刚塑性材料塑性动力学问题中的一般方程和通解

本文是文1～2]的继续。本文讨论了塑性流动理论中的理想刚塑性材料的动力学问题。在引入Dirac-Pauli表象的复变函数理论后,我们可以得到用流函数和理论比例系数表示的一组(两个)所谓"一般方程"。本文还证明了塑性动力学问题的时间发展方程既非耗散型的,又非弥散型的,而其本征方程却是以应力增量的偏张量为本征函数,以理论比例系数为本征值的定态Schr?dinger方程。于是,我们使非线性塑性动力学问题成为线性定态Schr?dinger方程的求解,由此可以得到刚塑性材料塑性动力学问题的通解。

On the General Equation and the General Solution in Problems for Plastodynamics with Rigid-Plastic Material

This work is the continuation of the discussion of refs.1-2].We discuss the dynamics problems of ideal rigid-plastic material in the flow theory of plasticity in this paper.From introduction of the theory of functions of complex variable under Dirac-Pauli representation we can obtain a group of the so-called "general equations"(i.e.have two scalar equations) expressed by the stream function and the theoretical ratio.In this paper we also testify that the equation of evolution for time in plastodynamics problems is neither dissipative nor disperive,and the eigen-equation in plastodynamics problems is a stationary Schr?dinger equation,in which we take partial tensor of stress-increment as eigenfunctions and take theoretical ratio as eigenvalues.Thus,We turn nonlinear plastodynamics problems into the solution of linear stationary Schrbdinger equation,and from this we can obtain the general solution of plastodynamics problems with rigid-plastic material.