定常围压作用时平面应变理想塑性体Mises屈伏条件的精确解
The Exact Solutions of von Mises Yielding Criterion for Ideally Plastic Body under Uniform Pressure in Case of Plane Strain
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摘要: 把应力函数引入平面问题的Mises屈状条件后那个二阶非线性偏微分方程分解为两个二阶线性偏微分方程,用柯西积分公式求出这两个方程右端的已知函数,然后解这个方程,由此定出弹塑性区域的分界线和求出塑性区内的各应力分量,给出一个例题说明本文方法的应用.Abstract: This problem is solved by dividing the quadratic yielding criterion into two linear partial differential equations. With the help of Cauchy's integral, these two linear equations can be easily solved. An example is given to show the calculation of the stress components in the plastic domain and the determination of equation of the boundary line between the plastic and elastic domains.
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[1] Prager,William and Hodge,Philip G,The Theory of Perfectly Plastic Solids,(1951). [2] 钱伟长、叶开沅,《弹性力学》,科学出版社,(1956),207. [3] 徐芝纶.《弹性理论》,人民教育出版社,(1960),92-93. -
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