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*
A Finite Element——Mathematical Programming Method for Elastoplastic Problems Based on the Principle of Virtual Work
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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.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.
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Key words:
- elastoplasticity /
- principle of virtual work /
- mathematical programming /
- FEM
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[1] Maier,G.,A quadratic programming approach to certain classes of nonlinear structural problems,Mechanica,3(1968),121-130. [2] Kaneko,I.,Complete solutions for a class of elastoplastic structures,Comput.Struct.Appl.Mech.Eng.,21(1980),193-209. [3] Zhong Wan-xie and Zhang Rou-lei,The parametric variational principle for elastoplasticity,ACTA Mechanica Sinica,4,2,(1988). [4] 张柔雷、钟万据,参变量最小势能原理的有限元参数二次规划解,计算结构力学及其应用,4.1(1987). [5] 沙德松、孙焕纯,虚功原理的变分不等方程及在物理非线性问题中的应用,计算结构力学及其应用,7(2)(1990). [6] 王仁等著.《塑性力学基础》,科学出版社(1987). [7] Reklaitis,G.V.,et al.,Engineering Optimization,Method and Applications,John Wiley & Sons,Inc.(1983). -
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