ADAPTIVE ITERATIVE BEM-FEM COUPLING PROCEDURES TO ANALYZE INELASTIC MODELS
DOI:
https://doi.org/10.26512/ripe.v2i6.21470Keywords:
Iterative Coupling. Boundary Elements. Adaptive Finite Elements. Elastoplasticity.Abstract
The analysis of complex systems may be more effectively handled considering the combination of different numerical methods, in a way that each numerical technique can be applied to deal with the particularities of the model that better fit its positive features. In this sense, the adaptive iterative coupling of the Boundary Element Method (BEM) and of the Finite Element Method (FEM) is discussed here, taking into account static nonlinear models. Optimal relaxation parameters are employed to speed up the convergence of the iterative coupling, and non-matching discretizations at common interfaces, as well as adaptive refinement within the FEM subdomains, are allowed, enabling more versatile and accurate approaches. A single unified iterative loop is considered in order to deal with all the focused iterative solutions simultaneously (i.e., the nonlinear analysis, the adaptive analysis and the coupling analysis), rendering a very efficient methodology. In this context, multiple sequential iterative loops, which represent a rather computationally demanding approach, can be avoided without significantly increase the number of the iterative steps of the dominant iterative process, considerably improving the performance of the method. At the end of the paper, numerical results are presented, illustrating the potentialities and the effectiveness of the proposed techniques.
Downloads
References
Belytschko, T., Liu, W.K., Moran, B., 2000. Nonlinear finite elements for continua & structures. New York: J. Wiley & Sons.
Bendali, A., Boubendir, Y., Fares, M., 2007. A FETI-like domain decomposition method for coupling finite elements and boundary elements in large-size problems of acoustic scattering. Computers & Structures, vol. 85, pp. 526”“535.
Boumaiza, D., Aour, B., 2014. On the efficiency of the iterative coupling FEM”“BEM for solving the elasto-plastic problems. Engineering Structures, vol. 72, pp. 12”“25.
Brebbia, C.A., Dominguez, J., 1998. Boundary elements, an introductory course. Southampton: WIT press.
Brebbia, C.A., Telles, J.C.F., Wrobel, L.C., 1984. Boundary element techniques. Berlin: Springer-Verlag.
Chen, L., Zhang, C.S., 2006. AFEM@matlab: a Matlab package of adaptive finite element methods. University of Maryland at College Park.
Chen, W.F., Han, D.J., 1988. Plasticity for structural engineers. New York: Spring-Verlag.
Coulier, P., François, S., Lombaert, G., Degrande, G., 2014. Coupled finite element ”“hierarchical boundary element methods for dynamic soil”“structure interaction in the frequency domain. International Journal for Numerical Methods in Engineering, vol. 97, pp.505”“530.
Elleithy, W.M., 2012. Multi-region adaptive finite element-boundary element method for elasto-plastic analysis. International Journal of Computer Mathematics, vol. 89, pp. 1525”“ 1539.
Elleithy, W.M., Al-Gahtani, H.J., El-Gebeily, M., 2001. Iterative coupling of BE and FE methods in elastostatics. Engineering Analysis with Boundary Elements, vol. 25, pp. 685”“695.
Elleithy, W.M., Grzhibovskis, R., 2009. An adaptive domain decomposition coupled finite element”“boundary element method for solving problems in elasto-plasticity. International Journal for Numerical Methods in Engineering, vol. 79, pp. 1019”“104.
Elleithy, W.M., Tanaka, M., Guzik, A., 2004. Interface relaxation FEM”“BEM coupling method for elasto-plastic analysis. Engineering Analysis with Boundary Elements, vol. 28, pp. 849”“857.
Jahromi, H.Z., Izzuddin, B.A., Zdravkovic, L., 2009. A domain decomposition approach for coupled modelling of nonlinear soil-structure interaction. Computer Methods in Applied Mechanics and Engineering, vol. 198, pp. 2738”“2749.
Khan, A.S., Huang, S., 1995. Continuum theory of plasticity. New York: John Wiley & Sons.
Lin, C.C., Lawton, E.C., Caliendo, J.A., Anderson, L.R., 1996. An iterative finite element ”“boundary element algorithm. Computers & Structures, vol. 39, pp. 899”“909.
Simo, J.C., Hughes, T.J.R., 1998. Computational inelasticity. New York: Springer.
Soares, D., 2008. An optimised FEM”“BEM time-domain iterative coupling algorithm for dynamic analyses. Computers & Structures, vol. 86, pp. 1839”“44.
Soares, D., 2012. FEM-BEM iterative coupling procedures to analyze interacting wave propagation models: fluid-fluid, solid-solid and fluid-solid analyses. Coupled Systems Mechanics, vol. 1, pp. 19”“37.
Soares, D., Godinho, L., 2012. An optimized BEM-FEM iterative coupling algorithm for acoustic-elastodynamic interaction analyses in the frequency domain. Computers & Structures, vol. 106-107, pp. 68”“80.
Soares, D., Godinho, L., 2014. An overview of recent advances in the iterative analysis of coupled models for wave propagation. Journal of Applied Mathematics, Article ID 426283.
Soares, D., Godinho, L., 2015. Inelastic 2D analysis by adaptive iterative BEM-FEM coupling procedures. Computers & Structures, vol. 156, pp. 134”“148.
Soares, D., von Estorff, O., Mansur, W.J., 2004. Iterative coupling of BEM and FEM for nonlinear dynamic analyses. Computational Mechanics, vol. 34, pp. 67”“73.
Downloads
Published
How to Cite
Issue
Section
License
Given the public access policy of the journal, the use of the published texts is free, with the obligation of recognizing the original authorship and the first publication in this journal. The authors of the published contributions are entirely and exclusively responsible for their contents.
1. The authors authorize the publication of the article in this journal.
2. The authors guarantee that the contribution is original, and take full responsibility for its content in case of impugnation by third parties.
3. The authors guarantee that the contribution is not under evaluation in another journal.
4. The authors keep the copyright and convey to the journal the right of first publication, the work being licensed under a Creative Commons Attribution License-BY.
5. The authors are allowed and stimulated to publicize and distribute their work on-line after the publication in the journal.
6. The authors of the approved works authorize the journal to distribute their content, after publication, for reproduction in content indexes, virtual libraries and similars.
7. The editors reserve the right to make adjustments to the text and to adequate the article to the editorial rules of the journal.
