flw3i8e.m

用于在matlab平台上进行有限元分析

function [Ke,fe]=flw3i8e(ex,ey,ez,ep,D,eq)
% Ke=flw3i8e(ex,ey,ez,ep,D)
% [Ke,fe]=flw3i8e(ex,ey,ez,ep,D,eq)
%-------------------------------------------------------------
% PURPOSE
%  Compute element stiffness (conductivity)
%  matrix for 8 node isoparametric field element
%
%  INPUT:  ex = [x1 x2 x3 ... x8] 
%          ey = [y1 y2 y3 ... y8]       element coordinates
%          ez = [z1 z2 z3 ... z8] 
%  
%          ep = [ir]                    Ir: Integration rule
%
%          D  = [kxx kxy kxz;
%                kyx kyy kyz;
%                kzx kzy kzz]           constitutive matrix
%
%          eq                           heat supply per unit 
%                                       volume  
%
%  OUTPUT: Ke :  element 'stiffness' matrix (8 x 8)
%
%          fe :  element load vector (8 x 1)
%-------------------------------------------------------------

% LAST MODIFIED: K Persson    1995-08-24
% Copyright (c)  Division of Structural Mechanics and
%                Department of Solid Mechanics.
%                Lund Institute of Technology
%-------------------------------------------------------------
  ir=ep(1);  ngp=ir*ir*ir;
  if nargin==5; eq=0 ; end


  if ir==2
    g1=0.577350269189626; w1=1;
    gp(:,1)=[-1; 1; 1;-1;-1; 1; 1;-1]*g1; w(:,1)=[ 1; 1; 1; 1; 1; 1; 1; 1]*w1;
    gp(:,2)=[-1;-1; 1; 1;-1;-1; 1; 1]*g1; w(:,2)=[ 1; 1; 1; 1; 1; 1; 1; 1]*w1;
    gp(:,3)=[-1;-1;-1;-1; 1; 1; 1; 1]*g1; w(:,3)=[ 1; 1; 1; 1; 1; 1; 1; 1]*w1;
  elseif ir==3
    g1=0.774596669241483; g2=0.;
    w1=0.555555555555555; w2=0.888888888888888;

    I1=[-1; 0; 1;-1; 0; 1;-1; 0; 1]';
    I2=[ 0;-1; 0; 0; 1; 0; 0; 1; 0]';
    gp(:,1)=[I1 I1 I1]'*g1;
    gp(:,1)=[I2 I2 I2]'*g2+gp(:,1)
    I1=abs(I1);
    I2=abs(I2);
    w(:,1)=[I1 I1 I1]'*w1;
    w(:,1)=[I2 I2 I2]'*w2+w(:,1);
    I1=[-1;-1;-1; 0; 0; 0; 1; 1; 1]';
    I2=[ 0; 0; 0; 1; 1; 1; 0; 0; 0]';
    gp(:,2)=[I1 I1 I1]'*g1;
    gp(:,2)=[I2 I2 I2]'*g2+gp(:,2);
    I1=abs(I1);
    I2=abs(I2);
    w(:,2)=[I1 I1 I1]'*w1;
    w(:,2)=[I2 I2 I2]'*w2+w(:,2);
    I1=[-1;-1;-1;-1;-1;-1;-1;-1;-1]';
    I2=[ 0; 0; 0; 0; 0; 0; 0; 0; 0]';
    I3=abs(I1);
    gp(:,3)=[I1 I2 I3]'*g1;
    gp(:,3)=[I2 I3 I2]'*g2+gp(:,3);
    w(:,3)=[I3 I2 I3]'*w1;
    w(:,3)=[I2 I3 I2]'*w2+w(:,3);
  else
    disp('Used number of integration points not implemented');
    return
  end

  wp=w(:,1).*w(:,2).*w(:,3);


  xsi=gp(:,1);  eta=gp(:,2); zet=gp(:,3);  r2=ngp*3;

  N(:,1)=(1-xsi).*(1-eta).*(1-zet)/8;  N(:,5)=(1-xsi).*(1-eta).*(1+zet)/8;
  N(:,2)=(1+xsi).*(1-eta).*(1-zet)/8;  N(:,6)=(1+xsi).*(1-eta).*(1+zet)/8;
  N(:,3)=(1+xsi).*(1+eta).*(1-zet)/8;  N(:,7)=(1+xsi).*(1+eta).*(1+zet)/8;
  N(:,4)=(1-xsi).*(1+eta).*(1-zet)/8;  N(:,8)=(1-xsi).*(1+eta).*(1+zet)/8;

  dNr(1:3:r2,1)=-(1-eta).*(1-zet);    dNr(1:3:r2,2)= (1-eta).*(1-zet);
  dNr(1:3:r2,3)= (1+eta).*(1-zet);    dNr(1:3:r2,4)=-(1+eta).*(1-zet);
  dNr(1:3:r2,5)=-(1-eta).*(1+zet);    dNr(1:3:r2,6)= (1-eta).*(1+zet);
  dNr(1:3:r2,7)= (1+eta).*(1+zet);    dNr(1:3:r2,8)=-(1+eta).*(1+zet);
  dNr(2:3:r2+1,1)=-(1-xsi).*(1-zet);  dNr(2:3:r2+1,2)=-(1+xsi).*(1-zet);
  dNr(2:3:r2+1,3)= (1+xsi).*(1-zet);  dNr(2:3:r2+1,4)= (1-xsi).*(1-zet);
  dNr(2:3:r2+1,5)=-(1-xsi).*(1+zet);  dNr(2:3:r2+1,6)=-(1+xsi).*(1+zet);
  dNr(2:3:r2+1,7)= (1+xsi).*(1+zet);  dNr(2:3:r2+1,8)= (1-xsi).*(1+zet);
  dNr(3:3:r2+2,1)=-(1-xsi).*(1-eta);  dNr(3:3:r2+2,2)=-(1+xsi).*(1-eta);
  dNr(3:3:r2+2,3)=-(1+xsi).*(1+eta);  dNr(3:3:r2+2,4)=-(1-xsi).*(1+eta);
  dNr(3:3:r2+2,5)= (1-xsi).*(1-eta);  dNr(3:3:r2+2,6)= (1+xsi).*(1-eta);
  dNr(3:3:r2+2,7)= (1+xsi).*(1+eta);  dNr(3:3:r2+2,8)= (1-xsi).*(1+eta);
  dNr=dNr/8.;


  Ke1=zeros(8,8);  fe1=zeros(8,1);
  JT=dNr*[ex;ey;ez]';

  for i=1:ngp
    indx=[ 3*i-2; 3*i-1; 3*i ];
    detJ=det(JT(indx,:));
    if detJ<10*eps
      disp('Jacobideterminanten lika med noll!')
    end
    JTinv=inv(JT(indx,:));
    B=JTinv*dNr(indx,:);
    Ke1=Ke1+B'*D*B*detJ*wp(i);
    fe1=fe1+N(i,:)'*detJ*wp(i);
  end

  Ke=Ke1; fe=fe1*eq;
%--------------------------end--------------------------------