单侧接触问题的拟有效集方法

基金项目: 国家自然科学基金资助项目(59775065)

Unilateral Contact Problems Using Quasi-Active Set Strategy

1.
School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, P.R.China;
2.
Research Institute of Engineering Mechanics, Dalian University of Technology, Dalian 116024, P.R.China

摘要: 单侧接触问题可以模型化为一个带不等式约束的数学规划问题。针对不等式约束问题求解的困难,提出了一个拟有效集方法。在每次迭代中,先利用上次迭代得到的解将问题转化为一个无接触问题,然后以其解作为当前迭代的初始解,且在每次迭代里可以同时更换一组接触点对,而不是象Lemke方法那样每次迭代仅更换一个接触点对。因而,该算法极大地提高了求解效率,算例表明了该算法的高效性和可靠性。
- 单侧接触问题 /
- 数学规划 /
- 拟有效集
Abstract: The unilateral contact problem can be formulated as a mathematical programming with inequality constraints.To resolve the difficulty in dealing with inequality constraints,a quasi-active set strategy algorithm was presented.At each iteration,it transforms the problem into one without contact in terms of the solution obtained in last iteration and initiates the current iteration using the solution of the transformed problem,and updates a group of contact pairs compared with Lemke algorithm that uqdates only one pair of contact points.The present algorithm greatly enhances the efficiency and numerical examples demonstrate the effectiveness and robustness of the proposed algorithm.
- unilateral contact /
- mathematical programming /
- quasi-active set

[1]	Bisbos C D. A Cholesky condensation method for unilateral contact problems[J]. Solid Mechanics Archives,1985,11(1):1-23.
[2]	Panagiotopoulos P D. A nonlinear programming approach to the unilateral contact and friction boundary value problem in the theory of elasticity[J]. Ingenieur Archiv,1974,44(3):421-432.
[3]	Kikuchi N, Oden J T. Contact Problems in Elasticity: A Study of Variational Inequalities and FEM[M]. Philadelphia:SIAM,1988.
[4]	Zhong W X, Sun S M. A parametric quadratic programming approach to elastic contact problems with friction[J]. Comput & Structures,1989,32(1):37-43.
[5]	Xuan Z C, Li X S, Sui Y K. Surrogate dual problem of quadratic programming and the algorithm[J]. Chinese J Numer Math Appl,1999,21(1):45-53.
[6]	Rosen J B, Suzuki S. Construction of nonlinear programming test problems[J]. Comm of the ACM,1965,8(2):113.
[7]	Simunovic S, Saigal S. A linear programming formulation for incremental contact analysis[J]. Internat J Numer Methods Engrg,1995,38(16):2703-2725.