理想塑性问题中的一般方程、双调和方程和本征方程

本文推广了文39]、19]和37]中关于理想塑性轴对称问题的结果,得到了三维理想塑性问题的一般方程。在引入量子电动力学中著名的Pauli矩阵后,本文以不同于文7]的方法,使理想刚塑性材料的平面应变问题,最后归结为求解双调和方程。本文还以应力增量的偏张量为本征函数,导出了理想塑性问题的本征方程,从而使非线性成为线性方程的求解。

On the General Equations,Double Hormonic Equation and Eigen-Equation in the Problems of Ideal Plasticity

In this paper the outcome of axisymmetric problems of ideal plasticity in paper 39], 19] and 37] is directly extended to the three-dimensional problems of ideal plasticity, and get at the general equation in it. The problem of plane strain for material of ideal rigid-plasticity can be solved by putting into double harmonic equation by famous Pauli matrices of quantum electrodynamics different from the method in paper 7]. We lead to the eigen equation in the problems of ideal plasticity, taking partial tenson of stress-increment as eigenfunctions, and we are to transform from nonlinear equations into linear equation in this paper.