felp2dt3.m

大量的有限元法求解偏微分方程的实例程序

function [k]=felp2dt3(x1,y1,x2,y2,x3,y3)

%-------------------------------------------------------------------
%  Purpose:
%     element matrix for two-dimensional Laplace's equation
%     using three-node linear triangular element
%
%  Synopsis:
%     [k]=felp2dt3(x1,y1,x2,y2,x3,y3) 
%
%  Variable Description:
%     k - element stiffness matrix (size of 3x3)   
%     x1, y1 - x and y coordinate values of the first node of element
%     x2, y2 - x and y coordinate values of the second node of element
%     x3, y3 - x and y coordinate values of the third node of element
%-------------------------------------------------------------------

% element matrix

 A=0.5*(x2*y3+x1*y2+x3*y1-x2*y1-x1*y3-x3*y2); % area of the triangule
 k(1,1)=((x3-x2)^2+(y2-y3)^2)/(4*A);
 k(1,2)=((x3-x2)*(x1-x3)+(y2-y3)*(y3-y1))/(4*A);
 k(1,3)=((x3-x2)*(x2-x1)+(y2-y3)*(y1-y2))/(4*A);
 k(2,1)=k(1,2);
 k(2,2)=((x1-x3)^2+(y3-y1)^2)/(4*A);
 k(2,3)=((x1-x3)*(x2-x1)+(y3-y1)*(y1-y2))/(4*A);
 k(3,1)=k(1,3);
 k(3,2)=k(2,3);
 k(3,3)=((x2-x1)^2+(y1-y2)^2)/(4*A);