Dynamic Analysis of Nonlinear Models with Infinite Extension by Boundary Elements
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:64390", author = "Delfim Soares Jr. and Webe J. Mansur", title = "Dynamic Analysis of Nonlinear Models with Infinite Extension by Boundary Elements", 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.", volume = "7", number = "1", pages = "144-6", }