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- 1970-1-1
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发表于 2011-12-6 18:56:03
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显示全部楼层
来自 北京
我推了一下平面矩形单元的刚度矩阵,好复杂,结果如下:
K=4ab*
[ (e*(h/2 - 1/2)*(1/(4*b) - x/(4*a*b))^2)/(h^2 - 1) - (e*(1/(4*a) - y/(4*a*b))^2)/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1) - (e*h*(1/(4*a) - y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1), (e*(1/(4*a) - y/(4*a*b))^2)/(h^2 - 1) + (e*(h/2 - 1/2)*(1/(4*b) - x/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), - (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1) - (e*h*(1/(4*a) - y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*(1/(4*a) - y/(4*a*b))*(1/(4*a) + y/(4*a*b)))/(h^2 - 1) - (e*(h/2 - 1/2)*(1/(4*b) - x/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*h*(1/(4*a) - y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) - (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1), - (e*(h/2 - 1/2)*(1/(4*b) - x/(4*a*b))^2)/(h^2 - 1) - (e*(1/(4*a) - y/(4*a*b))*(1/(4*a) + y/(4*a*b)))/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1) + (e*h*(1/(4*a) - y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1)]
[ (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1) - (e*h*(1/(4*a) - y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))^2)/(h^2 - 1) - (e*(1/(4*b) - x/(4*a*b))^2)/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) + (e*h*(1/(4*a) - y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1), - (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))^2)/(h^2 - 1) - (e*(1/(4*b) - x/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*h*(1/(4*a) + y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1) - (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*(1/(4*b) - x/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) - (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*a) + y/(4*a*b)))/(h^2 - 1), - (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1) - (e*h*(1/(4*a) + y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1), (e*(1/(4*b) - x/(4*a*b))^2)/(h^2 - 1) + (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*a) + y/(4*a*b)))/(h^2 - 1)]
[ (e*(1/(4*a) - y/(4*a*b))^2)/(h^2 - 1) + (e*(h/2 - 1/2)*(1/(4*b) - x/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) + (e*h*(1/(4*a) - y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*b) + x/(4*a*b))^2)/(h^2 - 1) - (e*(1/(4*a) - y/(4*a*b))^2)/(h^2 - 1), (e*h*(1/(4*a) - y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) - (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), - (e*(h/2 - 1/2)*(1/(4*b) + x/(4*a*b))^2)/(h^2 - 1) - (e*(1/(4*a) - y/(4*a*b))*(1/(4*a) + y/(4*a*b)))/(h^2 - 1), - (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) - (e*h*(1/(4*a) - y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*(1/(4*a) - y/(4*a*b))*(1/(4*a) + y/(4*a*b)))/(h^2 - 1) - (e*(h/2 - 1/2)*(1/(4*b) - x/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) - (e*h*(1/(4*a) - y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1)]
[ - (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1) - (e*h*(1/(4*a) - y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), - (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))^2)/(h^2 - 1) - (e*(1/(4*b) - x/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*h*(1/(4*a) - y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) - (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))^2)/(h^2 - 1) - (e*(1/(4*b) + x/(4*a*b))^2)/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) + (e*h*(1/(4*a) + y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*(1/(4*b) + x/(4*a*b))^2)/(h^2 - 1) + (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*a) + y/(4*a*b)))/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1) - (e*h*(1/(4*a) + y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*(1/(4*b) - x/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) - (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*a) + y/(4*a*b)))/(h^2 - 1)]
[ (e*(1/(4*a) - y/(4*a*b))*(1/(4*a) + y/(4*a*b)))/(h^2 - 1) - (e*(h/2 - 1/2)*(1/(4*b) - x/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*h*(1/(4*a) + y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1) - (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), - (e*(h/2 - 1/2)*(1/(4*b) + x/(4*a*b))^2)/(h^2 - 1) - (e*(1/(4*a) - y/(4*a*b))*(1/(4*a) + y/(4*a*b)))/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) + (e*h*(1/(4*a) + y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*b) + x/(4*a*b))^2)/(h^2 - 1) - (e*(1/(4*a) + y/(4*a*b))^2)/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) - (e*h*(1/(4*a) + y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*(1/(4*a) + y/(4*a*b))^2)/(h^2 - 1) + (e*(h/2 - 1/2)*(1/(4*b) - x/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), - (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) - (e*h*(1/(4*a) + y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1)]
[ (e*h*(1/(4*a) - y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) - (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1), (e*(1/(4*b) - x/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) - (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*a) + y/(4*a*b)))/(h^2 - 1), - (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) - (e*h*(1/(4*a) - y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*(1/(4*b) + x/(4*a*b))^2)/(h^2 - 1) + (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*a) + y/(4*a*b)))/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) - (e*h*(1/(4*a) + y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))^2)/(h^2 - 1) - (e*(1/(4*b) + x/(4*a*b))^2)/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1) + (e*h*(1/(4*a) + y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), - (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))^2)/(h^2 - 1) - (e*(1/(4*b) - x/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1)]
[ - (e*(h/2 - 1/2)*(1/(4*b) - x/(4*a*b))^2)/(h^2 - 1) - (e*(1/(4*a) - y/(4*a*b))*(1/(4*a) + y/(4*a*b)))/(h^2 - 1), - (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1) - (e*h*(1/(4*a) + y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1), (e*(1/(4*a) - y/(4*a*b))*(1/(4*a) + y/(4*a*b)))/(h^2 - 1) - (e*(h/2 - 1/2)*(1/(4*b) - x/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1) - (e*h*(1/(4*a) + y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*(1/(4*a) + y/(4*a*b))^2)/(h^2 - 1) + (e*(h/2 - 1/2)*(1/(4*b) - x/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1) + (e*h*(1/(4*a) + y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*b) - x/(4*a*b))^2)/(h^2 - 1) - (e*(1/(4*a) + y/(4*a*b))^2)/(h^2 - 1), (e*h*(1/(4*a) + y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1) - (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1)]
[ (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1) + (e*h*(1/(4*a) - y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1), (e*(1/(4*b) - x/(4*a*b))^2)/(h^2 - 1) + (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*a) + y/(4*a*b)))/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) - (e*h*(1/(4*a) - y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1), (e*(1/(4*b) - x/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) - (e*(h/2 - 1/2)*(1/(4*a) - y/(4*a*b))*(1/(4*a) + y/(4*a*b)))/(h^2 - 1), - (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1) - (e*h*(1/(4*a) + y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1), - (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))^2)/(h^2 - 1) - (e*(1/(4*b) - x/(4*a*b))*(1/(4*b) + x/(4*a*b)))/(h^2 - 1), (e*h*(1/(4*a) + y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1) - (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))*(1/(4*b) - x/(4*a*b)))/(h^2 - 1), (e*(h/2 - 1/2)*(1/(4*a) + y/(4*a*b))^2)/(h^2 - 1) - (e*(1/(4*b) - x/(4*a*b))^2)/(h^2 - 1)]
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