理想塑性问题中的一般方程、双调和方程和本征方程
On the General Equations, Double Hormonic Equation and Eigen-Equation in the Problems of Ideal Plasticity
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摘要: 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。Abstract: 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.
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