一种基于虚功原理的求解弹塑性问题的有限元——数学规划法<sup>*</sup>

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一种基于虚功原理的求解弹塑性问题的有限元——数学规划法^*

基金项目: *国家自然科学基金资助项目

摘要: 本文通过将屈服函数按台劳级数展开,并略去二阶以上高阶项,从而将弹塑性本构方程写为线性互补形式这一思路,从熟知的虚功原理出发,结合有限元离散技术,简捷地得到了一种求解弹塑性力学问题的线性互补方法.所得方法可用于满足关联及非关联流动法则的材料.另外,本文还讨论了该方法解的存在性唯一性问题,给出了几个有用的结论.
- 弹塑性 /
- 虚功原理 /
- 数学规划 /
- 有限元
Abstract: By expanding the yielding function according to Taylor series and neglecting the high order terms,the elastoplastic constitutive equation is written in a linear complementary form.Based on this linear complementary form and the principle of virtual work,a finite element-complementary method is derived for elastoplastic problem.This method is available for materials which satisfy either associated or nonassociated flow rule.In addition,the existence and uniqueness of solution for the method are also discussed and some useful conclusions have been reached.
- elastoplasticity /
- principle of virtual work /
- mathematical programming /
- FEM

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