An adaptive domain decomposition coupled finite element–boundary element method for solving problems in elasto‐plasticity

Abstract

SUMMARYThe purpose of this paper is to present an adaptive finite element-boundary element method (FEM-BEM) coupling method that is valid for both two-and three-dimensional elasto-plastic analyses. The method takes care of the evolution of the elastic and plastic regions. It eliminates the cumbersome of a trial and error process in the identification of the FEM and BEM sub-domains in the standard FEM-BEM coupling approaches. The method estimates the FEM and BEM sub-domains and automatically generates/adapts the FEM and BEM meshes/sub-domains, according to the state of computation. The results for two-and three-dimensional applications in elasto-plasticity show the practicality and the efficiency of the adaptive FEM-BEM coupling method.

Inelastic 2D analysis by adaptive iterative BEM–FEM coupling procedures

“…Eqs. (7)(8) only intend to summarily describe the boundary element formulation considered here; for further details on the topic, the following references are suggested [23,24].…”

“…Adaptive BEM-FEM coupled analyses, taking into account elastoplastic models, have been reported by Elleithy et al [8,9]. In these works, an interesting adaptive procedure is presented, in which the FEM subdomains are expanded (and BEM subdomains are shrunk) as the plastic zones evolve.…”

“…For both coupling approaches, optimal relaxation parameters are employed to speed up and/or to ensure the convergence of the iterative coupling analysis. As it has been previously remarked [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], this procedure is highly important to guarantee the effectiveness of the technique.…”

“…In fact, it did not take long until some researchers started to combine the BEM and the FEM in order to profit from their respective advantages, trying to evade their disadvantages, and nowadays several works dealing with BEM-FEM coupling are available [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. However, standard coupling procedures of BEM/FEM can lead to several problems with respect to efficiency, accuracy and flexibility.…”

“…Initially, static problems were studied considering iterative coupling approaches, and linear and nonlinear behavior have been simulated [5][6][7][8][9][10][11]. Later on, dynamic problems were focused, and time [12][13][14][15] and frequency domain [16][17][18][19] iterative analyses have been implemented (in this case, an overview is presented by Soares and Godinho [20]).…”