Abstract
In this paper a numerical method for the solution of elliptic boundary value problems is presented. As an application we will analyze problems in linear elasticity. Especially we want to resolve zones with high stress gradients, for example the surrounding of notches in a loaded machine part. The stress peak may occur the failure of the whole structure.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Carmine, R. (1989): Ein Kopplungsverfahren von FEM und BEM zur Berechnung ebener Spannungskonzentrationsprobleme. Doctoral Thesis, Karlsruhe University
Chaudonneret, M. (1977): Sur la discontinué du vecteur contrainte dans les calculs de structure par la methode des équations intégrates. CRAS, Paris, Série A 284, 463–466
Clenshaw, C.W., Curtis, A.R. (1960): A method for numerical integration on an automatic computer. Numer. Math. 2, 197–205
Costabel, M., Wendland, W.L. (1986): Strong ellipticity of boundary integral operators. Krelles Journal für die Reine und Angewandte Mathematik 372, 34–63
Cruse, T.A. (1969): Numerical Solutions in Three Dimensional Elastostatics. Int. J. Solids Struct. 5, 1259–1273
Davis, RJ., Rabinowitz, P. (1984): Methods of numerical integration. Second edition, Academic Press, New York
Grannell, J.J. (1987): On simplified hybrid methods for coupling of finite elements and boundary elements. In: Brebbia, C.A., Wendland, W.L., Kuhn, G. (eds.) Boundary elements IX, Vol. 1. Springer, Berlin, pp. 447–460
Guiggiani, M., Gigante, A. (1990): A general algorithm for multidimensional Cauchy principal value integrals in the boundary element method. ASMEJ. Applied Mechanics 57, 907–915
Haack, W., Wendland, W.L. (1969): Vorlesungen über Partielle und Pfaffsche Differentialgleichungen. Birkhauser Verlag, Basel Stuttgart
Hahn, H.G. (1963): Uber den Einflußdes Flankenwinkels auf die Spannungskonzentration an Kerben. Doctoral Thesis, University of Munich
Hsiao, G.C. (1988): The Coupling of BEM and FEM - A Brief Review. In: Brebbia, C.A. et al. (eds.) Boundary Elements X, Vol. 1. Springer, Berlin, pp. 431-445
Hsiao, G.C. (1990): The Coupling of Boundary Element and Finite Element Methods. ZAMM, Z. angew. Math. Mech. 70, 493–503
Hsiao, G.C., Schnack, E., Wendland, W.L. (1995): A Hybrid Coupled Finite-Boundary Element Method. Preprint 95-11, Universit”at Stuttgart, Mathematisches Institut A
Karaosmanoglu, N. (1989): Kopplung von Randelement- und Finite-Element-Verfahren für dreidimensionale elastische Strukturen. Doctoral Thesis, Karlsruhe University
Kieser, R., Schwab, C., Wendland, W.L. (1992): Numerical evaluation of singular and finite part integrals on curved surfaces using symbolic manipulation. Computing 49, 279-301
Kupradze, V.D., Gegelia, T.G., Basheleishvili, M.O., Burchuladze, T.V. (1979): Three dimensional problems of the mathematical theory of elasticity and thermoelasticity. North-Holland Series in Applied Mathematics and Mechanics, Vol. 25, North-Holland Publishing Company, Amsterdam New York Oxford
Kutt, H.R. (1975): The numerical evaluation of principal value integrals by finite-part integration. Numer. Math. 24, 205–210
Lachat, J.C., Watson, J.O. (1976): Effective Numerical Treatment of Boundary Integral Equations: A Formulation for Three- Dimensional Elastostatics. Int. J. Num. Meth. Engng. 10, 991–1005
Li, H.B., Han, G.H., Mang, A.H., Torzick, R (1986): A New Method for Coupling of Finite Elements and Boundary Elements Discretized Subdomains of Elastic Bodies. Computer Methods in Applied Mechanics Engng. 54, 161–185
Nečas, J. (1967): Les methodes directes en théorie des équations elliptiques. Masson, Paris
Neumann, C. (1877): Untersuchungen über das logarithmische und Newtonsche Potential. Teubner, Leipzig
Polizzotto, C., Zito, M. (1994): Variational Formulations for Coupled BE/FE Methods in Elastostatics. ZAMM, Z. angew. Math. Mech. 74, 533–543
Rabinowitz, P., Richter, N. (1970): New error coefficients for estimating quadrature errors for analytic functions. Math. Comp. 24, 561–570
Rieder, G. (1962): Iterationsverfahren und Operatorgleichungen in der Elastizitätstheorie. Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft, Band XIV, Fried. Vieweg k Sohn Verlag, Braunschweig
Schnack, E. (1973): Beitrag zur Berechnung rotationssymmetrischer Spannungskonzentrationsprobleme mit der Methode der Finiten Elemente. Doctoral Thesis, Technical University of Munich
Schnack, E. (1985): Stress Analysis with a Combination of HSM and BEM. Proceedings of the MAFELAP 1984 Conference on “The Mathematics of Finite Elements and Applications”, Academic Press, pp. 273-281
Schnack, E. (1987): A Hybrid BEM-Model. Int. J. Num. Meth. Engng. 24, No. 5, 1015–1025
Schnack, E. (1990): Macro-Elements for 2D- and 3D-Elasticity with BEM. In: Tanaka, M., Brebbia, C.A., Honma, T. (eds.) Boundary Elements XII, Vol. I. Springer, Berlin Heidelberg, pp. 21–31
Schwab, C., Wendland, W.L. (1992): On numerical cubatures of singular surface integrals in boundary element methods. Numer. Math. 62, 343–369
Stroud, A.H., Secrest, D. (1966): Gaussian quadrature formulas. Prentice-Hall Inc., Englewood Cliffs, New York
Taylor, A.E. (1958): Introduction to functional analysis. John Wiley & Sons, New York London Sydney
Telles, J.C.F. (1987): A Self- Adaptive Co-ordinate Transformation for Efficient Numerical Evaluation of General Boundary Element Integrals. Int. J. Num. Meth. Engng. 24, 959–973
Tong, P., Pian, T.H.H., Lasry, S.J. (1973):: A hybrid element approach to crack problems in plane elasticity. Int. J. Num. Meth. Engng. 7, 297–308
Türke, K. (1995): Eine Zweigitter-Methode zur Kopplung von FEM and BEM. Doctoral Thesis, University of Karlsruhe
Wendland, W.L. (1965): Lösung der ersten und zweiten Randwertaufgaben des Innen- und Außengebietes für die Potentialgleichung im R3 durch Randbelegungen. Doctoral Thesis, Technical University of Berlin
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schnack, E., Türke, K. (1997). Coupling of BEM and FEM for Elastic Structures. In: Wendland, W.L. (eds) Boundary Element Topics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60791-2_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-60791-2_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64554-9
Online ISBN: 978-3-642-60791-2
eBook Packages: Springer Book Archive