Research On The Coupling Of Finite Element Method And Local Boundary Integral Equation For Plane Problem In Linear Elasticity

The appearance and application of computer is a turning point in developmental history of computational method for mechanics. During the last fifty years, numerical methods have a rapid development. This paper briefly introduces some numerical methods: finite difference method(DFM),finite element method(FEM), boundary element method(BEM) and meshless method, which occupy an important status in history. As meshless method is a new numerical method, This paper concludes and summarizes its fundamental, theory of approximation, choice of weight function and the method of implementing essential boundary.Local boundary integral equation method (LBIE) is a special meshless method. It based on the traditional boundary integral equation , and introduces the value of the fundamental solution substract the companion solution as test function,and integrates in subdomains. It has the advantages of FEM, BEM and meshless method, and exhibits great potential for in linear and nonlinear problems. on the basis of common meshless method, using moving least square approximation(MLS) to construct approximate function, Gauss function and Spline function as weight functions, This paper deduces LBIE for plane problems in linear elasticity, establishes the discrete equation, and proposes the method of dealing with integral singularity,Because all numerical methods have own advantages and disadvantages, and with the aim of using their advantages and avoiding their disadvantages, the ideas of coupling and parallel computation are appeared. The coupling of FEM and LBIE for plane problem in linear elasticity has been proposed in this paper. At first, considering the coupling techniques which are the master methods at present and combining the characters of FEM and LBIE, The direct coupling technique for FEM and LBIE has been proposed. Due to introducing the fundmental solution into the LBIE, this coupling techniques is convenient and direct, with no large errors. Second, according to the coupling technique , The corresponding program has been proposed and used it to compute two examples, which are the cantilever beam with concentrated force at the free end and the infinite plate with circle hole in center and level equal pull stress at two perpendicular boundaries. Through comparing the computational results to the analytical solutions, The advices of choices of weight function and parameters have been proposed, and some results were received, such as the curves of displacement, stresses of some sections, the errors. According to the results, we know that this method which was proposed in this paper has definite precision and is feasible. At last, the developmental prospect and the research aspects have been proposed in conclusion.