The Application Of Regularization Algorithm Of The Nearly Singular Integrals In Boundary Element Methods To Multi-domain Technique And Contact Analysis

The application range of boundary element methods is reduced in engineering by the difficulty of evaluation of the nearly singular integrals for a long time. This dissertation introduces a regularization algorithm to tackle the problems of the nearly singular integrals. In the algorithm, the singular factor is removed from the kernel functions in the singular integrals by means of integration by parts. Therefore, the nearly singular and singular integrals are successfully calculated. This dissertation presents the scheme to apply the regularization algorithm to multi-domain boundary element methods (BEMs) and contact BEMs. The accuracy of the calculation of the nearly singular integrals in multi-domain BEMs and contact BEMs has been greatly improved.First of all, the basic theory of multi-domain boundary element methods is introduced. The general formulations of the application of regularization algorithm to multi-domain BEMs are given. Some typical examples illustrate that the proposed algorithm can effectively evaluate the mechanical parameters at inner points very close to the boundary. With the help of multi-domain BEMs, the interface stresses and displacements of the bending of composite-material laminated beam have been worked out in different thickness ratios of the layers. When the thickness ratio of the layers is smaller than 0.01, the calculated stresses and displacements become invalided accordingly in the conventional boundary element methods. If we adopt the regularization algorithm, even the ratio of the layer thickness is smaller than 10-6, the accuracy of the calculated stresses and displacements are excellent agreement with the results obtained from MSC NASTARN, which is one of the popular finite element methods programs.Besides, the new algorithm is applied to the static contact BEMs. The paper puts forward an iterative process to searching for the contacted zone and the distribution of contact force, in the case of the outer loading has been known. The regularization algorithm is used to evaluate the mechanical parameters of the near-boundary points in contact bodies. In order to analysis the contact problem between elasticity roller and rigid plane, another iterative process is raised. Supposing the right contact point has been known, the left contact point has to be found and the distribution of stick zone and slip one have to be determined in each iterative process. The outer load is evaluated according to the solved force distribution in contact zone. For reducing the time of the iteration process, a new technique is proposed, in which the total number of equations is decreased through departing the roller into two parts and eliminating the freedom degrees of the system. The numerical experiments illustrate that the iterative time with this technique is about one-sixth of the conventional process. What's more, the regularization algorithm is utilized when calculating the physical quantities in the interior point very close to the boundary. The numerical results demonstrate that the accuracy and effectiveness of the algorithm is better than the conventional Gaussian quadrature.The mechanical parameters of the near-boundary-point in multi-domain BEMs and contact BEMs are evaluated successfully by utilizing the regularization algorithm. Thereafter, it makes that the application of boundary element methods in engineering is widened.