Skip to main content

Coupling of BEM and FEM for Elastic Structures

  • Conference paper
Boundary Element Topics
  • 158 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Carmine, R. (1989): Ein Kopplungsverfahren von FEM und BEM zur Berechnung ebener Spannungskonzentrationsprobleme. Doctoral Thesis, Karlsruhe University

    Google Scholar 

  2. 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

    MATH  Google Scholar 

  3. Clenshaw, C.W., Curtis, A.R. (1960): A method for numerical integration on an automatic computer. Numer. Math. 2, 197–205

    Article  MathSciNet  MATH  Google Scholar 

  4. Costabel, M., Wendland, W.L. (1986): Strong ellipticity of boundary integral operators. Krelles Journal für die Reine und Angewandte Mathematik 372, 34–63

    Article  MathSciNet  MATH  Google Scholar 

  5. Cruse, T.A. (1969): Numerical Solutions in Three Dimensional Elastostatics. Int. J. Solids Struct. 5, 1259–1273

    Article  MATH  Google Scholar 

  6. Davis, RJ., Rabinowitz, P. (1984): Methods of numerical integration. Second edition, Academic Press, New York

    MATH  Google Scholar 

  7. 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

    Google Scholar 

  8. 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

    MathSciNet  Google Scholar 

  9. Haack, W., Wendland, W.L. (1969): Vorlesungen über Partielle und Pfaffsche Differentialgleichungen. Birkhauser Verlag, Basel Stuttgart

    MATH  Google Scholar 

  10. Hahn, H.G. (1963): Uber den Einflußdes Flankenwinkels auf die Spannungskonzentration an Kerben. Doctoral Thesis, University of Munich

    Google Scholar 

  11. 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

    Google Scholar 

  12. Hsiao, G.C. (1990): The Coupling of Boundary Element and Finite Element Methods. ZAMM, Z. angew. Math. Mech. 70, 493–503

    Article  MATH  Google Scholar 

  13. 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

    Google Scholar 

  14. Karaosmanoglu, N. (1989): Kopplung von Randelement- und Finite-Element-Verfahren für dreidimensionale elastische Strukturen. Doctoral Thesis, Karlsruhe University

    Google Scholar 

  15. 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

    Google Scholar 

  16. 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

    Google Scholar 

  17. Kutt, H.R. (1975): The numerical evaluation of principal value integrals by finite-part integration. Numer. Math. 24, 205–210

    Article  MathSciNet  MATH  Google Scholar 

  18. 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

    Article  MATH  Google Scholar 

  19. 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

    Article  MATH  Google Scholar 

  20. Nečas, J. (1967): Les methodes directes en théorie des équations elliptiques. Masson, Paris

    Google Scholar 

  21. Neumann, C. (1877): Untersuchungen über das logarithmische und Newtonsche Potential. Teubner, Leipzig

    Google Scholar 

  22. Polizzotto, C., Zito, M. (1994): Variational Formulations for Coupled BE/FE Methods in Elastostatics. ZAMM, Z. angew. Math. Mech. 74, 533–543

    Article  MathSciNet  MATH  Google Scholar 

  23. Rabinowitz, P., Richter, N. (1970): New error coefficients for estimating quadrature errors for analytic functions. Math. Comp. 24, 561–570

    Article  MathSciNet  MATH  Google Scholar 

  24. Rieder, G. (1962): Iterationsverfahren und Operatorgleichungen in der Elastizitätstheorie. Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft, Band XIV, Fried. Vieweg k Sohn Verlag, Braunschweig

    Google Scholar 

  25. Schnack, E. (1973): Beitrag zur Berechnung rotationssymmetrischer Spannungskonzentrationsprobleme mit der Methode der Finiten Elemente. Doctoral Thesis, Technical University of Munich

    Google Scholar 

  26. 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

    Google Scholar 

  27. Schnack, E. (1987): A Hybrid BEM-Model. Int. J. Num. Meth. Engng. 24, No. 5, 1015–1025

    Article  MATH  Google Scholar 

  28. 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

    Google Scholar 

  29. Schwab, C., Wendland, W.L. (1992): On numerical cubatures of singular surface integrals in boundary element methods. Numer. Math. 62, 343–369

    Article  MathSciNet  MATH  Google Scholar 

  30. Stroud, A.H., Secrest, D. (1966): Gaussian quadrature formulas. Prentice-Hall Inc., Englewood Cliffs, New York

    MATH  Google Scholar 

  31. Taylor, A.E. (1958): Introduction to functional analysis. John Wiley & Sons, New York London Sydney

    MATH  Google Scholar 

  32. 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

    Article  MATH  Google Scholar 

  33. 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

    Article  MATH  Google Scholar 

  34. Türke, K. (1995): Eine Zweigitter-Methode zur Kopplung von FEM and BEM. Doctoral Thesis, University of Karlsruhe

    Google Scholar 

  35. 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

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints 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

Publish with us

Policies and ethics