plate-bending/GaussQuadrature.m at master · quaesito/plate-bending · GitHub

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function [Gausspoint,Gaussweight] = GaussQuadrature(order)
%-------------------------------------------------------------------
%  Purpose:
%     Determine the integration points and weighting coefficients
%     of Gauss-Legendre quadrature
%
%  Synopsis:
%     [point,weight]=GaussQuadrature(order)
%
%  Variable Description:
%     order - order of the Gaussian integration
%     Gausspoint - matrix containing integration points
%     Gaussweight - vector containing weighting coefficients
%-------------------------------------------------------------------

switch order
     case 'third'

        % corresponding integration points and weights
        % 3-point quadrature rule
        Gausspoint = [-sqrt(3/5)     -sqrt(3/5);
                       0             -sqrt(3/5);
                       sqrt(3/5)     -sqrt(3/5);
                       -sqrt(3/5)     0;
                       0              0;
                       sqrt(3/5)      0;
                       -sqrt(3/5)     sqrt(3/5);
                       0              sqrt(3/5);
                       sqrt(3/5)      sqrt(3/5)
                       ] ;
        Gaussweight = [25/81 ;40/81 ;25/81 ; 40/81 ; 64/81 ; 40/81 ;  25/81;  40/81; 25/81];

    case 'second'


        % corresponding integration points and weights
        % 2-point quadrature rule
        Gausspoint = [-0.577350269189626 -0.577350269189626;
                       0.577350269189626  -0.577350269189626;
                       0.577350269189626 0.577350269189626;
                       -0.577350269189626  0.577350269189626] ;
        Gaussweight = [1 ;1;1; 1];
    case 'first'

        % Corresponding integration points and weigts
        % 1-point quadrature eule
        Gausspoint = [0 0] ;
        Gaussweight = [4] ;

end