A combined parametric quadratic programming and iteration method for 3-D elastic-plastic frictional contact problem analysis

Abstract This paper is concerned with the formulation and numerical realization of elastic—plastic frictional contact problems. Comparing with two-dimensional elastic-plastic contact problems, three-dimensional elastic-plastic contact problems with friction are more difficult to deal with, because of the unknown slip direction of the tangential force and exhausting computing time when the double nonlinear problems are considered. In order to avoid these difficulties, a combined PQP (Parametric Quadratic Programming) and iteration method is constructed in this paper. The stiffness matrix of a 3-D contact element is introduced by means of a penalty function expression of the contact pressure and frictional force. The contact condition and the flow rule are expressed by the same form as in a non-associated plastic flow problem, and the penalty factors can be eliminated by using a definite numerical technique. The iteration algorithm, whose functions are to give a precise discretization of space Coulomb's friction law, is used along with the PQP method and alleviates the difficulty of unknown slip direction and cuts down computing costs. Also, the additional complementary conditions are discussed here, so that the non-physical ray solutions caused by original mathematical model can be eliminated. Numerical examples are given to demonstrate the validity of the present method.