find the element geometry
var fromPoint= toTf3D(setup.nodes[element.source].position);
var toPoint= toTf3D(setup.nodes[element.target].position);
var dofs=[];
dofs.push(...setup.nodes[element.source].degrees_of_freedom);
dofs.push(...setup.nodes[element.target].degrees_of_freedom);
var element_vector=tf.sub (toPoint,fromPoint);
var x_axis=tf.tensor ([1,0,0]);
var y_axis=tf.tensor ([0,1,0]);
var z_axis=tf.tensor ([0,0,1]);
// # find rotated mass and stifness matrices
var tau = rotation_matrix(element_vector, x_axis,y_axis,z_axis);
var global_displacements=tf.tensor([setup.nodes[element.source].displacement.x,setup.nodes[element.source].displacement.y,setup.nodes[element.source].displacement.z,
setup.nodes[element.source].angle.x,setup.nodes[element.source].angle.y,setup.nodes[element.source].angle.z,
setup.nodes[element.target].displacement.x,setup.nodes[element.target].displacement.y,setup.nodes[element.target].displacement.z,
setup.nodes[element.target].angle.x,setup.nodes[element.target].angle.y,setup.nodes[element.target].angle.z]) //# todo change
// # nodal displacement
var q=tf.dot(tau,global_displacements);
// console.log("q");
// q.print();
var q=tf.unstack(q);
// console.log(q);
var strain=tf.div(tf.sub(q[6],q[0]),element_vector.norm()); //todo check smarter way to do it
//stress x axis
var E = tf.scalar(element.stiffness);
var stress=tf.mul(E,strain);
stresses.push(stress);
}
return tf.stack(stresses,0);
}
///////utils////////
function rotation_matrix(element_vector,x_axis, y_axis, z_axis){ //todo check again
var L=element_vector.norm().arraySync();
element_vector=element_vector.arraySync();
// x1 = self.iNode.X
// x2 = self.jNode.X
// y1 = self.iNode.Y
// y2 = self.jNode.Y
// z1 = self.iNode.Z
// z2 = self.jNode.Z
// L = self.L
// # Calculate direction cosines for the transformation matrix
var l = (element_vector[0])/L;
var m = (element_vector[1])/L;
var n = (element_vector[2])/L;
var D = ( l**2+ m **2+n**2)**0.5;
// console.log(D);
// if l == 0 and m == 0 and n > 0:
// dirCos = matrix([[0, 0, 1],
// [0, 1, 0],
// [-1, 0, 0]])
// elif l == 0 and m == 0 and n < 0:
// dirCos = matrix([[0, 0, -1],
// [0, 1, 0],
// [1, 0, 0]])
// else:
// dirCos = matrix([[l, m, n],
// [-m/D, l/D, 0],
// [-l*n/D, -m*n/D, D]])
var transMatrix=tf.tensor([
[ 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]
]);
// # Build the transformation matrix
// transMatrix = zeros((12, 12))
// transMatrix[0:3, 0:3] = dirCos
// transMatrix[3:6, 3:6] = dirCos
// transMatrix[6:9, 6:9] = dirCos
// transMatrix[9:12, 9:12] = dirCos
return transMatrix;
}
function direction_cosine(vec1, vec2){
return tf.div(tf.dot(vec1,vec2) ,tf.mul( vec1.norm() , vec2.norm()));
}