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

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base/ElemStiffElasMatP1Bb.m
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    00001 function [Elem]=ElemStiffElasMatP1Bb(q1,q2,q3,area,lambda,mu)
    00002 % function [Elem]=ElemStiffElasMatP1Bb(q1,q2,q3,area,lambda,mu)
    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 block numbering
    00006 %
    00007 %  The elasticity matrix obtained from Hooke's law is given by:
    00008 %  ``C=\left\{\begin{array}[ccc]
    00009 %     &\lambda+2\mu  &\lambda &0\\
    00010 %     &\lambda  &\lambda+2\mu  &0\\
    00011 %     &0 &0  &\mu
    00012 %   \end{array}
    00013 %   \right.``
    00014 %
    00015
    00016 %  C=[L + 2*M       L       0]
    00017 %    [      L L + 2*M       0]
    00018 %    [      0       0       M]
    00019 %  Numbering of local points in reference element is :
    00020 %    P=[(0, 0), (1, 0), (0, 1)]
    00021 %
    00022 % Parameters:
    00023 %  q1           : array of coordinates of the first point of the triangle
    00024 %  q2           : array of coordinates of the second point of the triangle
    00025 %  q3           : array of coordinates of the third point of the triangle
    00026 %  area         : triangle area
    00027 %  lambda       : first  Lame coefficient in Hooke's law
    00028 %  mu           : second Lame coefficient in Hooke's law
    00029 %
    00030 % Return values:
    00031 %  Elem         : element stiffness elasticity matrix, 6-by-6 matrix
    00032 %
    00033 % Example:
    00034 %    @verbatim
    00035 %    q1=[0;0];q2=[1;0];q3=[0;1];
    00036 %    area=1/2.;
    00037 %    lambda=1.; mu=1.;
    00038 %    KElem=ElemStiffElasMatP1Bb(q1,q2,q3,area,lambda,mu);
    00039 %    @endverbatim
    00040
    00041 % Copyright:
    00042 %   See \ref license
    00043
    00044 u=q2-q3;
    00045 v=q3-q1;
    00046 w=q1-q2;
    00047 % Matrice de Hooke
    00048 C=[lambda+2*mu,lambda,0;lambda,lambda+2*mu,0;0,0,mu];
    00049 % Matrice des déformations (x par 2*area)
    00050 B=[u(2),v(2),w(2),0,0,0; ...
    00051    0,0,0,-u(1),-v(1),-w(1); ...
    00052    -u(1),-v(1),-w(1),u(2),v(2),w(2)];
    00053 Elem=B'*C*B/(4*area);

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