梯度塑性理论的计算方法与应用

杜修力; 侯世伟; 路德春; 梁国平; 安超

梯度塑性理论的计算方法与应用 English Version

1.北京工业大学城市与工程安全减灾教育部重点实验室，北京100124; 2. 中国科学院数学与系统科学研究院飞箭软件有限公司，北京100098; 3. 北京大学地球与空间科学学院地球物理系，北京 100871

基金项目: 国家重点基础研究发展计划(973 计划）项目(2011CB013600)；教育部博士点基金项目(20101103110011)；国家高技术研究发展计划(863 计划）(2009AA044501)

详细信息

作者简介:
杜修力 (1962 – ),男，四川广安人，博士，教授，博士生导师，主要从事水工抗震、抗爆等方面的研究。

中图分类号: TU411
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出版历程
- 发布日期: 2012-06-19

Application of gradient plastic theory based on FEPG platform

1. Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, China; 2. Beijing FEGEN Software Co., Ltd., Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100098, China; 3. School of Earth and Space Science, Peking University , Beijing 100871, China

摘要

摘要: 基于有限元自动生成系统 (FEPG) ，开发使用梯度塑性理论的有限元程序，用于解决应变软化后的网格依赖性问题。提出带阻尼因子的算法，联立求解位移方程和屈服面方程，既可同时解得位移和塑性乘子，又避免了广泛使用的应力返回算法中的应力拉回运算。在 D-P 准则中引入软化模量和材料内部特征长度，使本构模型能够考虑软化和梯度效应。在软化问题求解上使用阻尼牛顿法，算例结果表明，带阻尼因子的算法能够计算应变软化问题，以有限元弱形式表达的梯度塑性理论，使用一阶单元就能够得到合理的结果，在一定网格范围能够得到稳定的应力应变曲线。
- 梯度塑性理论 /
- 算法 /
- 阻尼牛顿法 /
- 应变软化 /
- 网格依赖性
Abstract: Based on the FEPG platform, the finite element program using gradient plastic theory is developed to solve mesh dependence after strain softening. A algorithm with damp factor is proposed, which can solve the equation of displacement and yield surface simultaneously. The algorithm can not only get displacement and plastic multiplier together, but also avoid the stress haul back calculation in stress return algorithm widely used in finite element solution procedures. The softening modulus and the internal character length are introduced into D-P yield function, and the constitutive model can consider strain softening and gradient effect. The damp Newton algorithm is used to calculate softening problems. The results of a case study show that the algorithm with damp factor can be used to solve softening problems, the gradient plastic theory described by finite element weak form has no requirement of continuity, and appropriate outcome can be obtained by the first-order element, thus the mesh dependence of simulation is basically solved.
- gradient plastic theory /
- μ-λ algorithm /
- damp Newton method /
- strain softening /
- mesh dependence

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参考文献(15)

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