A 3-D boundary element method for dynamic analysis of anisotropic elastic solids

CMES - Computer Modeling in Engineering and Sciences

Volumn 1, Issue 4, 2000, Pages 27-43

  Kogl M ^a   Gaul, L ^a  

^a NONE

Author keywords

Anisotropy; Boundary element method; Dual reciprocity method; Dynamic analysis; Fundamental solution; Particular solution

Indexed keywords

EID: 0042593569     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (32)

1. Agnantiaris, J. P.; Polyzos, D.; Beskos, D. E. (1998): Three-dimensional structural vibration analysis by the dual reciprocity BEM. Computational Mechanics, vol. 21, pp. 372-381.
2. Ahmad, S.; Banerjee, P. K. (1986): Free vibration analysis by BEM using particular integrals. Journal of Engineering Mechanics ASCE, vol. 112, no. 7, pp. 682-695.
3. Atkinson, K. E. (1985): The numerical evaluation of particular solutions for Poisson's equation. IMA Journal of Numerical Analysis, vol. 5, pp. 319-338.
4. Bacon, D. J.; Barnett, D. M.; Scattergood, R. O. (1980): Progress in materials science, volume 23, chapter 2: Anisotropic continuum theory of lattice defects, pp. 51-262. Pergamon Press, Oxford, 1980.
5. Banerjee, P. K. (1994): The boundary element methods in engineering. McGraw-Hill, London, second edition.
6. Barnett, D. M. (1972): The precise evaluation of derivatives of the anisotropic elastic Green's functions. phys. stat. sol. (b), vol. 49, pp. 741-748.
7. Brebbia, C.; Telles, J.; Wrobel, L. (1984): Boundary element techniques. Springer-Verlag, Berlin.
8. Deb, A. (1991): Advanced development of the BEM for linear and nonlinear analyses of anisotropic solids. PhD thesis, Buffalo State University, 1991.
9. Dederichs, P. H.; Leibfried, G. (1969): Elastic Green's function for anisotropic cubic crystals. Phys. Rev., vol. 188, no. 3, pp. 1175-1183.
10. Ding, H.; Liang, J.; Chen, B. (1997): The united point force solution for both isotropic and transversely isotropic media. Communications in Numerical Methods in Engineering, vol. 13, no. 2, pp. 95-102.
11. Dominguez, J. (1993): Boundary elements in dynamics. Computational Mechanics Publications, Southampton.
12. Gaul, L.; Fiedler, C. (1996): Boundary Element Methods in Statics and Dynamics (in German). Verlag Vieweg, Braunschweig.
13. Gel'fand, I. M.; Graev, M. I.; Vilenkin, N. Y. (1966): Generalized functions, volume 5: Integral geometry and representation theory. Academic Press, New York.
14. Golberg, M. A. (1995): The numerical evaluation of particular solutions in the BEM - a review. Boundary Element Communications, vol. 6, pp. 99-106.
15. Golberg, M. A.; Chen, C. S. (1994): The theory of radial basis functions applied to the BEM for inhomogeneous partial differential equations. Boundary Element Communications, vol. 5, pp. 57-61.
16. Gründemann, H. (1989): A general procedure transferring domain integrals onto boundary integrals in BEM. Engineering Analysis with Boundary Elements, vol. 6, no. 4, pp. 214-222.
17. Houbolt, J. C. (1950): A recurrence matrix solution for the dynamic response of elastic aircraft. J. Aeronautical Sciences, vol. 17, pp. 540-550.
18. Nardini, D.; Brebbia, C. A. (1982): A new approach to free vibration analysis using boundary elements. In Boundary element methods in engineering, pp. 312-326, Berlin. Springer-Verlag.
19. Nardini, D.; Brebbia, C. A. (1985): Topics in boundary element research, volume 2: Time-dependent and vibration problems, chapter 7: Boundary integral formulation of mass matrices for dynamic analysis, pp. 191-208. Springer-Verlag, Berlin, 1985.
20. Nardini, D.; Brebbia, C. A. (1986): Transient boundary element elastodynamics using the dual reciprocity method and modal superposition. In Boundary elements VIII, pp. 435-443, Berlin. Springer-Verlag.
21. Newmark, N. M. (1959): A method of computation for structural dynamics. ASCE. Journal of the Engineering Mechanics Division, vol. 85, pp. 67-94.
22. Pan, Y. C.; Chou, T. W. (1976): Point force solution for an infinite transversely isotropic solid. J. Appl. Mech., vol. 43, no. 4, pp. 608-612.
23. Polyzos, D.; Dassios, G.; Beskos, D. E. (1994). On the equivalence of dual reciprocity and particular integral approaches in the BEM. Boundary Element Communications, vol. 5, pp. 285-288.
24. Powell, M. J. D. (1992): Advances in numerical analysis, volume II, chapter 3: The theory of radial basis function approximation in 1990, pp. 105-210. Oxford Science Publ., Oxford, 1992.
25. Schclar, N. A. (1994): Anisotropic analysis using boundary elements. Computational Mechanics Publications.
26. Vogel, S. M.; Rizzo, F. J. (1973): An integral equation formulation of three dimensional anisotropic elastostatic boundary value problems. J. Elasticity, vol. 3, no. 3, pp. 203-216.
27. Wang, C.-Y.; Achenbach, J. D. (1993): A new method to obtain 3-D Green's functions for anisotropic solids. Wave Motion, vol. 18, pp. 273-289.
28. Wang, C.-Y.; Achenbach, J. D. (1994): Elastodynamic fundamental solutions for anisotropic solids. Geophys. J. Int., vol. 118, pp. 384-392.
29. Wang, C.-Y.; Achenbach, J. D. (1995): Three-dimensional time-harmonic elastodynamic Green's functions for anisotropic solids. Proc. Royal Soc. London A, vol. 449, pp. 441-458.
30. Wang, C. Y.; Achenbach, J. D.; Hirose, S. (1996): Two-dimensional time domain BEM for scattering of elastic waves in solids of general anisotropy. Int. J. Solids Structures, vol. 33, no. 26, pp. 3843-3864.
31. Wilson, R. B.; Cruse, T. A. (1978): Efficient implementation of anisotropic three dimensional boundary-integral equation stress analysis. Int. J. Numer. Meth. Engng., vol. 12, pp. 1383-1397.
32. Zheng, T.; Dravinski, M. (2000): Scattering of elastic waves by a 3D anisotropic basin. Earthquake Engng. Struct. Dyn., vol. 29, pp. 419-439.