This paper reports on the development of a finite element -boundary element coupling procedure for the analysis of arbitrary shaped elastic bodies subjected to dynamic loads. The coupling is accomplished through equilibrium and compatibility considerations along the boundary element -finite element interface.
Several numerical studies are performed where one part of a uniform body is treated by finite elements, whereas the remaining region is discretized by boundary elements. The examples demonstrate the influence of different finite element approaches and the applicability and the accuracy of the proposed procedure.
1 Introduction
The numerical analysis of elastic bodies subjected to dynamic loads has received considerable attention in recent years. Especially, when dealing with problems like soil-structure interaction, vibration isolation or wave propagation, researchers have to decide whether they intend to use a domain-type method (the finite difference method and the finite element method) or a boundary-type formulation (the Trefftz method and the boundary element method).
Depending on the kind of the problem, either domain-type or boundary-type formulations may be more advantageous. The domain-type methods are well suited to treat inhomogeneous, anisotropic materials as well as geometric and material nonlinear behavior in a system. However, for problems involving infinite domains (halfspace problems) and regions of high stress concentrations (crack problems), boundary-type methods are undoubtedly superior to the domain-type methods.
In order to profit from the advantages of each of the two basic approaches, while evading their disadvantages, it seemed to be quite promising to develop combined formulations. Zienkiewicz, Kelly and Bettes (1977) were among the first authors who proposed the coupling of finite and boundary elements. Since then, there have been quite a few papers suggesting coupling techniques; a summary with references and further details were given, e.g., by Brebbia, Telles and Wrobel (1984) and by Vallabhan (1987).
While in early publications mostly potential and fluid-structure interaction problems were considered, in the following years also elastostatic problems were solved successfully using combined Boundary Element Method-Finite Element Method (BEM-FEM) algorithms. Fundamental work in this field has been done, e.g., by Brebbia and Georgiou (1979); Beer and Meek (1981);Li, Han, Mang and Torzicky (1986);Swoboda, Mertz and Beer (1987). Geotechnical engineering, in particular, was found to have a large number of problems where coupling techniques could be effectively employed.
Recently, some researchers have also focused their attention on the development of coupling procedures for elastodynamic problems. Among others (see, e.g., review by Beskos 1987), Kobayashi and Mori (1986) have used a combination of the BEM with the FEM for the solution of soil-structure interaction problems. While their model was formulated in the frequency domain, Spyrakos andBeskos (1986), andKarabalis andBeskos (1987), respectively, considered plane and three-dimensional soil-foundation problems in the time domain using boundary elements