46 lines
1.8 KiB
Mathematica
46 lines
1.8 KiB
Mathematica
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function[shapeFunction]=ShapeFunction(xi,eta,ShapeOption)
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% Database of shape functions and their natural derivatives (xi,eta)
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% 'quad1': 4 nodes
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% 'quad2': 8 nodes
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% 'quad3': 9 nodes
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shapeFunction=struct();
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switch ShapeOption
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case 'Q4'
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shapeFunction.fun=1/4*[(1-xi)*(1-eta)
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(1+xi)*(1-eta)
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(1+xi)*(1+eta)
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(1-xi)*(1+eta)];
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shapeFunction.dfun=1/4*[-(1-eta),-(1-xi)
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1-eta,-(1+xi)
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1+eta,1+xi
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-(1+eta),1-xi];
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case 'Q8'
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shapeFunction.fun=[1/4*xi*(1-xi)*eta*(1-eta)
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-1/2*xi*(1-xi)*(1+eta)*(1-eta)
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-1/4*xi*(1-xi)*eta*(1+eta)
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1/2*(1+xi)*(1-xi)*(1+eta)*eta
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1/4*xi*(1+xi)*eta*(1+eta)
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1/2*xi*(1+xi)*(1+eta)*(1-eta)
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-1/4*xi*(1+xi)*eta*(1-eta)
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-1/2*(1+xi)*(1-xi)*(1-eta)*eta];
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shapeFunction.dfun=[...
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1/4*eta*(-1+eta)*(-1+2*xi) 1/4*xi*(-1+xi)*(-1+2*eta)
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-1/2*(1+eta)*(-1+eta)*(-1+2*xi) -xi*(-1+xi)*eta
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1/4*eta*(1+eta)*(-1+2*xi) 1/4*xi*(-1+xi)*(1+2*eta)
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-xi*eta*(1+eta) -1/2*(1+xi)*(-1+xi)*(1+2*eta)
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1/4*eta*(1+eta)*(1+2*xi) 1/4*xi*(1+xi)*(1+2*eta)
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-1/2*(1+eta)*(-1+eta)*(1+2*xi) -xi*(1+xi)*eta
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1/4*eta*(-1+eta)*(1+2*xi) 1/4*xi*(1+xi)*(-1+2*eta)
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-xi*eta*(-1+eta) -1/2*(1+xi)*(-1+xi)*(-1+2*eta)];
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case 'Q9'
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error('work in progress');
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end
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return
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