Boundary Element Method For Moving And Rolling Contact Of 2D Elastic Bodies With Defects

The mechanical behaviour of a variety of engineering systems such as transmitting gears, sliding and rolling bearings, sealing screw threads, train wheels and rail, depends on the interaction of contacting bodies. Performance prediction, strength assessment and lifetime prediction in the design phase, design modifications as well as in the full life of operation, require proper mechanical and mathematical models. The inherently non-linear processes at the contact zone further complicate the problem. Therefore only very few simple contact problems can be solved analytically, to solve the complex contact problem is only possible using effective numerical approaches and associated algorithms. Among them the finite element method and boundary element method have played important role.Boundary element method is developed in recent 40 years as a comparatively accurate and efficient numerical method for engineering analysis. For the boundary-nonlinear problems, such as contact problem, the boundary displacements and boundary tractions are just the basic variables of the boundary integral equation, and the contact conditions can be satisfied with higher accuracy. Therefore, the BEM can solve the contact problem more accurately.For the BEM, the early references adopted the node-to-node scheme to formulate contact conditions, but this scheme is difficult to be applied to more complicated cases such as moving contact problem. A kind of interpolation schemes, which utilizes shape function to impress interfacial constraint conditions (node to point) to prevent penetration between the contacted surfaces, is adopted generally in the references, as used in the FEM. Some good characteristics of BEM are lost as a significant cost.In this thesis, a scheme for moving contact of 2D elastic bodies using conforming discretization is presented, which preserve the good characteristics of BEM, under the assumption of small strain. Both the displacement and the traction boundary conditions are satisfied on the contacted region in the sense of discretization. An algorithm to deal with the moving of the contact boundary on a large possible contact region is presented. The algorithm is generalized to the rolling contact as well.Some numerical examples are given to show the effectiveness and higher accuracy of the presented schemes. It is emphasized to the moving and rolling contact of 2D elastic bodies with hole-type defect or crack in the vicinity of contact region. For such kind of problems, instead of the moving and rolling contact it is treated as moving loads corresponding to the Hertz solution in the references. In this way the coupling effect between defects, crack and moving, rolling contact has been neglected. But the presented numerical examples show that such coupling effect could not be neglected, provided the defect located in the vicinity of the contact region.For the computation of the crack, it is adopted the sub-region approach as generally used in BEM analysis. For the crack in the vicinity of contact surfaces, not only occur the coupling between the moving contact and crack, but also the contact of the crack surfaces. Moving contact with friction combined the frictional contact of crack surfaces further complicate the problem, and it should be solved by double iteration scheme of BEM, which frequently fail to converge during the iteration. It is presented successfully some results of coupling analysis, the moving contact of bodies with crack of different orientation in the vicinity of contact region.Pu Junping (Solid Mechanics) Supervised by Prof. Dr. Yao Zhenhan...