Study On Coupling Of Finite Element Method And Boundary Element Method In Semi-Infinite Domain With Independent Time Steps

FEM and BEM are two main methods for numerical analysis.Among them,finite element method has been widely used in research and engineering.Mature finite element analysis software has also become very popular.Boundary Element Method(BEM),as a numerical method which only needs to be discretized on the boundary,has the characteristics of fewer discrete elements and high precision.Moreover,it has natural advantages in dealing with infinite or semi-infinite problems.The coupling method combining the two can integrate the advantages of boundary element and finite element in dealing with near-domain nonlinear problems,and play an important role in dealing with the interaction between structures and semi-infinite soils.In this paper,the establishment,discretization and assembly of the boundary integral equation for the semi-infinite domain time domain boundary element method are firstly derived.When dealing with the infinity of free surface,according to the principle of wave propagation in medium,an adaptive boundary element is constructed to eliminate the reflection of waves at the directly truncated boundary.At the same time,when the boundary is discretized,the force and displacement are discretized completely linearly in space and time,which improves the calculation accuracy.For singularity problem,finite integral method is used in this paper,and Gaussian integral method is used to calculate elements without singularity.Then the validity and applicability of the proposed method are verified by a numerical example.After the establishment of the semi-infinite domain boundary element method,this paper coupled it with the ABAQUS finite element method.Here,explicit and direct coupling of central difference was adopted to avoid the iterative process on the public interface when implicit calculation was adopted.At the same time,in order to make use of the step size of each optimum time,the coupling method of different time step is adopted,and the responses of each other at the corresponding time are obtained through interpolation calculation in time.Then,by writing ABAQUS script file to realize the data interaction between the time domain boundary element program and ABAQUS,so as to give full play to the powerful function of the finite element software,greatly expanding the application scope and convenience of the coupling method.Finally,radial load and harmonic load are applied to the semi-infinite domain model respectively,and the results are analyzed to verify the validity of the coupling method.