A MATHEMATICAL-PROGRAMMING APPROACH TO 3-DIMENSIONAL CONTACT PROBLEMS WITH FRICTION

作     者：KLARBRING, A 

作者机构：Linköping Institute of Technology Department of Mechanical Engineering Division of Solid Mechanics and Strength of Materials S-581 83 Linköping Sweden 

出 版 物：《COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING》 (应用力学和工程技术中的计算机方法)

年 卷 期：1986年第58卷第2期

页      面：175-200页

核心收录：

学科分类：08[工学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

主　　题：MATHEMATICAL PROGRAMMING 

摘      要：The present study is concerned with the numerical treatment of linear elastic contact problems with friction. Making the restriction that the contact surface is constant during the loading history, we obtain a variational inequality formulation, which justifies a finite element approximation. The finitedimensional problem so obtained is shown to be equivalent to a problem of mathematical programming—namely, a parametric linear complementarity problem (LCP) involving derivatives. A solution procedure for such problems has previously been suggested. In this paper, the conditions under which this procedure defines a unique solution map, which describes the evolution of contact stresses and displacements for a prescribed load history, are given. As an application of the theory presented, the indentation of a halfspace by a flat-ended square punch is considered. Both the loading cases of a vertical displacement of the punch that increases monotonically and the gradual removal of the same displacement are considered.