Boundary Element Method For Moving Contact Of 3D Elastic Bodies

As an effective numerical analysis method of scientific and engineering problems developed following Finite Element Method (FEM), Boundary Element Method (BEM) has some attractive advantages, such as easier simulating complex boundary shape, high accuracy and dimension reduction. For the boundary nonlinear problems, such as elastic 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 in BEM; therefore, the BEM can be applied to solve the elastic contact problem more accurately. In this dissertation, some basic investigations on the BEM of 3D elastic contact problem have been carried out, which can be listed as follows:At first, an early investigation of authors' group, on direct error estimation of BEM solution for elasticity problem, is extended from 2D problem to 3D elastic contact problem. An accurate and efficient algorithm for the determination of boundary displacement, which is continuous with the displacement solution within the domain of an elastic body, is then presented. Based on the difference between the corresponding limit of displacement from both side of contacted bodies, a local direct error estimator of BEM solution for 3D elastic contact problem is presented, and then a scheme of adaptive BEM is suggested. This scheme can be used to estimate the error of the complicated contact problems without corresponding analytical solution.To solve the 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 of BEM, as used in the FEM. Some good characteristics of BEM are lost as a significant cost; the contact boundary conditions can not be satisfied on whole boundary, even in the sense of discretization. In this thesis, based on the previous investigation on 2D moving and rolling contact problem by BEM, the conforming discretization is generalized to 3D cases, and a scheme of BEM for moving contact of 3D elastic solids with prescribed moving direction using conforming discretization is presented. Both the displacement and traction boundary conditions are satisfied on the contacted region in the sense of discretization. In this way the good characteristics of BEM can be preserved.Some numerical examples are given to show the effectiveness and higher accuracy of the presented scheme of moving contact. It is emphasized to the moving and rolling contact of 3D elastic bodies with hole-type defect in the vicinity of contact region. For such kind of problems, instead of the moving contact it is treated as moving loads corresponding to the Hertz solution in the references. In this way the coupling effect between defects and moving 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.Finally, a scheme of BEM for moving contact of 3D elastic solids with unknown or variable moving direction using conforming discretization is presented. Both the displacement and traction boundary conditions are satisfied on the contacted region in the sense of discretization.