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MultiRod.m
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477 lines (400 loc) · 18.1 KB
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classdef MultiRod
properties
n_nodes
n_edges
n_faces
n_edges_rod_only
n_edges_shell_only
n_edges_dof
n_DOF
Nodes
Edges
face_shell_edges
face_nodes_shell
edge_combos
q0
q
u
refLen
voronoiRefLen
voronoiArea
faceA
MassMat
massVec
Fg
EI1
EI2
EA
GJ
ks
kb
nu_shell
rho
h
r0
tangent
a1
a2
m1
m2
undef_refTwist
refTwist
face_edges
sign_faces
init_ts
init_fs
init_cs
init_xis
fixed_nodes
fixed_edges
fixedDOF
freeDOF
end
methods
function obj = MultiRod(geom, material, twist_angles, Nodes, Edges, rod_edges, shell_edges, rod_shell_joint_edges, rod_shell_joint_total_edges, face_nodes, sign_faces, face_edges, face_shell_edges, sim_params, environment)
% Declare local vars to store important parameters
obj.r0 = geom.rod_r0;
obj.h = geom.shell_h;
obj.rho = material.density;
Y_rod = material.youngs_rod;
Y_shell = material.youngs_shell;
nu_rod = material.poisson_rod;
obj.nu_shell = material.poisson_shell;
% Node and edge counts
obj.n_nodes = size(Nodes,1);
n_rod_edges = size(rod_edges,1);
n_shell_edges = size(shell_edges,1);
n_edges_rod_shell_joint_total = size(rod_shell_joint_total_edges,1);
obj.n_edges = size(Edges,1);
obj.n_edges_dof = n_rod_edges + n_edges_rod_shell_joint_total;
obj.n_faces = size(face_nodes,1);
obj.n_edges_rod_only = n_rod_edges;
obj.n_edges_shell_only = n_shell_edges;
% Store nodes and edges
obj.Nodes = Nodes;
obj.Edges = Edges;
obj.face_nodes_shell = face_nodes;
obj.face_shell_edges = face_shell_edges;
% DOF vector
obj.n_DOF = 3*obj.n_nodes + n_rod_edges + n_edges_rod_shell_joint_total;
q0 = zeros(obj.n_DOF,1);
q_nodes = reshape(Nodes', [numel(Nodes), 1]);
q0(1:3*obj.n_nodes) = q_nodes;
q0(3*obj.n_nodes + 1 : 3*obj.n_nodes + obj.n_edges_dof) = twist_angles;
if sim_params.use_midedge
obj.n_DOF = obj.n_DOF + n_shell_edges;
xi_s = zeros(n_shell_edges, 1);
q0 = [q0; xi_s];
end
obj.q0 = q0;
obj.q = q0;
% Reference lengths and areas
obj.refLen = obj.calculateRefLen();
obj.voronoiRefLen = obj.calculateVoronoiRefLen();
obj.voronoiArea = obj.calculateVoronoiArea();
obj.faceA = obj.calculateFaceArea();
% Mass matrix
[obj.MassMat, obj.massVec] = obj.calculateMassMatrix(geom);
% Weight
if isfield(environment, 'g') && ~isempty(environment.g)
obj.Fg = getGravityForce(obj,environment);
else
obj.Fg = [];
end
% Stiffnesses
G_rod = Y_rod / (2 * (1 + nu_rod));
if isfield(geom, 'Axs') && ~isempty(geom.Axs)
obj.EA = Y_rod * geom.Axs;
else
obj.EA = Y_rod * pi * obj.r0^2;
end
if isfield(geom, 'Ixs1') && ~isempty(geom.Ixs1) && isfield(geom, 'Ixs2') && ~isempty(geom.Ixs2)
obj.EI1 = Y_rod * geom.Ixs1;
obj.EI2 = Y_rod * geom.Ixs2;
else
obj.EI1 = Y_rod * pi * obj.r0^4 / 4;
obj.EI2 = Y_rod * pi * obj.r0^4 / 4;
end
if isfield(geom, 'Jxs') && ~isempty(geom.Jxs)
obj.GJ = G_rod * geom.Jxs;
else
obj.GJ = G_rod * pi * obj.r0^4 / 2;
end
obj.ks = sqrt(3)/2 * Y_shell * obj.h * obj.refLen;
obj.kb = 2/sqrt(3) * Y_shell * (obj.h^3) / 12;
if sim_params.use_midedge
if(obj.nu_shell==1)
error("poisson's ratio 1 for shell is not supported since (1-nu^2) terms appears in the denominator of the stiffness leading to inifinity")
else
obj.kb = Y_shell * obj.h^3 / (24 * (1 - obj.nu_shell^2));
% obj.kb = Y_shell * obj.h^3 / (24 * (1 + obj.nu_shell)); % if nu = 1
obj.ks = 2*(Y_shell * obj.h/(1-obj.nu_shell^2)) * obj.refLen;
% obj.ks = sqrt(3)/2 * Y_shell * obj.h * obj.refLen; % if nu = 1
end
end
% Other properties
% obj.edge_combos = obj.construct_possible_edge_combos([rod_edges; rod_shell_joint_edges]);
obj.edge_combos = obj.construct_edge_pairs_with_min_gap([rod_edges; rod_shell_joint_edges], 3);
obj.u = zeros(size(obj.q0));
obj.a1 = zeros(obj.n_edges_dof, 3);
obj.a2 = zeros(obj.n_edges_dof, 3);
obj.m1 = zeros(obj.n_edges_dof, 3);
obj.m2 = zeros(obj.n_edges_dof, 3);
% Store additional shell face info if using midedge
if sim_params.use_midedge
obj.face_edges = face_edges;
obj.sign_faces = sign_faces;
[obj.init_ts, obj.init_fs, obj.init_cs, obj.init_xis] = obj.initialCurvatureMidedge(); % calculate initial values for c,t,f,xi
else
obj.face_edges = [];
obj.sign_faces = [];
obj.init_ts = [];
obj.init_cs = [];
obj.init_fs = [];
obj.init_xis = [];
end
end
function refLen = calculateRefLen(obj)
refLen = zeros(obj.n_edges, 1);
for c = 1:obj.n_edges
node1_index = obj.Edges(c, 1);
node2_index = obj.Edges(c, 2);
refLen(c) = norm(obj.Nodes(node2_index, :) - obj.Nodes(node1_index, :));
end
end
function voronoiRefLen = calculateVoronoiRefLen(obj)
voronoiRefLen = zeros(obj.n_nodes, 1);
for c = 1:obj.n_edges_dof
node1_index = obj.Edges(c, 1);
node2_index = obj.Edges(c, 2);
voronoiRefLen(node1_index) = voronoiRefLen(node1_index) + 0.5 * obj.refLen(c);
voronoiRefLen(node2_index) = voronoiRefLen(node2_index) + 0.5 * obj.refLen(c);
end
end
function voronoiArea = calculateVoronoiArea(obj)
voronoiArea = zeros(obj.n_nodes, 1);
for c = 1:size(obj.face_nodes_shell, 1)
node1ind = obj.face_nodes_shell(c, 1);
node2ind = obj.face_nodes_shell(c, 2);
node3ind = obj.face_nodes_shell(c, 3);
face_A = 0.5 * norm(cross(obj.Nodes(node2ind, :) - obj.Nodes(node1ind, :), obj.Nodes(node3ind, :) - obj.Nodes(node2ind, :)));
voronoiArea(node1ind) = voronoiArea(node1ind) + face_A / 3;
voronoiArea(node2ind) = voronoiArea(node2ind) + face_A / 3;
voronoiArea(node3ind) = voronoiArea(node3ind) + face_A / 3;
end
end
function faceA = calculateFaceArea(obj)
faceA = zeros(obj.n_faces, 1);
for c = 1:size(obj.face_nodes_shell, 1)
node1ind = obj.face_nodes_shell(c, 1);
node2ind = obj.face_nodes_shell(c, 2);
node3ind = obj.face_nodes_shell(c, 3);
faceA(c) = 0.5 * norm(cross(obj.Nodes(node2ind, :) - obj.Nodes(node1ind, :), obj.Nodes(node3ind, :) - obj.Nodes(node2ind, :)));
end
end
function [massMat, massVec] = calculateMassMatrix(obj, geom)
massVec = zeros(obj.n_DOF, 1);
% Shell faces
for i = 1:obj.n_faces
node1ind = obj.face_nodes_shell(i, 1);
node2ind = obj.face_nodes_shell(i, 2);
node3ind = obj.face_nodes_shell(i, 3);
face_A = 0.5 * norm(cross((obj.Nodes(node2ind, :) - obj.Nodes(node1ind, :)), (obj.Nodes(node3ind, :) - obj.Nodes(node2ind, :))));
Mface = obj.rho * face_A * obj.h;
massVec(mapNodetoDOF(node1ind)) = massVec(mapNodetoDOF(node1ind)) + Mface / 3 * ones(3, 1);
massVec(mapNodetoDOF(node2ind)) = massVec(mapNodetoDOF(node2ind)) + Mface / 3 * ones(3, 1);
massVec(mapNodetoDOF(node3ind)) = massVec(mapNodetoDOF(node3ind)) + Mface / 3 * ones(3, 1);
end
% Rod nodes
for cNode = 1:obj.n_nodes
if isfield(geom, 'Axs') && ~isempty(geom.Axs)
dm = obj.voronoiRefLen(cNode) * geom.Axs * obj.rho;
else
dm = obj.voronoiRefLen(cNode) * pi * obj.r0^2 * obj.rho;
end
ind = mapNodetoDOF(cNode);
massVec(ind) = massVec(ind) + dm * ones(3, 1);
end
% Rod edges
for cEdge = 1:obj.n_edges_dof
if isfield(geom, 'Axs') && ~isempty(geom.Axs)
dm = obj.refLen(cEdge) * geom.Axs * obj.rho;
edge_mass = dm * geom.Jxs/geom.Axs; % I = m*(J/A)
else
dm = obj.refLen(cEdge) * pi * obj.r0^2 * obj.rho;
edge_mass = dm * obj.r0^2 / 2; % I = 1/2 m r^2
end
ind = mapEdgetoDOF(cEdge, obj.n_nodes);
massVec(ind) = edge_mass;
end
massMat = diag(massVec);
end
function [init_ts, init_fs, init_cs, init_xis] = initialCurvatureMidedge(obj)
init_ts = zeros(3,3,obj.n_faces);
init_fs = zeros(3,obj.n_faces);
init_cs = zeros(3,obj.n_faces);
init_xis = zeros(3,obj.n_faces);
edge_common_to = zeros(obj.n_edges,1);
n_avg = zeros(3,obj.n_edges);
tau_0 = zeros(3,obj.n_edges);
e = zeros(3,obj.n_edges);
for c = 1:obj.n_faces
node1_number = obj.face_nodes_shell(c,1);
node2_number = obj.face_nodes_shell(c,2);
node3_number = obj.face_nodes_shell(c,3);
node1_position = obj.q(3*node1_number-2:3*node1_number);
node2_position = obj.q(3*node2_number-2:3*node2_number);
node3_position = obj.q(3*node3_number-2:3*node3_number);
% face normal calculation:
face_normal = cross(([node2_position]-[node1_position]),([node3_position]-[node1_position]));
face_unit_normal = face_normal .* 1/norm(face_normal);
% face edge map
edge1_idx = obj.face_edges(c,1);
edge2_idx = obj.face_edges(c,2);
edge3_idx = obj.face_edges(c,3);
edge_common_to(edge1_idx) = edge_common_to(edge1_idx)+1;
edge_common_to(edge2_idx) = edge_common_to(edge2_idx)+1;
edge_common_to(edge3_idx) = edge_common_to(edge3_idx)+1;
n_avg(:,edge1_idx) = n_avg(:,edge1_idx) + face_unit_normal;
n_avg(:,edge1_idx) = n_avg(:,edge1_idx)/ norm(n_avg(:,edge1_idx));
n_avg(:,edge2_idx) = n_avg(:,edge2_idx) + face_unit_normal;
n_avg(:,edge2_idx) = n_avg(:,edge2_idx)/ norm(n_avg(:,edge2_idx));
n_avg(:,edge3_idx) = n_avg(:,edge3_idx) + face_unit_normal;
n_avg(:,edge3_idx) = n_avg(:,edge3_idx)/ norm(n_avg(:,edge3_idx));
% ensure that edge is common to only 2 triangle faces (to avoid bugs)
assert(edge_common_to(edge1_idx)<3, "edge is common to more than 2 faces!");
assert(edge_common_to(edge2_idx)<3, "edge is common to more than 2 faces!");
assert(edge_common_to(edge3_idx)<3, "edge is common to more than 2 faces!");
end
for i=1:obj.n_edges
e(:,i) = obj.q(3*obj.Edges(i,2)-2:3*obj.Edges(i,2)) - obj.q(3*obj.Edges(i,1)-2:3*obj.Edges(i,1));
tau_0(:,i) = cross(e(:,i), n_avg(:,i));
tau_0(:,i) = tau_0(:,i)/norm(tau_0(:,i));
end
for i=1:obj.n_faces
Face_i_nodes = obj.face_nodes_shell(i,:);
Face_i_edges = obj.face_edges(i,:);
p_is = zeros(3,3);
xi_is = zeros(3,1);
tau_0_is = zeros(3,3);
for j=1:3
p_is(:,j) = obj.q(3*Face_i_nodes(j)-2:3*Face_i_nodes(j));
xi_is(j) = obj.q(3*obj.n_nodes + Face_i_edges(j));
tau_0_is(:,j) = tau_0(:,Face_i_edges(j));
end
s_is = obj.sign_faces(i,:);
init_xis(:,i) = xi_is;
[init_t, init_f, init_c] = obj.calculateInit_t_f_c_midedge(p_is, tau_0_is, s_is);
init_ts(:,:,i) = init_t;
init_fs (:,i) = init_f';
init_cs (:,i) = init_c';
end
end
end
methods (Static)
function [ts, fs, cs] = calculateInit_t_f_c_midedge(p_s, tau0_s, s_s)
pi = p_s(:,1);
pj = p_s(:,2);
pk = p_s(:,3);
tau_i0 = s_s(1)*tau0_s(:,1);
tau_j0 = s_s(2)*tau0_s(:,2);
tau_k0 = s_s(3)*tau0_s(:,3);
% edges
vi = pk - pj ; % 3*1 edge i vector
vj = pi - pk ; % 3*1 edge j vector
vk = pj - pi ; % 3*1 edge k vector
% edge lengths
li = norm(vi);
lj = norm(vj);
lk = norm(vk);
% triangle face normal
normal = cross(vk, vi);
A = norm(normal)/2; % area of triangular face
unit_norm = normal/norm(normal); % normalized triangle face normal vector
% t_i's (tangent (perpendicular to edge, in plane of triangle) of length =
% |vi|)
t_i = cross(vi,unit_norm);
t_j = cross(vj,unit_norm);
t_k = cross(vk,unit_norm);
% c_i's : scalars
c_i = 1/( A*li*dot((t_i/norm(t_i)),tau_i0) );
c_j = 1/( A*lj*dot((t_j/norm(t_j)),tau_j0) );
c_k = 1/( A*lk*dot((t_k/norm(t_k)),tau_k0) );
% f_i's : scalars
f_i = dot(unit_norm,tau_i0);
f_j = dot(unit_norm,tau_j0);
f_k = dot(unit_norm,tau_k0);
fs = [f_i, f_j, f_k]; % (1*3)
ts = [t_i , t_j , t_k]; % t_i are columns
cs = [c_i, c_j, c_k]; % (1*3)
end
function [edge_combos, edge_combos_idx] = construct_possible_edge_combos(edges)
% Construct list of all possible edge combinations without duplicates (excluding adjacent edges)
% Inputs:
% edges:- n_edges*2 array of edge node indices
% Outputs:
% edge_combos:- no. of possible edge_combos for collision*4 (node indices xi, xi+1, xj, xj+1)
% edge_combos_idx:- no. of possible edge_combos for collision*2 (edge indices ei, ej)
% ___________________________________________________________________________________________
no_of_edges = size(edges, 1);
edge_combos_idx = [0, 0]; % jugaad for using ismember
for i=1:no_of_edges
for j=1:no_of_edges
temp_combo = [i , j];
% check if edge is itself or adjacent
if(edges(i,1) == edges(j,1) || edges(i,1) == edges(j,2) || edges(i,2) == edges(j,1) || edges(i,2) == edges(j,2) )
% not valid combination
elseif (ismember(temp_combo, edge_combos_idx, "rows") || ismember([j,i], edge_combos_idx,"rows"))
% already counted combination
else
edge_combos_idx = [edge_combos_idx; temp_combo];
end
end
end
edge_combos_idx = edge_combos_idx(2:end,:); % remove the jugaad for using ismember
edge_combos = zeros(size(edge_combos_idx,1),4);
for k = 1:size(edge_combos_idx,1)
edge_combos(k,:) = [edges(edge_combos_idx(k,1),:), edges(edge_combos_idx(k,2),:)];
end
end
function [edge_combos, edge_combos_idx] = construct_edge_pairs_with_min_gap(edges, k)
%CONSTRUCT_EDGE_PAIRS_WITH_MIN_GAP
% Construct all edge pairs (ei, ej) such that:
% - ei < ej (no duplicates / orderless pairs)
% - ej - ei >= k ("k-apart" in edge index)
%
% This is for the consecutive-edge case like:
% edges = [1 2; 2 3; 3 4; ...]
%
% Inputs:
% edges : N x 2 array of edge node indices
% k : minimum index separation between edges (integer >= 1)
%
% Outputs:
% edge_combos_idx : M x 2 array of edge index pairs [ei, ej]
% edge_combos : M x 4 array of node index pairs
% [edges(ei,1), edges(ei,2), edges(ej,1), edges(ej,2)]
no_of_edges = size(edges, 1);
if no_of_edges <= 1
edge_combos_idx = zeros(0, 2);
edge_combos = zeros(0, 4);
return;
end
% All upper-triangular index pairs (ei < ej)
[I, J] = find(triu(true(no_of_edges), 1)); % k=1 on diag offset gives ei<ej
% Apply k-apart condition on indices
mask = (J - I) >= k;
I_valid = I(mask);
J_valid = J(mask);
if isempty(I_valid)
edge_combos_idx = zeros(0, 2);
edge_combos = zeros(0, 4);
return;
end
% Edge index pairs
edge_combos_idx = [I_valid, J_valid];
% Corresponding node index pairs: [xi, x_{i+1}, xj, x_{j+1}]
edge_combos = [edges(I_valid, :), edges(J_valid, :)];
end
end
end