×

Symmetric coupling of multi-zone curved Galerkin boundary elements with finite elements in elasticity. (English) Zbl 0986.74073

The paper presents an efficient symmetric coupling of a symmetric Galerkin multi-zone curved boundary element method with a finite element method (FEM) for two-dimensional elastic problems. The existing collocation-based multi-zone boundary element methods are not symmetric. Thus, when they are coupled with FEM, it is very difficult to achieve the symmetry by increasing the computational work to solve the problem. Here the authors present a fully symmetric curved multi-zone Galerkin boundary element approach that is coupled to 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.

MSC:

74S15 Boundary element methods applied to problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Brebbia, Applied Mathematical Modelling 3 pp 212– (1979) · Zbl 0406.73009
[2] 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, Journal Acoustical Society of America 88 pp 2459– (1990)
[4] Sirtori, International Journal for Numerical Methods in Engineering 35 pp 255– (1992) · Zbl 0768.73089
[5] Maier, Computer Methods in Applied Mechanics and Engineering 92 pp 193– (1991) · Zbl 0744.73043
[6] Polizzotto, Computer Methods in Applied Mechanics and Engineering 69 pp 167– (1988) · Zbl 0629.73069
[7] Hartman, Ingenieur-Archiv 55 pp 440– (1985) · Zbl 0573.73094
[8] Maier, Computer Methods in Applied Mechanics and Engineering 60 pp 175– (1987) · Zbl 0602.73081
[9] A variational approach to boundary element methods. In Boundary Element Methods in Applied Mechanics, (eds). Pergamon Press: Oxford, UK, 1989; 13-24.
[10] Gray, International Journal for Numerical Methods in Engineering 29 pp 1133– (1990) · Zbl 0717.73081
[11] Gray, Engineering Analysis with Boundary Elements 6 pp 165– (1991)
[12] Guiggiani, Journal of Applied Mechanics 59 pp 604– (1991) · Zbl 0765.73072
[13] Holzer, Communication in Applied Numerical Methods
[14] The symmetric Galerkin BEM in elasticity: FEM/BEM coupling, Integration and Adaptivity. Unpublished personal communication.
[15] 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, (ed.). 7-11 September, 1992, Elsevier Science Publishers: Amsterdam, 1992.
[16] Kane, International Journal for Numerical Methods in Engineering 36 pp 2157– (1993) · Zbl 0802.73077
[17] Symbolic computation of hypersingular boundary integrals. In Advances in Boundary Element Techniques. (eds), Springer: Berlin, 1993.
[18] Balakrishna, Computer Methods in Applied Mechanics and Engineering 111 pp 335– (1994) · Zbl 0846.73071
[19] Balakrishna, Computer Methods in Applied Mechanics and Engineering 117 pp 157– (1994) · Zbl 0851.73073
[20] Layton, International Journal for Numerical Methods in Engineering 40 pp 2913– (1997) · Zbl 0909.73084
[21] Ganguly, International Journal for Numerical Methods in Engineering 44 pp 991– (1999) · Zbl 0966.74075
[22] Li, Computer Methods in Applied Mechanics 54 pp 161– (1986) · Zbl 0566.73070
[23] On asymptotic error estimates for the combined boundary and finite element method. Fachbereich Mathematik, Technische Hochschule Darmstadt, Preprint No. 929.
[24] Mitsui, International Journal Numerical Analytical Methods Geomechanics 9 pp 161– (1985) · Zbl 0558.73070
[25] Zienkiewicz, International Journal for Numerical Methods in Engineering 11 pp 355– (1977) · Zbl 0347.65048
[26] Coupling boundary element methods with other numerical methods. In Developments in Boundary Element Methods, (ed.). vol. 1, chapter. 10. Applied Science: London, 1979.
[27] Solution of soil-structure interaction problems by coupled boundary element-finite element method. Ph.D. Dissertation, Virginia Polytechnic Institute and State University, 1986.
[28] The coupling of BEM and FEM for exterior boundary value problems. In Boundary Elements. (ed.) Pergamon Press: Oxford, 1986; 77-86.
[29] Hsiao, ZAMM 70 pp 493– (1990) · Zbl 0732.73062
[30] Integrated techniques for coupled elastoplastic BEM and FEM analysis. Masters Thesis, The University of New Mexico, 1992.
[31] Chia-Ching, Computers and Structures 39 pp 899– (1996)
[32] Rigby, International Journal for Numerical Methods in Engineering 38 pp 1507– (1995) · Zbl 0830.73076
[33] Boundary Element Analysis in Engineering Continuum Mechanics. Prentice-Hall: Englewood Cliffs, NJ, 1992.
[34] Symmetric coupling of Galerkin boundary elements with finite elements. Ph.D. Dissertation, Clarkson University, 1997.
[35] Cruse, Mathematical Computational Modeling 15 pp 103– (1991) · Zbl 0725.73089
[36] Martinez, International Journal for Numerical Methods in Engineering 20 pp 1941– (1984) · Zbl 0539.73123
[37] Boundary Element Techniques. Springer: Berlin, 1984.
[38] 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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.