Boundary Integral Formulation of Mass Matrices for Dynamic Analysis

  • D. Nardini
  • C. A. Brebbia
Part of the Topics in Boundary Element Research book series (TBOU, volume 2)

Abstract

A novel alternative method for dynamic analysis in solid mechanics using boundary elements is presented in this chapter. The basic principles of vibrations of solids are briefly reviewed in order to provide the necessary background for the derivation of the method and interpretation of the numerical results. For a more detailed study of elastodynamics, [1–3] are recommended.

Keywords

Crest Summing Pentech 

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References

  1. 1.
    Achenbach, J.D., Wave Propagation in Elastic Solids. North Holland, 1973Google Scholar
  2. 2.
    Love, A.E.H., A Treatise on the Mathematical Theory of Elasticity. Dover, 1944Google Scholar
  3. 3.
    Clough, R.W. and Penzien, J., Dynamics of Structures. McGraw-Hill, 1975Google Scholar
  4. 4.
    Cruse, T.A. and Rizzo, F.J., A Direct Formulation and Numerical Solution of the General Transient Elastodynamic Problem. J. Math. Anal. Appl. 22, 1968Google Scholar
  5. 5.
    Wong, G.I.K. and Hutchinson, J.R., An Improved Boundary Element Method for Plate Vibrations, in Boundary Element Methods. Ed. C.A. Brebbia, Springer-Verlag, Berlin, 1981Google Scholar
  6. 6.
    Niwa, Y., Kobayashi, S., and Kitahara, M., Application of the Boundary Integral Equation Method to Eigenvalue Problems in Elastodynamics, in Boundary Element Methods in Engineering. Ed. C.A. Brebbia, Springer-Verlag, Berlin, 1982Google Scholar
  7. 7.
    Manolis, G.D. and Beskos, D.E., Dynamic Stress Concentration Studies by Boundary Integral and Laplace Transform. Int. J. Numerical Methods in Engineering 17, 573 — 599, 1981Google Scholar
  8. 8.
    Bellman, R.E., Kalaba, R.E., and Lockett, J., Numerical Inversion of the Laplace Transform. Elsevier, New York, 1966MATHGoogle Scholar
  9. 9.
    Nardini, D. and Brebbia, C.A., A New Approach to Free Vibration Analysis Using Boundary Elements, in Boundary Element Methods in Engineering. Ed. C.A. Brebbia, Springer-Verlag, 1982Google Scholar
  10. 10.
    Brebbia, C.A. and Nardini, D., Dynamic Analysis in Solid Mechanics by an Alternative Boundary Element Procedure. Int. Jour. Soil Dyn. Earthquake Eng. 2, 1983Google Scholar
  11. 11.
    Nardini, D. and Brebbia, C.A., Transient Dynamic Analysis by the Boundary Element Method, in Boundary Elements. Ed. C.A. Brebbia, Springer-Verlag, Berlin, 1983Google Scholar
  12. 12.
    Dominguez, J. and Alarcon, E., Elastodynamics, in Progress in Boundary Elements 1, Ed. C.A. Brebbia, Pentech Press and Wiley, 1981Google Scholar
  13. 13.
    Geers, T.L., Boundary Element Methods for Transient Response Analysis, in Computational Methods for Transient Analysis. Ed. T. Belytschko and T.J.R. Hughes, North Holland, 1983Google Scholar
  14. 14.
    Cole, D.M., Kosloff, D.D., and Minster, J.B., A Numerical Boundary Integral Equation Method for Elastodynamics. Bull. Seism. Soc. Amer. 68, 1978Google Scholar
  15. 15.
    Mansur, W. and Brebbia, C.A., Transient Dynamic Analysis by the Boundary Element Method, in Boundary Elements. Ed. C.A. Brebbia, Springer-Verlag, Berlin and New York, 1983Google Scholar
  16. 16.
    Mansur, W. and Brebbia, C.A., Elastodynamics, Chapt. 5 in this volumeGoogle Scholar
  17. 17.
    Brebbia, C.A., J. Telles, and L. Wrobel, Boundary Element Techniques — Theory and Applications in Engineering. Springer-Verlag, Berlin and New York, 1984CrossRefMATHGoogle Scholar
  18. 18.
    Danson, D.J., A Boundary Element Formulation of Problems in Linear Isotropic Elasticity with Body Forces, in Boundary Element Methods. Ed. C.A. Brebbia, Springer-Verlag, 1983Google Scholar
  19. 19.
    Wilkinson, J.H., The Algebraic Eigenvalue Problem. Oxford University Press, 1965Google Scholar
  20. 20.
    Bathe, K.J. and Wilson, E.L., Stability and Accuracy Analysis of Direct Integration Methods. Int. Journ. Earthq. Eng. Struc. Dyn. 1, 1973Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • D. Nardini
  • C. A. Brebbia

There are no affiliations available

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