Artigo Revisado por pares

Symmetric coupling of multi-zone curved Galerkin boundary elements with finite elements in elasticity

2000; Wiley; Volume: 48; Issue: 5 Linguagem: Inglês

10.1002/(sici)1097-0207(20000620)48

ISSN

1097-0207

Autores

S. Ganguly, Jeffrey B. Layton, C. Balakrishna,

Tópico(s)

Vibration and Dynamic Analysis

Resumo

International Journal for Numerical Methods in EngineeringVolume 48, Issue 5 p. 633-654 Research Article Symmetric coupling of multi-zone curved Galerkin boundary elements with finite elements in elasticity S. Ganguly, Corresponding Author S. Ganguly [email protected] Mechanical and Aeronautical Engineering Department, Clarkson University, Postdam, NY 13699, U.S.A. Ph.D. Candidate. Currently, Scientist, SID, NAL Bangalore-560017, India117 Benaras Road, Salkia, Howrah, West Bengal 711106, IndiaSearch for more papers by this authorJ. B. Layton, J. B. Layton Mechanical and Aeronautical Engineering Department, Clarkson University, Postdam, NY 13699, U.S.A. Assistant Professor. Currently, Senior Engineer, Flight Sciences Group, Lockheed-Martin Aeronautical Systems, Marietta GeorgiaSearch for more papers by this authorC. Balakrishna, C. Balakrishna Mechanical and Aeronautical Engineering Department, Clarkson University, Postdam, NY 13699, U.S.A. Director of Computer Simulation, Center for the Advancement of Instruction in Science and Engineering (CAISE) Currently, Robust Engineer, GM Truck Group 2000 Centerpoint Pky, Pontiac, MI 48341-3147, U.S.A.Search for more papers by this author S. Ganguly, Corresponding Author S. Ganguly [email protected] Mechanical and Aeronautical Engineering Department, Clarkson University, Postdam, NY 13699, U.S.A. Ph.D. Candidate. Currently, Scientist, SID, NAL Bangalore-560017, India117 Benaras Road, Salkia, Howrah, West Bengal 711106, IndiaSearch for more papers by this authorJ. B. Layton, J. B. Layton Mechanical and Aeronautical Engineering Department, Clarkson University, Postdam, NY 13699, U.S.A. Assistant Professor. Currently, Senior Engineer, Flight Sciences Group, Lockheed-Martin Aeronautical Systems, Marietta GeorgiaSearch for more papers by this authorC. Balakrishna, C. Balakrishna Mechanical and Aeronautical Engineering Department, Clarkson University, Postdam, NY 13699, U.S.A. Director of Computer Simulation, Center for the Advancement of Instruction in Science and Engineering (CAISE) Currently, Robust Engineer, GM Truck Group 2000 Centerpoint Pky, Pontiac, MI 48341-3147, U.S.A.Search for more papers by this author First published: 20 April 2000 https://doi.org/10.1002/(SICI)1097-0207(20000620)48:5 3.0.CO;2-KCitations: 22 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract The coupling of Finite Element Method (FEM) with a Boundary Element Method (BEM) is a desirable result that exploits the advantages of each. This paper examines the efficient symmetric coupling of a Symmetric Galerkin Multi-zone Curved Boundary Element Analysis method with a Finite Element Method for 2-D elastic problems. Existing collocation based multi-zone boundary element methods are not symmetric. Thus, when they are coupled with FEM, it is very difficult to achieve symmetry, increasing the computational work to solve the problem. This paper uses a fully Symmetric curved Multi-zone Galerkin Boundary Element Approach that is coupled to an FEM in a completely symmetric fashion. The symmetry is achieved by symmetrically converting the boundary zones into equivalent 'macro finite elements', that are symmetric, so that symmetry in the coupling is retained. This computationally efficient and fast approach can be used to solve a wide range of problems, although only 2-D elastic problems are shown. Three elasticity problems, including one from the FEM-BEM literature that explore the efficacy of the approach are presented. Copyright © 2000 John Wiley & Sons, Ltd. REFERENCES 1 Brebbia CA, Georgion P. Combination of boundary and finite elements in elastostatics. Applied Mathematical Modelling 1979; 3: 212–220. 2 Eberhardsteiner J, Mang HA, Torzicky P. Three dimensional elasto-plastic BE-FE stress analysis of the excavation of a tunnel bifurcation on the basis of a substructuring technique. In Advances in Boundary Element Techniques. Springer: Berlin, 1993; 103–128. 3 Jeans RA, Matthews IC. Solution of fluid-structure interaction problems using a coupled finite element and vibrational boundary element technique. Journal Acoustical Society of America 1990; 88: 2459–2466. 4 Sirtori S, Maier G, Novati G, Miccoli S. A Galerkin symmetric boundary-element method in elasticity: formulation and implementation. International Journal for Numerical Methods in Engineering 1992; 35: 255–282. 5 Maier G, Diligenti M, Carini A. A variational approach to boundary element elastodynamic analysis and extension to multidomain problems. Computer Methods in Applied Mechanics and Engineering 1991; 92: 193–213. 6 Polizzotto C. An energy approach to the boundary element method, part I: elastic solids. Computer Methods in Applied Mechanics and Engineering 1988; 69: 167–184. 7 Hartman F, Katz C, Protopsaltis B. Boundary elements and symmetry. Ingenieur-Archiv 1985; 55: 440–449. 8 Maier G, Polizzotto C. A Galerkin approach to boundary element elastoplastic analysis. Computer Methods in Applied Mechanics and Engineering 1987; 60: 175–194. 9 Polizzotto C, Zito M. A variational approach to boundary element methods. In Boundary Element Methods in Applied Mechanics, M Tanaka, T Cruse (eds). Pergamon Press: Oxford, UK, 1989; 13–24. 10 Gray LJ, Martha LF, Ingraffea AR. Hypersingular integral in boundary element fracture analysis. International Journal for Numerical Methods in Engineering 1990; 29: 1133–1158. 11 Gray LJ. Boundary element methods for regions with thin internal cavities. Engineering Analysis with Boundary Elements 1991; 6: 165–174. 12 Guiggiani M, Krishnasamy G, Rudolphi TJ, Rizzo FJ. A general algorithm for numerical solution of hypersingular boundary integral equations. Journal of Applied Mechanics 1991; 59: 604–614. 13 Holzer SM. How to deal with hypersingular integrals in the symmetric BEM. No. 670, Communication in Applied Numerical Methods, submitted for publication. 14 Holzer SM. The symmetric Galerkin BEM in elasticity: FEM/BEM coupling, Integration and Adaptivity. Unpublished personal communication. 15 Holzer SM. The symmetric Galerkin BEM for plane elasticity: scope and applications. In Numerical Methods in Engineering '92. Proceedings of the First European Conference on Numerical Methods in Engineering, Brussels, Ch Hirsch. (ed.). 7–11 September, 1992, Elsevier Science Publishers: Amsterdam, 1992. 16 Kane JH, Balakrishna C. Symmetric Galerkin boundary formulations employing curved elements. International Journal for Numerical Methods in Engineering 1993; 36: 2157–2187. 17 Gray LJ. Symbolic computation of hypersingular boundary integrals. In Advances in Boundary Element Techniques. JH Kane, G Maier, N Tosaka, SN Atluri (eds), Springer: Berlin, 1993. 18 Balakrishna C, Gray LJ, Kane JH. Efficient analytical integration of symmetric Galerkin boundary integrals over curved elements. Thermal conduction formulation. Computer Methods in Applied Mechanics and Engineering 1994; 111: 335–355. 19 Balakrishna C, Gray LJ, Kane JH. Efficient analytical integration of symmetric Galerkin boundary integral over curved elements; elasticity formulation. Computer Methods in Applied Mechanics and Engineering 1994; 117: 157–179. 20 Layton JB, Ganguly S, Balakrishna C, Kane JH. A symmetric Galerkin multi-zone boundary element formulation. International Journal for Numerical Methods in Engineering 1997; 40: 2913–2931. 21 Ganguly S, Layton JB, Balakrishna C, Kane JH. A fully symmetric Galerkin multi-zone boundary element formulation. International Journal for Numerical Methods in Engineering 1999; 44: 991–1009. 22 Li H-B, Han G-M, Mang HA, Torzicky P. A new method for the coupling of finite element and boundary element discretized subdomains of elastic bodies. Computer Methods in Applied Mechanics 1986; 54: 161–185. 23 Wendland WL. On asymptotic error estimates for the combined boundary and finite element method. Fachbereich Mathematik, Technische Hochschule Darmstadt, Preprint No. 929. 24 Mitsui Y, Ichikawa Y, Obara Y, Kawamato T. A coupling scheme for boundary and finite elements using a joint element. International Journal Numerical Analytical Methods Geomechanics 1985; 9: 161–175. 25 Zienkiewicz OC, Kelly DW, Bettes P. The coupling of finite element and boundary solution procedures. International Journal for Numerical Methods in Engineering 1977; 11: 355–375. 26 Kelly DW, Mustoe G, Zienkiewicz OC. Coupling boundary element methods with other numerical methods. In Developments in Boundary Element Methods, OC Zienkiewicz (ed.). vol. 1, chapter. 10. Applied Science: London, 1979. 27 Zerco MA. Solution of soil-structure interaction problems by coupled boundary element-finite element method. Ph.D. Dissertation, Virginia Polytechnic Institute and State University, 1986. 28 Hsiao GC, Porter JF. The coupling of BEM and FEM for exterior boundary value problems. In Boundary Elements. Qinghua Du (ed.) Pergamon Press: Oxford, 1986; 77–86. 29 Hsiao GC. The coupling of boundary and finite element methods. ZAMM 1990; 70: 493–450. 30 Prasad NNV. Integrated techniques for coupled elastoplastic BEM and FEM analysis. Masters Thesis, The University of New Mexico, 1992. 31 Chia-Ching Lin, Lawton EC, Caliendo JA, Anderson LR. An iterative finite element-boundary element algorithm. Computers and Structures 1996; 39: 899–909. 32 Rigby RH, Alliabadi MH. Out of core solver for large, multi-zone boundary element matrices. International Journal for Numerical Methods in Engineering 1995; 38: 1507–1533. 33 Kane JH. Boundary Element Analysis in Engineering Continuum Mechanics. Prentice-Hall: Englewood Cliffs, NJ, 1992. 34 Ganguly S. Symmetric coupling of Galerkin boundary elements with finite elements. Ph.D. Dissertation, Clarkson University, 1997. 35 Cruse TA, Osias JR. Issues in merging the finite element and boundary integral equation methods. Mathematical Computational Modeling, 1991; 15: 103–118. 36 Martinez J, Dominguez J. On the use of quarter-point boundary elements for stress intensity factor computations. International Journal for Numerical Methods in Engineering 1984; 20: 1941–1950. 37 Brebbi CA, Tellis JCF, Wroble LC. Boundary Element Techniques. Springer: Berlin, 1984. 38 Wawtzynek P, Gray L, Ingraffea A. A new boundary element formulation for the simulation of discrete damage in composite joints. AIAA Paper 97-1125, Presented at the AIAA/ASME/ASCE/AHS/ACS structures. Structural Dynamics and Materials Conference, Kissimmee, FL, April 1997. Citing Literature Volume48, Issue520 June 2000Pages 633-654 ReferencesRelatedInformation

Referência(s)