| OptFEM2DP1 Toolbox 1.2b4 Matlab/Octave Optimized P1-Lagrange Finite Element Method in 2D

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base/ElemStiffElasMatBa2DP1.m
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    00001 function Ke=ElemStiffElasMatBa2DP1(ql,area,C)
    00002 % function [Elem]=ElemStiffElasMatBa2DP1(ql,area,C)
    00003 %  Computation of the element stiffness elasticity matrix for
    00004 %  `P_1`-Lagrange method.
    00005 %  The method for numbering the degrees of freedom is local alternate numbering (classical method)
    00006 %
    00007 %  Hooke's matrix :
    00008 %  C=[L + 2*M       L       0]
    00009 %    [      L L + 2*M       0]
    00010 %    [      0       0       M]
    00011 %  Numbering of local points in reference element is :
    00012 %    P=[(0, 0), (1, 0), (0, 1)]
    00013 %
    00014 % Parameters:
    00015 %  ql           : array of coordinates of the vertices of the triangle, 2-by-3 matrix (double)
    00016 %  area         : triangle area (double)
    00017 %  C            : Hooke's matrix (3-by-3 double)
    00018 %
    00019 % Return values:
    00020 %  Elem         : element stiffness elasticity matrix, 6-by-6 matrix (double)
    00021 %
    00022 % Example:
    00023 %  @verbatim
    00024 %    ql=[0 1 0;0 0 1];
    00025 %    area=1/2.;
    00026 %    lambda=1.; mu=1.;
    00027 %    C=[lambda+2*mu, lambda, 0;lambda, lambda + 2*mu, 0;0, 0, mu];
    00028 %    Elem=ElemStiffElasMatBa2DP1(ql,area,C);
    00029 %  @endverbatim
    00030 % Copyright:
    00031 %   See \ref license
    00032 u=ql(:,2)-ql(:,3);
    00033 v=ql(:,3)-ql(:,1);
    00034 w=ql(:,1)-ql(:,2);
    00035 % Matrice des déformations (x par 2*area)
    00036 B=[u(2),0,v(2),0,w(2),0; ...
    00037    0,-u(1),0,-v(1),0,-w(1); ...
    00038    -u(1),u(2),-v(1),v(2),-w(1),w(2)];
    00039 Ke=B'*C*B/(4*area);

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