文档介绍：Chapter 3 solution of plane problems in rectangular coordinates 第三章平面问题直角坐标解答
solution by polynomials
多项式解答
徐汉忠第一版2000/7
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弹性力学第三章
Review: Inverse method 逆解法
Select  satisfying patibility equation
设定,并满足相容方程4 =0 ()
find the ponents by 由下式求出应力分量
x=2/y2-Xx y= 2/x2-Yy xy=-2/xy ()
find the surface ponents by
由下式对给定坐标的物体求出面力分量
(lx+m yx)s = X (my+lxy)s =Y ()
Identify the problem which the  selected can solve确定所设定的能解决的问题
徐汉忠第一版2000/7
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弹性力学第三章
A. =a+bx+cy , X=0, Y=0
It satisfies patibility equation 4 =0
find the ponents by x=2/y2=0 y= 2/x2=0 xy=-2/xy=0
find the surface ponents by (lx+m yx)s=X=0 (my+lxy)s =Y=0
a linear stress function corresponds to the case of no surface forces and no stress .
The superposition of a linear function to the stress function for any problem does not affect the stresses.
徐汉忠第一版2000/7
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弹性力学第三章
A. =a+bx+cy , X=0 Y=0
满足相容方程4 =0
由下式求出应力分量x=2/y2=0 y= 2/x2=0 xy=-2/xy=0
由下式对给定坐标的物体求出面力分量(lx+m yx)s=X=0 (my+lxy)s =Y=0
确定所设定的能解决的问题为:任意物体无体力,无面力,无应力。
应力函数加或减一个线性项不影响应力。
徐汉忠第一版2000/7
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弹性力学第三章
B. =ax2 , X=0, Y=0
It satisfies patibility equation 4 =0
find the ponents by x=2/y2=0 y= 2/x2=2a xy=-2/xy=0
for a rectangular plate with its edges parallel to the coordinate axes, find the surface ponents by (lx+m yx)s=X
(my+lxy)s =Y
the stress function =ax2 can solve the problem of uniform tension (a>0) or pression (a<0) of a rectangular plate in y direction. P37 (a)
徐汉忠第一版2000/7
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弹性力学第三章
B. =ax2 , X=0, Y=0
满足相容方程4 =0
由下式求出应力分量x=2/y2=0 y= 2/x2=2a xy=-2/xy=0
对和坐标轴平行的矩形板求出面力分量知=ax2 能解决矩形板y向受均匀拉力(a>0)或均匀压力(a<0)的问题。P37 (a)
徐汉忠第一版2000/7
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弹性力学第三章
徐汉忠第一版2000/7
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弹性力学第三章
C. =cy2 , X=0, Y=0
It satisfies patibility equation 4 =0
find the ponents by x=2/y2=2c y= 2/x2=0 xy=-2/xy=0
for a rectangular plate with its edges parallel to the coordinate axes, find the surface ponen