29 lines
1.3 KiB
Matlab
29 lines
1.3 KiB
Matlab
%%%%%%%%%%% 一阶六面体单元形参程序 %%%%%%%%%%%
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% N局部坐标下的形函数矩阵
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% NDerivative形函数矩阵对全局坐标的导数
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% JacobiDET雅可比行列式
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% GaussPoint高斯点坐标
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% ElementNodeCoordinate单元节点坐标（8*3，每一行代表一个节点的坐标）
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function [N,NDerivative,JacobiDET] = ShapeFunction(GaussPoint,ElementNodeCoordinate)
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%等参元坐标 每一列代表一个点的坐标
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ParentNodes=[-1 1 1 -1 -1 1 1 -1;
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-1 -1 1 1 -1 -1 1 1;
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-1 -1 -1 -1 1 1 1 1];
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N=zeros(8,1); %初始化形函数矩阵8*1
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ParentNDerivative=zeros(3,8);%初始化形函数对局部坐标的导数矩阵3*8
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%计算形函数及形函数对局部坐标导数
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for I=1:8
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XPoint = ParentNodes(1,I);
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YPoint = ParentNodes(2,I);
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ZPoint = ParentNodes(3,I);
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ShapePart = [1+GaussPoint(1)*XPoint 1+GaussPoint(2)*YPoint 1+GaussPoint(3)*ZPoint]; %定义中间变量
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N(I) = 0.125*ShapePart(1)*ShapePart(2)*ShapePart(3);%1*8
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ParentNDerivative(1,I) = 0.125*XPoint*ShapePart(2)*ShapePart(3);
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ParentNDerivative(2,I) = 0.125*YPoint*ShapePart(1)*ShapePart(3);
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ParentNDerivative(3,I) = 0.125*ZPoint*ShapePart(1)*ShapePart(2);
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end
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Jacobi = ParentNDerivative*ElementNodeCoordinate;%计算雅可比矩阵
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JacobiDET = det(Jacobi);%计算雅可比行列式
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JacobiINV=inv(Jacobi);%对雅可比行列式求逆
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NDerivative=JacobiINV*ParentNDerivative;%利用雅可比行列式的逆计算形函数对结构坐标的导数3*8
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end |