The Theory And Application Research Of Taylor Series Multipole Bem For 3-D Elastic Contact Problems With Friction

Since the 1950s, the computational mechanics has developed greatly in various subdiscipline and interdisciplinary subject of solid mechanics, which has become the third means in addition to the theoretical and experimental research. Nowadays, the numerical methods have turned into main analytic tools in the field of modern science and engineering. Numerical simulation is an important component of science and engineering, and it has strong influence on the all analytic domains of science and engineering.The Boundary Element Method (BEM) is an important modern numerical analytic tool, and it is a unique numerical method after Finite Element Method (FEM). The basis idea of BEM is to transform the original different equations into the boundary integral equations, and in conjunction with the discrete technologies of FEM. It has become the important complement of FEM owing to the dimensionality reduction and semi analytical features. In some domains, the BEM method is even the irreplaceable numerical method. However, the linear system arising from the BEM is general dense and non-symmetrical matrix. For the large scale problems, the traditional solving scheme which is composed of the boundary integral equation, computing of numerical integration, form the linear system, and solving by elimination method results in expensive computational costs. It limits the BEM only be applied to the small and medium-sized problems. The Multipole-BEMs combine the Fast Multipole Method (FMM) with the BEM, accelerate the computation of influence coefficients, update the solving mode of traditional BEM, improve the efficiency evidently, and be suited to the computing of large scale problems. This dissertation is mainly research the theories and applications of Taylor Series Multipole BEM (TSMBEM).The Multipole-BEM is capable of improving the solving efficiency of BEM, and meanwhile the precision decreases in comparison with the traditional BEM. This dissertation presents an error analysis with regard to TSMBEM for 3-D elasticity. The error estimating formulas of TSMBEM are derived. The far-field partition criterion is present according to the requirement of precision. The influence factors of the solving accuracy of TSMBEM are specified.The Taylor series expressions of fundamental solutions are mostly expressed in tensor form. The vectorization expressions of Taylor Series Multipole boundary element formula for 3-D elasticity problems, which take account of the symmetric properties of fundamental solutions and the characteristic of component for 3-D problems. The vectorization expressions reduce the computational costs and storage required, thus improve the computational efficiency.For the large scale problems, the linear systems arising from BEM are general ill-conditioned, therefore the choice of iterative methods and preconditioning techniques is of great importance to the efficient solution. This dissertation investigates the Krylov subspace methods which are suited to the dense non-symmetric linear system arising from BEM. The comparative performances of different Krylov subspace solvers are studied, and several general preconditionrers are also considered and assessed. A near-field preconditioning techniques are presented, and it can accelerate the convergence, reduce the iterations, and be propitious to the special implicit linear systems arising from Multipole-BEM.The dissertation researches the TSMBEM for 3-D elastic contact with problem, presents a mathematical programming solution method base on Point-Surface contact model. The source codes are written in FORTRAN. A large scale numerical experiment is presented. The contact pressures of between rolls of HC mill are analyzed. The validity and efficiency of TSMBEM are proved by numerical experiments.This dissertation is mainly research the fundamental theories of TSMBEM, including the elasticity, contact problems, iterative methods and preconditioning techniques, which lay the foundation for the improvement of computational efficiency of BEM. The research subject is the frontline of computational mechanics, and has great academic value and wide engineering prospects.