轴对称平面应力大塑性变形问题的解析解

轴对称平面应力的大塑性变形问题是一个复杂的非线性问题；既是物理非线性，又是几何非线性．本文从塑性力学的基本方程出发，采用增量理论导出了该问题的速度方程──一个二阶非线性偏微分方程．通过变量代换进一步给出了该非线性偏微分方程的解析解．并根据具体的边界条件对变形区内应力、应变的分布以及变形高度及其随变形程度变化的规律进行了分析．在小变形条件下，增量理论与全量理论的结果完全一致．本文的结果为分析环形薄板复合成形规律和成形高度提供了理论基础

Analytical Solution to Large Plastic Deformation of Axisymmetric Plain Stress Problems

The large deformation problem of axisymmetric plain stress is a complecate non-linear problem-both physically and geometrically. Based on the plastic mechanic equations and incremental theory,this paper derived the velocity equation of the problem,i. e. a two order nonlinear partial differential equation. The analytical solution to the nonlinear equation is also given by the replacement of variations. The stress,strain distribution and deformation height and their changing regularity with the deformation were investigated as well.The relationship between stress,strain or height and deformation are analysed. The results of increamental theory are completely coincident with those of integral theory in small plastic deformation conditions. The results given in this paper provide a theoretical basis for analysing the combined deformation of cicular sheet.