Dynamic Analysis of Nonlinear Models with Infinite Extension by Boundary Elements

Authors: Delfim Soares Jr., Webe J. Mansur

Abstract:

The Time-Domain Boundary Element Method (TDBEM) is a well known numerical technique that handles quite properly dynamic analyses considering infinite dimension media. However, when these analyses are also related to nonlinear behavior, very complex numerical procedures arise considering the TD-BEM, which may turn its application prohibitive. In order to avoid this drawback and model nonlinear infinite media, the present work couples two BEM formulations, aiming to achieve the best of two worlds. In this context, the regions expected to behave nonlinearly are discretized by the Domain Boundary Element Method (D-BEM), which has a simpler mathematical formulation but is unable to deal with infinite domain analyses; the TD-BEM is employed as in the sense of an effective non-reflexive boundary. An iterative procedure is considered for the coupling of the TD-BEM and D-BEM, which is based on a relaxed renew of the variables at the common interfaces. Elastoplastic models are focused and different time-steps are allowed to be considered by each BEM formulation in the coupled analysis.

Keywords: Boundary Element Method, Dynamic Elastoplastic Analysis, Iterative Coupling, Multiple Time-Steps.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1084956

References:

[1] J.A.M. Carrer, and J.C.F. Telles, "A Boundary Element Formulation to Solve Transient Dynamic Elastoplastic Problems," Computers and Structures, vol. 45, pp. 707-713, 1992.
[2] J.A.M. Carrer, and W.J.Mansur, "Alternative Time-Marching Schemes for Elastodynamic Analysis with the Domain Boundary Element Method Formulation," Computational Mechanics, vol. 34, pp. 387-399, 2004.
[3] W.J.Mansur, A Time-stepping Technique to Solve Wave Propagation Problems Using the Boundary Element Method. Ph.D. Thesis, University of Southampton, England, 1983.
[4] J. Dominguez, Boundary Elements in Dynamics. Southampton and Boston: Computational Mechanics Publications, 1993.
[5] D. Soares Jr., O. von Estorff, and W.J. Mansur, "Iterative Coupling of BEM and FEM for Nonlinear Dynamic Analysis," Computational Mechanics, vol. 34, pp. 67-73, 2004.
[6] J.C. Houbolt, "A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft," Journal of the Aeronautical Sciences, vol. 17, pp. 540-550, 1950.
[7] J.C.F. Telles, The Boundary Element Method Applied to Inelastic Problems, Lecture Notes in Engineering, vol.1. Berlin, New York, Heidelberg, Tokyo: Springer-Verlag, 1983.
[8] D. Soares Jr., J.A.M. Carrer, J.C.F. Telles, and W.J. Mansur, "Timedomain BEM Formulation: Two Approaches for the Computation of Stress and Velocity," Computational Mechanics, vol. 30, pp. 38-47, 2002.
[9] P.C. Chow, and H.A. Koenig, "A Unified Approach to Cylindrical and Spherical Elastic Waves by Method of Characteristics," Transactions of the ASME, Journal of Applied Mechanics, vol. 33, pp. 159-167, 1966.