| 李建宇,张洪武.解Drucker-Prager塑性问题的二阶锥互补法[J].计算力学学报,2014,31(3):322~327 |
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| 解Drucker-Prager塑性问题的二阶锥互补法 |
| A second order cone complementarity approach for Drucker-Prager plasticity problems |
| 投稿时间：2012-09-19 修订日期：2013-03-14 |
| DOI：10.7511/jslx201403007 |
| 中文关键词: 弹塑性 锥规划 Drucker-Prager塑性 二阶锥互补 |
| 英文关键词:elastoplasticity conic programming Drucker-Prager plasticity second order cone complementarity |
| 基金项目:国家自然科学基金（10902077，11232003，11272234，11172209）资助项目. |
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| 中文摘要: |
| 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。 |
| 英文摘要: |
| 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. |
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