Improved finite element methods for elastic waves

Computer Methods in Applied Mechanics and Engineering

Volumn 166, Issue 1-2, 1998, Pages 143-164

  Harari, Isaac ^a   Haham, Shmuel ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; ELASTIC WAVES; GALERKIN METHODS; LEAST SQUARES APPROXIMATIONS; PROBLEM SOLVING;

TIME-HARMONIC ELASTIC WAVES;

FINITE ELEMENT METHOD;

EID: 0032206125     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(98)00088-7     Document Type: Article

References (27)

1. [1] J.D. Achenbach, Wave Propagation in Elastic Solids (Elsevier Science Publishers B.V., Amsterdam, 1984).
2. [2] L.P. Franca and E.G. Dutra do Carmo, The Galerkin gradient least-squares method, Comput. Methods Appl. Mech. Engrg. 74 (1989) 41-54.
3. [3] D.C. Gazis, Exact analysis of the plain-strain vibrations of thick-walled hollow cylinders, J. Acoust. Soc. Am. 30 (1958) 786-794.
4. [4] D.C. Gazis, Three-dimensional investigation of propagation of waves in hollow circular cylinders, J. Acoust. Soc. Am. 31 (1959) 568-578.
5. [5] D. Givoli, Numerical Methods for Problems in Infinite Domains (Elsevier Science Publishers, Amsterdam, 1992).
6. [6] D. Givoli and J.B. Keller, A finite element method for large domains, Comput. Methods Appl. Mech. Engrg. 76 (1989) 41-66.
7. [7] D. Givoli and J.B. Keller, Non-reflecting boundary conditions for elastic waves, Wave Motion 12 (1990) 261-279.
8. [8] K. Grosh and P.M. Pinsky, Complex wave-number dispersion analysis of Galerkin and Galerkin least-squares for fluid loaded plates, Comput. Methods Appl. Mech. Engrg. 113 (1994) 67-98.
9. [9] K. Grosh and P.M. Pinsky, Design of Galerkin generalized least squares methods for Timoshenko beams, Comput. Methods Appl. Mech. Engrg. 132 (1996) 1-16.
10. [10] M.J. Grote and J.B. Keller, On nonreflective boundary conditions, J. Comput. Phys. 122 (1995) 231-243.
11. [11] S. Haham, Improved finite element methods for elastic waves, M.Sc. Thesis, Tel Aviv University, Tel Aviv, Israel, 1997.
12. [12] I. Harari, Reducing spurious dispersion, anisotropy and reflection in finite element analysis of time-harmonic acoustics, Comput. Methods Appl. Mech. Engrg. 140 (1997) 39-58.
13. [13] I. Harari and T.J.R. Hughes, Finite element methods for the Helmholtz equation in an exterior domain: model problems, Comput. Methods Appl. Mech. Engrg. 87 (1991) 59-96.
14. [14] I. Harari and T.J.R. Hughes, Analysis of continuous formulation underlying the computation of time-harmonic acoustics in exterior domains, Comput. Methods Appl. Mech. Engrg. 97 (1992) 103-124.
15. [15] I. Harari and T.J.R. Hughes, Galerkin/least-squares finite element methods for the reduced wave equation with non-reflective boundary condition in unbounded domains, Comput. Methods Appl. Mech. Engrg. 98 (1992) 411-454.
16. [16] I. Harari and T.J.R. Hughes, Stabilized finite element methods for steady advection-diffusion with production, Comput. Methods Appl. Mech. Engrg. 115 (1994) 165-191.
17. [17] I. Harari and T.J.R. Hughes, Studies of domain-based formulations for computing exterior problems of acoustics, Int. J. Numer. Methods Engrg. 37 (1994) 2935-2950.
18. [18] I. Harari and Z. Shohet, On non-reflecting boundary conditions in unbounded elastic solids, Comput. Methods Appl. Mech. Engrg. 163 (1998) 123-139.
19. [19] T.J.R. Hughes, The Finite Element Method (Prentice-Hall, Englewood Cliffs, New Jersey, 1987).
20. [20] R. Mullen and T. Belytschko, Dispersion analysis of finite element semidiscretizations of two-dimensional wave equation, Int. J. Numer. Methods Engrg. 18 (1982) 11-29.
21. [21] Z. Shohet, Analysis of non-reflecting boundary conditions in unbounded elastic solids, M.Sc. Thesis, Tel Aviv University, Tel Aviv, Israel, 1996.
22. [22] I.S. Sokolnikoff, Mathematical Theory of Elasticity (McGraw-Hill Book Company, New York, 1956).
23. [23] I. Stakgold, Boundary Value Problems of Mathematical Physics, Vol. 2 (Macmillan, New York, 1968).
24. [24] L.L. Thompson and P.M. Pinsky, A Galerkin/least-squares finite element method for the two-dimensional Helmholtz equation, Int. J. Numer. Methods Engrg. 38 (1995) 371-397.
25. [25] S.P. Timoshenko and J.N. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1970).
26. [26] C.H. Wilcox, A generalization of theorems of Rellich and Atkinson, Proc. of Amer. Math. Soc. 7 (1956) 271-276.
27. [27] C.H. Wilcox, Scattering Theory for the d'Alembert Equation in Exterior Domains (Springer-Verlag, Berlin, 1975).