Nonsmooth Model for Plastic Limit Analysis and Its Smoothing Algorithm

LI Jian-yu; PAN Shao-hua; LI Xing-si

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Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(8): 940-946

LI Jian-yu, PAN Shao-hua, LI Xing-si. Nonsmooth Model for Plastic Limit Analysis and Its Smoothing Algorithm[J]. Applied Mathematics and Mechanics, 2006, 27(8): 940-946.

Citation:

LI Jian-yu, PAN Shao-hua, LI Xing-si. Nonsmooth Model for Plastic Limit Analysis and Its Smoothing Algorithm[J]. Applied Mathematics and Mechanics, 2006, 27(8): 940-946.

Citation:

LI Jian-yu, PAN Shao-hua, LI Xing-si. Nonsmooth Model for Plastic Limit Analysis and Its Smoothing Algorithm[J]. Applied Mathematics and Mechanics, 2006, 27(8): 940-946.

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Nonsmooth Model for Plastic Limit Analysis and Its Smoothing Algorithm

1.
State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, P. R. China;

Received Date: 2005-02-16
Rev Recd Date: 2006-03-18
Publish Date: 2006-08-15

Abstract

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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References(12)

References

[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
[9]	Chen C H,Mangasarian O L.Smoothing methods for convex linear inequalities and linear complementarity problems[J].Mathematical Programming,1995,71(1):51—69.
[10]	Rockafellar R T.Convex Analysis[M].Princeton N J:Princeton University Press,1970,392—393.
[11]	钱伟长.变分法及有限元[M].北京:科学出版社，1981,591—599.
[12]	Byrd R H, Lu P,Nocedal J,et al.A limited memory algorithm for bound constrained Optimization[J].SIAM Journal on Scientific Computing,1995,16(5):1190—1208. doi: 10.1137/0916069
[13]	Christiansen E.Computation of limit loads[J].International Journal for Numerical Methods in Engineering,1981,17(10):1547—1570. doi: 10.1002/nme.1620171009