塑性极限分析的不可微模型及其光滑化算法

李建宇; 潘少华; 李兴斯

塑性极限分析的不可微模型及其光滑化算法

大连理工大学工业装备结构分析国家重点实验室,大连 116023;2.华南理工大学应用数学系,广州 510641

基金项目: 国家自然科学基金资助项目(10572031;10332010)

详细信息

作者简介:
李建宇(1978- ),男,呼和浩特人,博士研究生(Tel:+86-411-84706349;E-mail:jianyuli@student.dlut.edu.cn);李兴斯(联系人.Tel:+86-411-84706349;Fax:+86-411-84708769;E-mail:lixs@dlut.edu.cn).

中图分类号: O344.5；O221.2
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出版历程
- 收稿日期: 2005-02-16
- 修回日期: 2006-03-18
- 刊出日期: 2006-08-15

Nonsmooth Model for Plastic Limit Analysis and Its Smoothing Algorithm

State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, P. R. China;

摘要

摘要: 藉助于凸规划的Lagrange对偶理论，建立了Mises屈服条件下理想刚塑性材料Hill最大塑性功原理的对偶问题，并据此建立了极限分析的一个不可微凸规划模型．该模型不仅避免了对屈服条件的线性化，而且其离散化形式为线性约束下Euclid模之和的极小化问题．针对Euclid模的不可微性，提出理想刚塑性体极限分析的一种光滑化算法．通过计算平面应力和平面应变问题的极限荷载因子和相应的坍塌机构，验证了算法的有效性．
- 塑性极限分析 /
- 对偶 /
- 不可微优化 /
- 光滑化
Abstract: By means of Lagrange duality theory of the convex program,a dual problem of Hill's maximum plastic work principle under Mises.yielding condition was derived and whereby a non-differentiable convex optimization model for the limit analysis were developed.With this model,it is not necessary to linearize the yielding condition and its discrete form becomes a minimization problem of the sum of Euclidean norms subjected to linear constraints.Aimed at resolving the non-differentiability of Euclidean norms,a smoothing algorithm for the limit analysis of perfect-plastic continuum media was prposed.Its efficiency was demonstrated by computing the limit load factor and the collapse state for some plane stress and plain strain problems.
- plastic limit analysis /
- duality /
- non-smooth optimization /
- smoothing method

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参考文献(12)

[1]	Dorn W S,Greenberg H J. Linear programming and plastic limit analysis of structures[J].Quart Appl Math Soc,1957,15(1):155—167.
[2]	Maier G,Munro J. Mathematical programming applications to engineering plastic analysis[J].Applied Mechanics Reviews,1982,35(12):1631—1643.
[3]	Charnes A, Lemke C,Zienkiewicz O C. Virtual work, linear programming and plastic limit analysis[J].Proceedings of the Royal Society, London,1959,251(1):110—116. doi: 10.1098/rspa.1959.0094
[4]	Overton M L. Numerical solution of a model problem from collapse load analysis[A].In:Lions J L,Glowinski R,Eds.Computing Methods in Applied Sciences and Engineering VI[C].Amsterdam:North-Holland,1984,421—437.
[5]	张丕辛，陆明万，黄克智.极限分析的无搜索数学规划算法[J].力学学报，1991，23(4)：433—441.[KG*2]. Liu Y H,Cen Z Z,Xu B Y.A numerical method for plastic limit analysis of 3-D structures[J].Internat J Solids Structures,1995,32(12):1645—1658. doi: 10.1016/0020-7683(94)00230-T
[7]	Andersen E D, Christiansen E,Conn A R,et al.An efficient primal-dual interior-point method for minimizing a sum of Euclidean Norms[J].SIAM Journal on Scientific Computing,2000,22(1):243—262. doi: 10.1137/S1064827598343954
[8]	Li X S.An entropy-based aggregate method for minimax optimization[J].Engineering Optimization,1992,18(2):277—285. doi: 10.1080/03052159208941026
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塑性极限分析的不可微模型及其光滑化算法

作者简介:
李建宇(1978- ),男,呼和浩特人,博士研究生(Tel:+86-411-84706349;E-mail:jianyuli@student.dlut.edu.cn);李兴斯(联系人.Tel:+86-411-84706349;Fax:+86-411-84708769;E-mail:lixs@dlut.edu.cn).

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Nonsmooth Model for Plastic Limit Analysis and Its Smoothing Algorithm

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塑性极限分析的不可微模型及其光滑化算法

作者简介: 李建宇(1978- ),男,呼和浩特人,博士研究生(Tel:+86-411-84706349;E-mail:jianyuli@student.dlut.edu.cn);李兴斯(联系人.Tel:+86-411-84706349;Fax:+86-411-84708769;E-mail:lixs@dlut.edu.cn).

计量

出版历程

Nonsmooth Model for Plastic Limit Analysis and Its Smoothing Algorithm

计量

出版历程

目录

作者简介:
李建宇(1978- ),男,呼和浩特人,博士研究生(Tel:+86-411-84706349;E-mail:jianyuli@student.dlut.edu.cn);李兴斯(联系人.Tel:+86-411-84706349;Fax:+86-411-84708769;E-mail:lixs@dlut.edu.cn).