Iterative coupling of BEM and FEM for nonlinear dynamic analyses

Abstract

The present work deals with the iterative coupling of boundary element and finite element methods. First, the domain of the original problem is subdivided into two subdomains, which are separately modeled by the FEM and BEM. Thus the special features and advantages of the two methodologies can be taken into account. Then, prescribing arbitrary transient boundary conditions, a successive renewal of the variables on the interface between the two subdomains is performed through an iterative procedure until the final convergence is achieved. In the case of local nonlinearities within the finite element subdomain, it is straightforward to perform the iterative coupling together with the iterations needed to solve the nonlinear system. The procedure turns out to be very efficient. Moreover, a special formulation allows taking into account different durations of the time steps in each subdomain.The numerical simulation of arbitrarily shaped continuous bodies subjected to harmonic or transient loads remains, despite much effort and progress over the last decades, a challenging area of research. In most cases, discrete techniques, such as the finite element method (FEM) and the boundary element method (BEM) have been employed and continuously further developed with respect to accuracy and efficiency. Both methodologies can be formulated in the time domain or in the frequency domain, and each approach has relative benefits and limitations. The finite element method, for instance, is well suited for inhomogeneous and anisotropic materials as well as for dealing with the nonlinear behavior of a body. For systems with infinite extension and regions of high stress concentration, however, the use of the boundary element method is by far more advantageous. More details are given, e.g., by Hughes [17] or Bathe [2] for the FEM and by Becker [3] or Dominguez [10] in the case of the BEM.In fact, it did not take long until some researchers started to combine the FEM and the BEM in order to profit from their respective advantages by trying to evade their disadvantages. Up to now, quite a few publications concentrate on such coupling approaches. Many details are given, e.g., by Zienkiewicz et al. [25,26], who were among the first suggesting a ''mariage à la mode -the best of two worlds'', by von Estorff and Prabucki [13], von Estorff and Antes [14], Belytschko and Lu [4], Yu et al. [23], or Rizos and Wang [21]. A rather complete overview is provided by Beskos [ [5][6][7]. It should be mentioned, that in most cases the BEM has been used to model those parts of the investigated bodies which are of semi-infinite extension, while finite parts were represented with the FEM. Moreover, it has been assumed that the considered systems behave linearly, which means that only elastic material and small displacements are considered.The FEM/BEM coupling in the time domain has also been successfully used to take into account nonlinear effects. Thus Pavlatos and Beskos [20] as well as Yazdchi et al. [24], for instance, modeled an inelastic structure ...

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