Study On Coupled Finite Element Boundary Element Methods By Domain Decomposition

The finite element method and boundary element method are two numerical analysis methods with their characteristics, the coupled finite element-boundary element method, giving full play to the advantages of both, can improve the ability to solve complex engineering problems significantly. So far, finite element coupling of boundary element method about wave propagation problem, mainly used the thought of combing the control equations to solve the problem in the frequency domain. And in the time domain, the coupling method of solving problems independently discrete areas still exists some shortage, following are the main points. Firstly, the two regional public boundary node position must be strictly limited in the dynamic problem. Secondly, dealing with problems of discontinuous surface force at angular point in boundary element are very difficult. Thirdly, adopting difference scheme to solve the finite element control equation, reduces the accuracy of solution. In view of the above points, specific research in this paper includes the following parts:Solve the plane elastic problem with coupling method by domain decomposition. The nodes Located in common boundary of finite element and boundary element regional are not haveto keep the condition of location consistency, Thus the two areas can be discrete of independence and freedom. Displacement transfer matrix and force transfer matrix is put forward, allows us to achieve the displacement and force exchange at common interface node of different position. In boundary element method, adopt non-confirming linear element with the nodes in the internal to discrete boundary, can avoid dealing with complex corner problems.The coupling of time domain boundary and the precise integration method. Using non-confirming linear element to numerical discrete boundary integral equation, the corresponding displacement influence coefficient matrix and the surface force influence matrix elements are deduced. Using the precise integration method to calculate the finite element control equation by degree reduction, get the half analytic formula to solve the dynamic problem. Through establishing the relationshipof displacement between the current time step and the next by finite element method, and by the boundary element method to establish the relationship between displacement and force at this step. By continuous loop iteration to obtain real displacement and force on the boundary nodes of common interface, realizing the semi-analytical precise integration method and time domain boundary element method to couple.Dual reciprocity boundary element coupled with direct integral method. The inertia in the domain integral in dual reciprocity boundary element method which based on the static fundamental solutions, by introducing the coordinate function and distance function, is transformed into boundary integral. In Newmark method to deal with two kinds of control equations, by assuming that the common boundary node displacement at each time step. Through multiple coupled iterations, this method can well solve the problem of a lot of the initial stress of the unknown.The coupling finite element boundary element domain iteration method validation. The cantilever beam under the action of shear stress as an example, verify the elastic mechanics problem of regional coupling method can abandon common interface node location consistent conditions. The cantilever beam under impact loading and harmonic loading as an example, to verify the correctness to deal with dynamic problem of coupling method of the time domain boundary element and the precise integral method. The retaining dam on the elastic foundation under the triangular distributed load as an example to verify the feasibility of dual reciprocity boundary element coupled with direct integral method.