Contact Problem Of Elastical Plane With Cracks

The contact mechanics is more and more important in modern engineer. Much investigation has been done in this area in the world. The range of its investigation is from single crack to multiple cracks, from rectilinear cracks to arbitrarily oriented cracks, from non-periodic problem to periodic problem. The material is from isotropic to anisotropic. The main methods are calculus of variations, finite element method and boundary element method. Complex analysis method is proved to be a effective method to investigate contact mechanics in practice, which has the virtue of high accuracy. The solution in closed form or exact solution can be obtained for some special cases by this method.There are four chapters in the present paper. Elastic contact problem is introduced in the first chapter. In the second chapter contact problem of a half-plane with periodic cracks under periodic rigid punch action is studied. Contact problem of compound material plane with cracks under a rigid punch action is studied in the third chapter. Contact problem of compound material plane with periodic cracks under periodic rigid punch action is studied in the fourth chapter. Contact of crack face is considered. Kolosov-Muskhelishvili complex potentials are constructed as integral representations. As a result, the considered problem is reduced to a system of singular integral equations of the first and the second kind. Stress intensity factors at vertical crack tips and numerical results of pressure under punch are obtained.