刚塑性广义变分不等原理及其在平面应变分析中的应用

Generalized Variational Inequalities in Rigid Plasticity and Its Application in Plane Strain Analysis

首先利用Lagrangian乘子法,从势能角度出发构造了考虑摩擦效应这一能导致变分不等形式的广义能量泛函,把一般的有条件的变分原理化为无条件的变分原理来唯一确定,得出了各Lagrangian乘子所代表的物理意义,建立了刚塑性理论中的Coulomb摩擦约束的广义变分不等原理。而后基于退化的摩擦约束广义变分等式原理,对长矩形板镦粗进行了塑性加工工步分析。所得结果与经典上限法结果相吻合。

In this paper, the generalized variational inequality principle in rigid plasticity subjected to Coulomb friction was established. By adopting Lagrangian multiplier and constructing a generalized energy functional that could result in variational inequality, the constraint conditions were converted to non-conditional restrictions and the physical representations of Lagrangian multipliers were determined. Then the plastic process analyses on rectangular plate upsetting were proceeded on the basis of the degenerated generalized variational principle, which showed the results are consistent with those of classical Upper Bound Method.