Development of a fundamental-solution-less boundary element method for exterior wave problems

Communications in Numerical Methods in Engineering

Volumn 24, Issue 4, 2008, Pages 257-279

  Song, Chongmin ^a   Bazyar, Mohammad Hossein ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Absorbing boundary; Scaled boundary finite element method; Transmitting boundary; Unbounded domain; Wave propagation

Indexed keywords

BOUNDARY ELEMENT METHOD; COMPUTATIONAL EFFICIENCY; FINITE ELEMENT METHOD; STIFFNESS MATRIX;

PARTIAL SCHUR DECOMPOSITION; SHAPE FUNCTIONS;

WAVE EQUATIONS;

BOUNDARY ELEMENT METHOD; COMPUTATIONAL EFFICIENCY; FINITE ELEMENT METHOD; STIFFNESS MATRIX; WAVE EQUATIONS;

EID: 42149173902     PISSN: 10698299     EISSN: 10990887     Source Type: Journal    
DOI: 10.1002/cnm.964     Document Type: Article

References (37)

1. Sommerfeld A. Partial Differential Equations in Physics (Chapter 28). Academic Press: New York, 1949.
2. Geers TL (ed.). Proceedings of the IUTAM Symposium on Computational Methods for Unbounded Domains. Kluwer Academic Publishers: Dordrecht, 1997.
3. Gazetas G. Analysis of machine foundation vibrations: state of the art. Soil Dynamics and Earthquake Engineering 1983; 2:2-42.
4. Wolf JP. A comparison of time-domain transmitting boundaries, Earthquake Engineering and Structural Dynamics 1986; 14:655-673.
5. Kausel E. Local transmitting boundaries. Journal of Engineering Mechanics (ASCE) 1988; 114:1011-1027.
6. Givoli D. High-order non-reflecting boundary conditions: a review. Wave Motion 2004; 39:319-326.
7. Wolf JP. Dynamic Soil-Structure Interaction. Prentice-Hall: Englewood Cliffs, NJ, 1985.
8. Wolf JP. Soil-Structure-Interaction Analysis in Time Domain. Prentice-Hall: Englewood Cliffs, NJ, 1988.
9. Wolf JP, Song Ch. Finite-Element Modelling of Unbounded Media. Wiley: Chichester, 1996.
10. Beskos DE. Boundary element methods in dynamic analysis. Applied Mechanics Reviews (ASME) 1987; 40:1-23.
11. Beskos DE. Boundary element methods in dynamic analysis: Part II (1986-1996). Applied Mechanics Reviews (ASME) 1997; 50:149-197.
12. Dominguez J. Boundary Elements in Dynamics. Computational Mechanics Publications: Southampton, 1993.
13. Hall WS, Oliveto G. Boundary Element Methods for Soil-Structure Interaction. Kluwer Academic Publishers: Dordrecht, 2003.
14. Song Ch, Wolf JP. Consistent infinitesimal finite-element-cell method: out-of-plane motion. Journal of Engineering Mechanics (ASCE) 1995; 121:613-619.
15. Wolf JP, Song Ch. Consistent infinitesimal finite-element cell method: in-plane motion. Computer Methods in Applied Mechanics and Engineering 1995; 123:355-370.
16. Song Ch, Wolf JP. Consistent infinitesimal finite-element cell method: three-dimensional vector wave equation. International Journal for Numerical Methods in Engineering 1996; 39:2189-2208.
17. Song Ch, Wolf JP. The scaled boundary finite-element method - alias consistent infinitesimal finite-element cell method - for elastodynamics. Computer Methods in Applied Mechanics and Engineering 1997; 147:329-355.
18. Wegner JL, Zhang X. Free-vibration analysis of a three-dimensional soil-structure system. Earthquake Engineering and Structural Dynamics 2001; 30:43-57.
19. Ekevid T, Wiberg NE. Wave propagation related to high-speed train: a scaled boundary FE-approach for unbounded domains. Computer Methods in Applied Mechanics and Engineering 2002; 191:3947-3964.
20. Yan JY, Zhang CH, Jin F. A coupling procedure of FE and SBFE for soil-structure interaction in the time domain. International Journal for Numerical Methods in Engineering 2004; 59:1453-1471.
21. Genes MC, Kocak S. Dynamic soil-structure interaction analysis of layered unbounded media via a coupled finite element/boundary element/ scaled boundary finite element model. International Journal for Numerical Methods in Engineering 2005; 62:798-823.
22. Wegner J, Yao M, Zhang X. Dynamic wave-soil-structure interaction analysis in the time domain. Computers and Structures 2005; 83:2206-2214.
23. Fan SC, Li SM, Yu GY. Dynamic fluid-structure interaction analysis using boundary finite element method-finite element method. Journal of Applied Mechanics (ASME) 2005; 72:591-598.
24. Lehmann L. An effective finite element approach for soil-structure analysis in the time-domain. Structural Engineering and Mechanics 2005; 21:437-450.
25. Song Ch. Weighted block-orthogonal base functions for static analysis of unbounded domains. Proceedings of the 6th World Congress on Computational Mechanics, Beijing, China, 5-10 September 2004; 615-620.
26. Song Ch. Dynamic analysis of unbounded domains by a reduced set of base functions. Computer Methods in Applied Mechanics and Engineering 2006; 195:4075-4094.
27. Song Ch, Bazyar MH. A boundary condition in Padé series for frequency-domain solution of wave propagation in unbounded domains. International Journal for Numerical Methods in Engineering, in press.
28. Wolf JP, Song Ch. The scaled boundary finite-element method - a primer: derivations. Computers and Structures 2000; 78:191-210.
29. Lehoucq RB, Sorensen DC, Yang C. ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM: Philadelphia, PA, 1998.
30. Song Ch. A matrix function solution for the scaled boundary finite-element equation in statics. Computer Methods in Applied Mechanics and Engineering 2004; 193:2325-2356.
31. Cook RD, Malkus DS, Plesha ME, Witt RJ. Concepts and Applications of Finite Element Analysis. Wiley: New York, 2002.
32. Hughes TJR. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice-Hall: Englewood Cliffs, NJ, 1987.
33. Fried I, Malkus DS. Finite element mass matrix lumping by numerical integration with no convergence rate loss. International Journal of Solids and Structures 1975; 11:461-466.
34. Canuto C, Hussaini MY, Quarteroni A, Zeng TA. Spectral Methods in Fluid Dynamics. Springer: Berlin, 1988.
35. Vu T, Deeks AJ. Use of higher-order shape functions in the scaled boundary finite element method. International Journal for Numerical Methods in Engineering 2006; 65:1714-1733.
36. Bazyar MH, Song Ch. Time-harmonic response of non-homogeneous elastic unbounded domains using the scaled boundary finite-element method. Earthquake Engineering and Structural Dynamics 2006; 35:357-383.
37. Rajapakse RKND, Wang Y. Elastodynamic green's functions of orthotropic half plane. Earthquake Engineering and Structural Dynamics 1991; 20:927-947.