求解摩擦接触问题的一个非内点光滑化算法

张洪武; 何素艳; 李兴斯

求解摩擦接触问题的一个非内点光滑化算法

大连理工大学工业装备结构分析国家重点实验室,大连116024

基金项目: 国家基础性研究专项基金(G1999032805)

详细信息

作者简介:
张洪武(1964- ),男,辽宁大连人,教授,工程力学博士,博士生导师(联系人.Tel:86-411-4706249;E-mail:zhanghw@dlut.edu.cn).

中图分类号: O221；O242.21
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出版历程
- 收稿日期: 2002-06-09
- 修回日期: 2003-09-03
- 刊出日期: 2004-01-15

Non-Interior Smoothing Algorithm for Frictional Contact Problems

State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116024, P. R. China

摘要

摘要: 给出了一个求解三维弹性有摩擦接触问题的新算法，即基于NCP函数的非内点光滑化算法．首先通过参变量变分原理和参数二次规划法，将三维弹性有摩擦接触问题的分析归结为线性互补问题的求解；然后利用NCP函数，将互补问题的求解转换为非光滑方程组的求解；再用凝聚函数对其进行光滑化，最后用NEWTON法解所得到的光滑非线性方程组．方法具有易于理解及实现方便等特点．通过线性互补问题的数值算例及接触问题实例证实了该算法的可靠性与有效性．
- 三维摩擦接触 /
- 参数二次规划法 /
- 线性互补问题 /
- NCP函数 /
- 凝聚函数 /
- 非内点光滑化算法
Abstract: A new algorithm for solving the three-dimensional elastic contact problem with friction is presented.The algorithm is a non-interior smoothing algorithm based on an NCP-function.The parametric variaxional principle and parametric quadratic programming methods wwe applied to the analysis of three-dimensional frictional contact problem.The solution of the contact problem was finally reduced to a linear complementarily problem,which was reformulated as a system of nonsmooth equalions via an NCP-function.A smoothing approximation to the nonsmooth equations was given by the aggregate function.A Newton method was used to solve the resulting smoothing nonlinear equations.The algorithm presented is easy to understand and implement.The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.
- three-dimensional frictional contact problem /
- parametic quadratic programming method /
- linear complementarity problem /
- NCP-function /
- aggregate function /
- non-interior smoothing algorithm

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参考文献(21)

[1]	Demyanov V F,Stavroulakis G E,Polyakova L N.Quasidifferentiability and Nonsmooth Modeling in Mechanics, Engineering and Economics[M].Dordrecht: Kluwer Academic Publishers, 1996.
[2]	Kikuchi N, Oden J T.Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods[M].Philadelphia: SIAM, 1988.
[3]	钟万勰，张洪武，吴承伟.参变量变分原理及其在工程中的应用[M]. 北京: 科学出版社，1997.
[4]	陈国庆，陈万吉，冯恩民. 三维接触问题非线性互补原理及算法[J]. 中国科学(A辑)，1995,25(11):1181—1190.
[5]	李学文，陈万吉. 三维接触问题的非光滑算法[J]. 计算力学学报，2000,17(1):43—49.
[6]	Christensen P W,Klarbring A,Pang J S，et al.Formulation and comparison of algorithms for frictional contact problems[J].International Journal for Numerical Methods in Engineering, 1998,42:145—173. doi: 10.1002/(SICI)1097-0207(19980515)42:1<145::AID-NME358>3.0.CO;2-L
[7]	ZHANG Hong-wu, ZHONG Wan-xie, GU Yuan-xian.A combined parametric quadratic programming and iteration method for 3D elastic-plastic frictional contact problem analysis[J].Comput Meths Appl Mech Engrg,1998,155: 307—324. doi: 10.1016/S0045-7825(97)00170-9
[8]	ZHANG Hong-wu. Parametric variational principle for elastic-plastic consolidation analysis of saturated porous media[J].Int J Numer Anal Meths Geomechanics， 1995,19: 851—867. doi: 10.1002/nag.1610191203
[9]	ZHANG Hong-wu,Schrefler B A. Gradient-dependent plasticity model and dynamic strain localisation analysis of saturated and partially saturated porous media: one dimensional model[J].European Journal of Solid Mechanics, A/Solids,2000,19(3): 503—524. doi: 10.1016/S0997-7538(00)00177-7
[10]	ZHANG Hong-wu, Galvanetto U, Schrefler B A. Local analysis and global nonlinear behaviour of periodic assemblies of bodies in elastic contact[J].Computational Mechanics,1999,24(4): 217—229. doi: 10.1007/s004660050510
[11]	张洪武，顾元宪，钟万勰. 传热与接触两类问题耦合作用的有限元分析[J]. 固体力学学报，2000,21(3):217—224.
[12]	Billups S C,Murty K G.Complementarity problems[J].Journal of Computational and Applied Mathematics,2000,124:303—318. doi: 10.1016/S0377-0427(00)00432-5
[13]	Wright S. J. Primal-Dual Interior-Point Methods[M]. Philadelphia: SIAM Publications, 1997.
[14]	修乃华，高自友. 互补问题算法的新进展[J]. 数学进展，1999,28(3):193—210.
[15]	Ferris M C， Kanzow C. Complementarity and related problems: A survey[A]. In:Pardalos P M,Resende M G C Eds:Handbook on Applied Optimization[C].New York:Oxford University Press,2002,514—530.
[16]	CHEN Chun-hui, Mangasarian O L. Smoothing methods for convex inequalities and linear complementarity problems[J].Mathematical Programming,1995,71: 51—69.
[17]	CHEN Bing-tong, XIU Nai-hua. A Global linear and local quadratic non-interior continuation method for nonlinear complementarity problems based on Chen-Mangasarian smoothing functions[J].SIAM Journal on Optimization, 1999,9:605—623. doi: 10.1137/S1052623497316191
[18]	Burke J V, XU Song.The global linear convergence of a non-interior path following algorithm for linear complementarity problems[J].Mathematics of Operations Research,1998,23:719—734. doi: 10.1287/moor.23.3.719
[19]	李兴斯. 一类不可微优化问题的有效解法[J]. 中国科学，A辑，1994,24(4):371—377.
[20]	Kanzow C.Some noninterior continuation methods for linear complementarity problems[J].SIAM J Matrix Anal Appl,1996,17(4):851—868. doi: 10.1137/S0895479894273134
[21]	Buczkowski R,Kleiber M.Elasto-plastic interface model for 3D-frictional orthotropic contact problems[J].International Journal for Numerical Methods in Engineering,1997,40:599—619. doi: 10.1002/(SICI)1097-0207(19970228)40:4<599::AID-NME81>3.0.CO;2-H

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求解摩擦接触问题的一个非内点光滑化算法

作者简介:
张洪武(1964- ),男,辽宁大连人,教授,工程力学博士,博士生导师(联系人.Tel:86-411-4706249;E-mail:zhanghw@dlut.edu.cn).

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Non-Interior Smoothing Algorithm for Frictional Contact Problems

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求解摩擦接触问题的一个非内点光滑化算法

作者简介: 张洪武(1964- ),男,辽宁大连人,教授,工程力学博士,博士生导师(联系人.Tel:86-411-4706249;E-mail:zhanghw@dlut.edu.cn).

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出版历程

Non-Interior Smoothing Algorithm for Frictional Contact Problems

计量

出版历程

目录

作者简介:
张洪武(1964- ),男,辽宁大连人,教授,工程力学博士,博士生导师(联系人.Tel:86-411-4706249;E-mail:zhanghw@dlut.edu.cn).