Multi-region adaptive finite element-boundary element method for elasto-plastic analysis

References

• Beer , G. 1983 . Finite element, boundary element and coupled analysis of unbounded problems in elastostatics . Int. J. Numer. Meth. Eng. , 19 ( 4 ) : 567 – 580 .
   Web of Science ®Google Scholar
• Beer , G. and Meek , J. L. 1981 . “ The coupling of boundary and finite element methods for infinite domain problems in elasticity ” . In Boundary Element Methods , Edited by: Brebbia , C. A. 575 – 591 . Berlin : Springer .
   Google Scholar
• Brebbia , C. A. and Georgion , P. 1979 . Combination of boundary and finite elements in elastostatics . Appl. Math. Model. , 3 : 212 – 220 .
   Web of Science ®Google Scholar
• Brink , U. , Klaas , O. , Niekamp , R. and Stein , E. 1995 . Coupling of adaptively refined dual mixed finite elements and boundary elements in linear elasticity . Adv. Eng. Software , 24 ( 1–3 ) : 13 – 26 .
   Web of Science ®Google Scholar
• Carstensen , C. 1997 . On the symmetric boundary element method and the symmetric coupling of boundary elements and finite elements . IMA J. Numer. Anal. , 17 ( 2 ) : 201 – 208 .
   Web of Science ®Google Scholar
• Carstensen , C. , Zarrabi , D. and Stephan , E. P. 1996 . On the h-adaptive coupling of FE and BE for viscoplastic and elasto-plastic interface problems . J. Comput. Appl. Math. , 75 ( 2 ) : 345 – 363 .
   Web of Science ®Google Scholar
• Chernov , A. , Geyn , S. , Maischak , M. and Stephan , E. P. 2006 . “ Finite element/boundary element coupling for two-body elastoplastic contact problems with friction ” . In Analysis and Simulation of Contact Problems , Edited by: Wriggers , P. and Nackenhorst , U. 171 – 178 . Berlin : Springer . Lecture Notes in Applied and Computational Mechanics Vol. 27
   Google Scholar
• Costabel , M. 1987 . “ Symmetric methods for the coupling of finite elements and boundary elements ” . In Boundary Elements IX , Edited by: Brebbia , C. , Wendland , W. and Kuhn , G. 411 – 420 . Berlin : Springer .
   Google Scholar
• Costabel , M. and Stephan , E. P. 1990 . Coupling of finite and boundary element methods for an elastoplastic interface problem . SIAM J. Numer. Anal. , 27 ( 5 ) : 1212 – 1226 .
   Web of Science ®Google Scholar
• Costabel , M. and Stephan , E. P. 1990 . Integral equations for transmission problems in linear elasticity . J. Integr. Eq. , 2 : 211 – 223 .
   Google Scholar
• DIANA finite element analysis user's manual release 9.4.3, TNO DIANA BV, Delft, The Netherlands, 2010. Available at www.tnodiana.com.
   Google Scholar
• El-Gebeily , M. , Elleithy , W. M. and Al-Gahtani , H. J. 2002 . Convergence of the domain decomposition finite element-boundary element coupling methods . Comp. Meth. Appl. Mech. Eng. , 191 ( 43 ) : 4851 – 4867 .
   Web of Science ®Google Scholar
• Elleithy , W. 2007 . Interface relaxation FEM–BEM coupling: dynamic procedures of determining the relaxation parameters . 6th Alexandria International Conference on Structural and Geotechnical Engineering (AICSGE6) . April 2007 , Alexandria , Egypt. pp. ST1 – ST15 .
   Google Scholar
• Elleithy , W. 2008 . Analysis of problems in elasto-plasticity via an adaptive FEM–BEM coupling method . Comp. Meth. Appl. Mech. Eng. , 197 ( 45–48 ) : 3687 – 3701 .
   Web of Science ®Google Scholar
• Elleithy , W. 2009 . Adaptive coupled finite element–boundary element method for elasto-plastic analysis . 7th UK Conference on Boundary Integral Methods . July 2009 , Nottingham , UK. pp. 67 – 80 .
   Google Scholar
• Elleithy , W. M. , Al-Gahtani , H. J. and El-Gebeily , M. 2001 . Iterative coupling of BE and FE methods in elastostatics . Eng. Anal. Bound. Elem. , 25 ( 8 ) : 685 – 695 .
   Web of Science ®Google Scholar
• Elleithy , W. and Grzibovskis , R. 2009 . An adaptive domain decomposition coupled finite element – boundary element method for solving problems in elasto-plasticity . Int. J. Numer. Meth. Eng. , 79 ( 8 ) : 1019 – 1040 .
   Web of Science ®Google Scholar
• Elleithy , W. and Langer , U. 2007 . Adaptive FEM–BEM coupling method for elasto-plastic analysis . 8th International Conference on Boundary Element Techniques (BeTeq 2007) . July 2007 , Naples , Italy. pp. 269 – 274 .
   Google Scholar
• Elleithy , W. and Langer , U. Efficient elasto-plastic analysis via an adaptive finite element–boundary element coupling method . Thirtieth International Conference on Boundary Elements and Other Mesh Reduction Methods (BEM/MRM XXX) . July , Maribor , Slovenia. pp. 229 – 238 .
   Google Scholar
• Elleithy , W. M. and Tanaka , M. 2003 . Interface relaxation algorithms for BEM–BEM coupling and FEM–BEM coupling . Comp. Meth. Appl. Mech. Eng. , 192 ( 26–27 ) : 2977 – 2992 .
   Web of Science ®Google Scholar
• Elleithy , W. M. , Tanaka , M. and Guzik , A. 2004 . Interface relaxation FEM–BEM coupling method for elasto-plastic analysis . Eng. Anal. Bound. Elem. , 28 ( 7 ) : 849 – 857 .
   Web of Science ®Google Scholar
• Of , G. , Steinbach , O. and Wendland , W. L. 2005 . Application of a fast multipole Galerkin in boundary element method in linear elastostatics . Comput. Visual. Sci. , 8 ( 3–4 ) : 201 – 209 .
   Google Scholar
• Ganguly , S. , Layton , J. B. and Balakrishma , C. 2000 . Symmetric coupling of multi-zone curved Galerkin boundary elements with finite elements in elasticity . Int. J. Numer. Meth. Eng. , 48 : 633 – 654 .
   Web of Science ®Google Scholar
• Gaul , L. and Wenzel , W. 2002 . A coupled symmetric BE–FE method for acoustic fluid-structure interaction . Eng. Anal. Bound. Elem. , 26 ( 7 ) : 629 – 636 .
   Web of Science ®Google Scholar
• Haas , M. , Helldörfer , B. and Kuhn , G. 2006 . Improved coupling of finite shell elements and 3D boundary elements . Arch. Appl. Mech. , 75 : 649 – 663 .
   Web of Science ®Google Scholar
• Haase , G. , Heise , B. , Kuhn , M. and Langer , U. 1998 . “ Adaptive domain decomposition methods for finite and boundary element equations ” . In Boundary Element Topics , Edited by: Wendland , W. 121 – 147 . Berlin : Springer-Verlag .
   Google Scholar
• Hass , M. and Kuhn , G. 2003 . Mixed-dimensional, symmetric coupling of FEM and BEM . Eng. Anal. Bound. Elem. , 27 ( 6 ) : 575 – 582 .
   Web of Science ®Google Scholar
• Holzer , S. M. 1992 . “ Das Symmetrische Randelementverfahren: Numerische Realisierung und Kopplung mit der Finite-Elemente-Methode zur Elastoplastischen Strukturanalyse ” . Munich : Technische Universität München .
   Google Scholar
• Langer , U. 1994 . Parallel iterative solution of symmetric coupled FE/BE-equation via domain decomposition . Contemp. Math. , 157 : 335 – 344 .
   Google Scholar
• Langer , U. and Steinbach , O. Coupled boundary and finite element tearing and interconnecting methods . Proceedings of the 15th International Conference on Domain Decomposition . July , Berlin , Germany. pp. 83 – 98 .
   Google Scholar
• Mund , P. and Stephan , P. 1999 . An adaptive two-level method for the coupling of nonlinear FEM–BEM equations . SIAM J. Numer. Anal. , 36 ( 4 ) : 1001 – 1021 .
   Web of Science ®Google Scholar
• Owen , D. R.J. and Hinton , E. 1980 . “ Finite Elements in Plasticity: Theory and Practice ” . Swansea , , UK : Pineridge Press .
   Google Scholar
• Polizotto , C. and Zito , M. 1994 . Variational formulations for coupled BE/FE methods in elastostatics . ZAMM , 74 ( 11 ) : 553 – 543 .
   Google Scholar
• Simo , J. C. and Hughes , T. J.R. 1998 . “ Computational Inelasticity ” . New York : Springer .
   Google Scholar
• Sirtori , S. 1979 . General stress analysis method by means of integral equations and boundary elements . Meccanica , 14 : 210 – 218 .
   Google Scholar
• Soares , D. Jr , von Estorff , O. and Mansur , W. J. 2005 . Efficient nonlinear solid-fluid interaction analysis by an iterative BEM/FEM coupling . Int. J. Numer. Meth. Eng. , 64 ( 11 ) : 1416 – 1431 .
   Web of Science ®Google Scholar
• de Souza Neto , E. A. , Periæ , D. and Owen , D. R.J. 2008 . “ Computational Methods for Plasticity: Theory and Applications ” . Chichester : Wiley .
   Google Scholar
• Springhetti , R. , Novati , G. and Margonari , M. 2006 . Weak coupling of the symmetric Galerkin BEM with FEM for potential and elastostatic problems . Comp. Model. Eng. Sci. , 13 : 67 – 80 .
   Web of Science ®Google Scholar
• Steinbach , O. 1998 . Fast solution techniques for the symmetric boundary element method in linear elasticity . Comp. Meth. Appl. Mech. Eng. , 157 : 185 – 191 .
   Web of Science ®Google Scholar
• Stephan , E. P. 2004 . “ Coupling of boundary element methods and finite element methods ” . In Encyclopedia of Computational Mechanics Vol. 1 Fundamentals , Edited by: Stein , E. , de Borst , R. and Hughes , T. J.R. 375 – 412 . Chichester : John Wiley & Sons . Chap. 13
   Google Scholar
• Swoboda , G. , Mertz , W. and Beer , G. 1987 . Rheological analysis of tunnel excavations by means of Coupled Finite Element (FEM)-Boundary Element (BEM) analysis . Int. J. Numer. Anal. Meth. Geomech. , 11 : 115 – 129 .
   Web of Science ®Google Scholar
• Von Estorff , O. and Hagen , C. 2005 . Iterative coupling of FEM and BEM in 3D transient elastodynamics . Eng. Anal. Bound. Elem. , 29 ( 8 ) : 775 – 787 .
   Web of Science ®Google Scholar
• Zienkiewicz , O. C. , Kelly , D. M. and Bettes , P. 1977 . The coupling of the finite element method and boundary solution procedures . Int. J. Numer. Meth. Eng. , 11 : 355 – 375 .
   Web of Science ®Google Scholar
• Zienkiewicz , O. C. , Kelly , D. M. and Bettes , P. 1979 . “ Marriage a la mode – the best of both worlds (Finite elements and boundary integrals) ” . In Energy Methods in Finite Element Analysis , Edited by: Glowinski , R. , Rodin , E. Y. and Zienkiewicz , O. C. 81 – 106 . London : Wiley . Chap. 5, R.
   Google Scholar