ElemStiffElasMatBbVecP1.m

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function [Kg]=ElemStiffElasMatBbVecP1(q,me,areas,lambda,mu)
% function [Kg]=ElemStiffElasMatBbVecP1(q,me,areas,lambda,mu)
% Global Computation of the element stiffness elasticity matrix.
% Block numbering
%
% Parameters:
%  q: Array of vertices coordinates, `2\times\nq` array. <br/>
%  `{\q}(\il,j)` is the
%  `\il`-th coordinate of the `j`-th vertex, `\il\in\{1,2\}` and
%  `j\in\ENS{1}{\nq}`
%  me: Connectivity array, `3\times\nme` array. <br/>
%  `\me(\jl,k)` is the storage index of the
%  `\jl`-th  vertex of the `k`-th triangle in the array `\q`, `\jl\in\{1,2,3\}` and
%       `k\in{\ENS{1}{\nme}}`.
%  areas: Array of areas, `1\times\nme` array. areas(k) is the area of the `k`-th triangle.
%  lambda: the first Lame coefficient in Hooke's law
%  mu: the second Lame coefficient in Hooke's law
%
%
% Return values:
%  Kg: `36\times \nme` global element stiffness elasticity matrix
%
% Copyright:
%   See \ref license
order=1;
ndf=(order+1)*(order+2)/2;
dim=2*ndf;
ndf2=dim*dim;
u=q(:,me(2,:))-q(:,me(3,:));
G1=[u(2,:);-u(1,:)];
u=q(:,me(3,:))-q(:,me(1,:));
G2=[u(2,:);-u(1,:)];
u=q(:,me(1,:))-q(:,me(2,:));
G3=[u(2,:);-u(1,:)];
clear u
coef=ones(2,1)*(0.5./sqrt(areas));
G1=G1.*coef;
G2=G2.*coef;
G3=G3.*coef;
clear coef
Kg=zeros(ndf2,size(me,2));
Kg(1,:)=(lambda + 2.*mu).*G1(1,:).^2 + mu.*G1(2,:).^2;
Kg(2,:)=(lambda + 2.*mu).*G1(1,:).*G2(1,:) + mu.*G1(2,:).*G2(2,:);
Kg(3,:)=(lambda + 2.*mu).*G1(1,:).*G3(1,:) + mu.*G1(2,:).*G3(2,:);
Kg(4,:)=lambda.*G1(1,:).*G1(2,:) + mu.*G1(1,:).*G1(2,:);
Kg(5,:)=lambda.*G1(1,:).*G2(2,:) + mu.*G1(2,:).*G2(1,:);
Kg(6,:)=lambda.*G1(1,:).*G3(2,:) + mu.*G1(2,:).*G3(1,:);
Kg(8,:)=(lambda + 2.*mu).*G2(1,:).^2 + mu.*G2(2,:).^2;
Kg(9,:)=(lambda + 2.*mu).*G2(1,:).*G3(1,:) + mu.*G2(2,:).*G3(2,:);
Kg(10,:)=lambda.*G1(2,:).*G2(1,:) + mu.*G1(1,:).*G2(2,:);
Kg(11,:)=lambda.*G2(1,:).*G2(2,:) + mu.*G2(1,:).*G2(2,:);
Kg(12,:)=lambda.*G2(1,:).*G3(2,:) + mu.*G2(2,:).*G3(1,:);
Kg(15,:)=(lambda + 2.*mu).*G3(1,:).^2 + mu.*G3(2,:).^2;
Kg(16,:)=lambda.*G1(2,:).*G3(1,:) + mu.*G1(1,:).*G3(2,:);
Kg(17,:)=lambda.*G2(2,:).*G3(1,:) + mu.*G2(1,:).*G3(2,:);
Kg(18,:)=lambda.*G3(1,:).*G3(2,:) + mu.*G3(1,:).*G3(2,:);
Kg(22,:)=(lambda + 2.*mu).*G1(2,:).^2 + mu.*G1(1,:).^2;
Kg(23,:)=(lambda + 2.*mu).*G1(2,:).*G2(2,:) + mu.*G1(1,:).*G2(1,:);
Kg(24,:)=(lambda + 2.*mu).*G1(2,:).*G3(2,:) + mu.*G1(1,:).*G3(1,:);
Kg(29,:)=(lambda + 2.*mu).*G2(2,:).^2 + mu.*G2(1,:).^2;
Kg(30,:)=(lambda + 2.*mu).*G2(2,:).*G3(2,:) + mu.*G2(1,:).*G3(1,:);
Kg(36,:)=(lambda + 2.*mu).*G3(2,:).^2 + mu.*G3(1,:).^2;
Kg([7, 13, 14, 19, 20, 21, 25, 26, 27, 28, 31, 32, 33, 34, 35],:)=Kg([2, 3, 9, 4, 10, 16, 5, 11, 17, 23, 6, 12, 18, 24, 30],:);