解Drucker-Prager塑性问题的二阶锥互补法

基于经典弹塑性理论中多数屈服准则具有凸锥数学结构的事实,将在大规模计算中更具潜力的锥规划法引入弹塑性分析。考虑到弹塑性流动理论有关联与非关联之分,本文提出利用锥型互补法求解弹塑性问题。具体以Drucker-Prager弹塑性模型为例,首先利用最大塑性功耗散原理和圆锥对偶理论等工具,建立了弹塑性本构方程的等价二阶锥互补模型;然后,基于参变量变分原理和有限元技术,建立了弹塑性增量分析的二阶锥线性互补模型;最后,利用一类半光滑Newton算法求解。数值算例表明了本文方法的有效性。

A second order cone complementarity approach for Drucker-Prager plasticity problems

In this paper we present a new approach for solving Drucker-Prager elastoplastic problems as second order cone complementarity problems (SOCCPs).Firstly,the classical Drucker-Prager elastoplastic constitutive equations with associative or non-associative flow rules are equivalently reformulated as second order cone complementarity conditions.Secondly,by employing parametric variational principle and the finite element method,we obtain a standard SOCCP formulation for the Drucker-Prager plasticity analysis,which can be solved efficiently by a class of semismooth Newton algorithm developed in the field of mathematical programming.Numerical results of a classical plasticity benchmark problem confirm the effectiveness and robustness of the proposal approach.