Finite element modeling of scattering problems involving infinite domains using drilling degrees of freedom

Computer Methods in Applied Mechanics and Engineering

Volumn 134, Issue 1-2, 1996, Pages 57-70

  Kim, Jaehwan ^a   Varadan, Vasundara V ^a   Varadan, Vijay K ^a  

^a The Pennsylvania State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC WAVE SCATTERING; COMPUTER SIMULATION; CONSTRAINT THEORY; EIGENVALUES AND EIGENFUNCTIONS; ELASTIC WAVES; ELECTROMAGNETIC FIELD THEORY; ELECTROMAGNETIC WAVE SCATTERING; FLUIDS; INTERFACES (MATERIALS); MATHEMATICAL MODELS; NUMERICAL ANALYSIS; SCATTERING;

DRILLING DEGREES OF FREEDOM; INFINITE DOMAINS; IRROTATIONAL FLUID; MATHEMATICAL BOUNDARY; MATHEMATICAL DOMAIN COMPLEX; SCATTERING PROBLEMS; SLOPE CONSTRAINT;

FINITE ELEMENT METHOD;

EID: 0030197229     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/0045-7825(96)01023-7     Document Type: Article

References (37)

1. C.A. Brebbia, The Boundary Element Method for Engineers (Wiley, New York, 1980).
2. D.T. Wilton, Acoustic radiation and scattering from elastic structures, Int. J. Numer. Methods Engrg. 13 (1978) 123-138.
3. F. Ursell, Irregular frequencies and the motion of floating bodies, J. Fluid Mech. 105 (1981) 143-156.
4. H.A. Schenck, Improved integral formulation for acoustic radiation problems, J. Acoust. Soc. Am. 44 (1968) 41-58.
5. A.J. Burton and G.F. Miller, The application of integral equation methods to the numerical solution of some exterior boundary value problems, Proc. R. Soc. London, Ser. A 323 (1971) 201-210.
6. S. Liapis, A method for suppressing the irregular frequencies from integral equations in water-structure interaction problems, Comput. Mech. 12 (1993) 59-68.
7. P. Bettess, Infinite elements, Int. J. Numer. Methods Engrg. 11 (1977) 53-64.
8. J.T. Hunt, M.R. Knittel, C.S. Nichols and D. Barach, Finite-element approach to acoustic scattering from elastic structures, J. Acoust. Soc. Am. 57(2) (1975) 287-299.
9. J.H. Su, V.V. Varadan and V.K. Varadan, Finite element eigenfunction method (FFEM) for elastic wave scattering by arbitrary three-dimensional axisymmetric scatterers, J. Appl. Mech., ASME 51 (1984) 1-8.
10. V.V. Varadan, K. Eswaran and V.K. Varadan, A hybrid FEM-T-matrix technique for the analysis of acoustic wave scattering by elastic shells of revolution, J. Wave-mat. Interaction 1 (1986) 237-250.
11. G.J. Fix and S.P. Marin, Variational methods for underwater acoustic problems, J. Comput. Phys. 28 (1978) 253-270.
12. C.I. Goldstein, A finite element method for solving Helmholtz type equations in waveguide and other unbounded domains, Math. Comput. 39(160) (1982) 309-324.
13. B. Engquist and A. Majda, Radiation boundary conditions for acoustic and elastic wave calculations, Comm. Pure Appl. Math. 32 (1979) 313-357.
14. R. Clayton and B. Engquist, Absorbing boundary conditions for acoustic and elastic wave equations, Bull. Seism. Soc. Am. 67(6) (1977) 1529-1540.
15. A. Bayliss and Eli Turkel, Radiation boundary conditions for wave-like equations, Comm. Pure Appl. Math. 33 (1980) 707-725.
16. O.M. Ramahi, A. Khebir and R. Mittra, Numerically derived absorbing boundary condition for the solution of open region scattering problems, IEEE Trans. Antennas Propagation 39(3) (1991) 350-353.
17. D. Givoli and J.B. Keller, Non-reflecting boundary conditions for elastic waves, Wave Motion 12 (1990) 261-279.
18. D. Givoli and J.B. Keller, A finite element method for large domains, Comput. Methods Appl. Mech. Engrg. 76 (1989) 41-66.
19. I. Harari and T.J. Hughes, Analysis of continuous formulations underlying the computation of time-harmonic acoustics in exterior domains, Comput. Methods Appl. Mech. Engrg. 97 (1992) 103-124.
20. D. Givoli and S. Vigdergauz, Finite element analysis of wave scattering from singularities, Wave Motion 20 (1994) 165-176.
21. V.V. Varadan, J. Kim and V.K. Varadan, Modeling the sensor/actuator response of a finite disk transducer flush mounted on a plate subject to fluid loading, J. Acoust. Soc. Am., Vol. 93, No. 4, Pt. 2, pp. 2352, Program of the 125th Meeting, 1993.
22. J. Kim, V.V. Varadan and V.K. Varadan, Finite element modeling of a finite piezoelectric sensor/actuator embedded in a fluid-loaded plate, Proc. North America Conf. on Smart Structures and Materials (SPIE), Vol. 2191, Orlando, FL, 1994.
23. J.H. Su, V.V. Varadan, V.K. Varadan and L. Flax, Acoustic wave scattering by a finite elastic cylinder in water, J. Acoust. Soc. Am. 68(2) (1980) 686-691.
24. Z. Celep and D. Turhan, Finite element solution for reflection of plane harmonic waves from the free surface of a half-space, Comput. Struct. 27(5) (1987) 593-599.
25. L. Jiang and R.J. Rogers, Effects of spatial discretization on dispersion and spurious oscillations in elastic wave propagation, Int. J. Numer. Methods Engrg. 29 (1990) 1205-1218.
26. T. Nakata, N. Takahashi, K. Fujiwara and Y. Shiraki, Comparison of different finite elements for 3-D eddy current analysis, IEEE Trans. Magnetics 26(2) (1990) 434-437.
27. A. Bossavit and I. Mayergoyz, Edge-elements for scattering problems, IEEE Trans. Magnetics 25(4) (1989) 2816-2821.
28. R.D. Cook, D.S. Malkus and M.E. Plesha, Concepts and Applications of Finite Element Analysis (John Wiley, New York, 1989).
29. T.J.R. Hughes and F. Brezzi, On drilling degrees of freedom, Comput. Methods Appl. Mech. Engrg. 72 (1989) 105-121.
30. K.Y. Sze and A. Ghali, A hybrid brick element with rotational degrees of freedom, Comput. Mech. 12 (1993) 147-163.
31. D.J. Allman, A quadrilateral finite element including vertex rotations for plane elasticity analysis, Int. J. Numer. Methods Engrg. 26 (1988) 717-730.
32. M. Iura and S.N. Atluri, Formulation of a membrane finite element with drilling degrees of freedom, Comput. Mech. 9 (1992) 417-428.
33. E.L. Wilson and M. Khalvati, Finite elements for the dynamic analysis of fluid-solid systems, Int. J. Numer. Methods Engrg. 19 (1983) 1657-1668.
34. M.A. Hamdi, Y. Ousset and G. Verchery, A displacement method for the analysis of vibrations of coupled fluid-structure systems, Int. J. Numer. Methods Engrg. 13 (1978) 139-150.
35. V.V. Varadan, Wave propagation and scattering, Lectures notes, The Pennsylvania State University, 1993.
36. L.M. Brekhovskikh, Waves in Layered Media, 2nd edition (Academic Press, New York, 1980).
37. Chongbin Zhao, S. Valliappan and Y.C. Wang, A numerical model for wave scattering problems in infinite media due to P-and SV-wave incidences, Int. J. Numer. Methods Engrg. 33 (1992) 1661-1682.