feglqd1.m

《The finite element method using Matlab》源程序及电子书 用Matlab进行有限元分析

function [point1,weight1]=feglqd1(ngl)

%-------------------------------------------------------------------
%  Purpose:
%     determine the integration points and weighting coefficients
%     of Gauss-Legendre quadrature for one-dimensional integration
%
%  Synopsis:
%     [point1,weight1]=feglqd1(ngl) 
%
%  Variable Description:
%     ngl - number of integration points
%     point1 - vector containing integration points   
%     weight1 - vector containing weighting coefficients 
%-------------------------------------------------------------------

%  initialization

   point1=zeros(ngl,1);
   weight1=zeros(ngl,1);

%  find corresponding integration points and weights

 if ngl==1           % 1-point quadrature rule
    point1(1)=0.0;
    weight1(1)=2.0;

 elseif ngl==2       % 2-point quadrature rule
    point1(1)=-0.577350269189626;
    point1(2)=-point1(1);
    weight1(1)=1.0;
    weight1(2)=weight1(1);

 elseif ngl==3       % 3-point quadrature rule
    point1(1)=-0.774596669241483;
    point1(2)=0.0;
    point1(3)=-point1(1);
    weight1(1)=0.555555555555556;
    weight1(2)=0.888888888888889;
    weight1(3)=weight1(1);

 elseif ngl==4       % 4-point quadrature rule
    point1(1)=-0.861136311594053;
    point1(2)=-0.339981043584856;
    point1(3)=-point1(2);
    point1(4)=-point1(1);
    weight1(1)=0.347854845137454;
    weight1(2)=0.652145154862546;
    weight1(3)=weight1(2);
    weight1(4)=weight1(1);
 
else                 % 5-point quadrature rule
    point1(1)=-0.906179845938664;
    point1(2)=-0.538469310105683;
    point1(3)=0.0;
    point1(4)=-point1(2);
    point1(5)=-point1(1);
    weight1(1)=0.236926885056189;
    weight1(2)=0.478628670499366;
    weight1(3)=0.568888888888889;
    weight1(4)=weight1(2);
    weight1(5)=weight1(1);

end