Finite element analysis of transient dynamic viscoelastic problems in time domain

Journal of Mechanical Science and Technology

Volumn 19, Issue 1, 2005, Pages 61-71

  Sim, Woo Jin ^a   Lee, Sung Hee ^a  

^a Kumoh National Institute of Technology   (South Korea)

Author keywords

Dynamic Stress Concentration; Finite Element; Viscoelastic; Wave Propagation

Indexed keywords

APPROXIMATION THEORY; DIFFRACTION; EQUATIONS OF MOTION; FINITE ELEMENT METHOD; FOURIER TRANSFORMS; GALERKIN METHODS; LAPLACE TRANSFORMS; STRESS ANALYSIS; TIME DOMAIN ANALYSIS; WAVE PROPAGATION;

DYNAMIC STRESS CONCENTRATION; FINITE ELEMENT; TRANSIENT DYNAMIC VISCOELASTIC PROBLEMS; VISCOELASTIC;

VISCOELASTICITY;

EID: 17044430710     PISSN: 1738494X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02916105     Document Type: Article

References (29)

1. Achenbach, J. D., 1975, Wave Propagation in Elastic Solids, North-Holland, Amsterdam.
2. Bagley, R. L. and Torvik, P. J., 1985, "Fractional Calculus in the Transient Analysis of Viscoelastically Damped Structures," AIAA, Vol. 23, No. 6, pp. 918-925.
3. Barrett, K. E. and Gotts, A. C., 2002, "Finite Element Analysis of a Compressible Dynamic Viscoelastic Sphere Using FFT," Comput. Struct., Vol. 80, pp. 1615-1625.
4. Bathe, K. J., 1996, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs.
5. Beskos, D. E. and Leung, K. L., 1984, "Dynamic Response of Plate Systems by Combining Finite Differences, Finite Elements and Laplace Transform," Comput. Struct., Vol. 19, No. 5-6, pp. 763-775.
6. Chen, X. and Cheng, C., 2000, "Discrete Inverse Method for Viscoelastic Medium with Complete Data," Comput. Methods Appl. Mech. Engrg., Vol. 189, pp. 77-90.
7. Christensen, R. M. 1982, Theory of Viscoelasticity, Academic Press, New York.
8. Dey, S. S. and Rao, V. T. 1997, "Transient Response of Circular Plates and Membranes: A Numerical Approach," Int. J. Mech. Sci., Vol. 39, No. 12, pp. 1405-1413.
9. Doyle, J. F., 1998, "A Spectrally Formulated Finite Element for Longitudinal Wave Propagation," Int. J. Analyt. Exper. Modal Anal., Vol. 3, pp. 1-5.
10. Eldred, L. B., Baker, W. P. and Palazotto, A. N., 1996, "Numerical Application of Fractional Derivative Model Constitutive Relations for Viscoelastic Materials," Comput. Struct., Vol. 60, No. 6, pp. 875-882.
11. Enelund, M., Mähler, L., Runesson, K. and Josefson, B. L., 1999, "Formulation and Integration of the Standard Linear Viscoelastic Solid with Fractional Order Rate Laws," Int. J. Solids Struct., Vol. 36, pp. 2417-2442.
12. Flügge, W., 1975, Viscoelasticity, 2nd edn., Spriger-Verlag, Berlin.
13. Gaul, L. and Schanz, M., 1999, "A Comparative Study of Three Boundary Element Approaches to Calculate the Transient Response of Viscoelastic Solids with Unbounded Domains," Comput. Methods Appl. Mech. Engrg., Vol. 179, pp. 111-123.
14. Golla, D. F. and Hughes, P. C., 1985, "Dynamics of Viscoelastic Structures - A Time-Domain Finite Element Formulation," J. Appl. Mech., Vol. 52, pp. 897-906.
15. Goudreau, G. L., 1970, "Evaluation of Discrete Methods for the Linear Dynamic Response of Elastic and Viscoelastic Solids," Report No. 69-15, Structures and Material Research, Department of Civil Engineering, Structural Engineering Laboratory, University of California, Berkeley, California.
16. Ha, T., Santos, J. E. and Sheen, D., 2002, "Nonconforming Finite Element Methods for the Simulation of Waves in Viscoelastic Solids," Comput. Methods Appl. Mech. Engrg., Vol. 191, pp. 5647-5670.
17. Lee, U. and Kim, J., 2001, "Spectral Element Modeling for the Beams Treated with Active Constrained Layer Damping," Int. J. Solids Struct., Vol. 38, pp. 5679-5702.
18. Li, X. J., Liao, Z. P. and Du, X. L., 1992, "An Explicit Finite Difference Method for Viscoelastic Dynamic Problems," Earthq. Engrg. Engrg. Vib., Vol. 12, No. 4, pp. 74-80.
19. Liu, J. and Sharan, S. K., 1995, "Analysis of Dynamic Contact of Cracks in Viscoelastic Media," Comput. Methods Appl. Mech. Engrg., Vol. 121, pp. 187-200.
20. Manolis, G. D. and Beskos, D. E., 1981, "Dynamic Stress Concentration Studies by Boundary Integrals and Laplace Transform," Int. J. Numer. Methods Eng., Vol. 17, pp. 573-599.
21. Nickell, R. E., 1968, "Stress Wave Analysis in Layered Thermoviscoelastic Materials by the Extended Ritz Method," Technical Report S-175, VII, Rohm & Haas Co., Redstone Research Laboratories, Huntsville, Al.
22. Nickell, R. E., 1971, "On the Stability of Approximation Operators in Problems of Structural Dynamics," Int. J. Solids Struct., Vol. 7, pp. 301-319.
23. Oden, J. T. and Reddy, J. N., 1976, Variational Methods in Theoretical Mechanics, Springer-Verlag, Berlin.
24. Pérez-Gavilán, J. J. and Aliabadi, M. H., 2001, "A Symmetric Galerkin Boundary Element Method for Dynamic Frequency Domain Viscoelastic Problems," Comput. Struct., Vol. 79, pp. 2621-2633.
25. Polyzos, D., Stamos, A. A. and Beskos, D. E., 1994, "BEM Computation of DSIF in Cracked Viscoelastic Plates," Commun. Numer. Methods Engng., Vol. 10, No. 1, pp. 81-87.
26. Sim, W. J. and Lee, S. H., 2002, "Transient Linear Elastodynamic Analysis in Time Domain Based on the Integro-Differential Equations," Int. J. Struct. Eng. Mech., Vol. 14, No. 1, pp. 71-84.
27. Spyrakos, C. C., 1987, "Exact Finite Element Method Analysis of Viscoelastic Tapered Structures to Transient Loads," in W. Pilkey and B. Pilkey, eds., NASA 58th Shock and Vibration Symposium, Vol. 1, NASA, Washington D.C. pp. 361-375.
28. Yi, S. and Hilton, H. H., 1994, "Dynamic Finite Element Analysis of Viscoelastic Composite Plates in the Time Domain," Int. J. Numer. Methods Eng., Vol. 37, pp. 4081-4096.
29. Zienkiewicz, O. C. and Taylor, R. L., 1991, The Finite Element Method, Vol. II, 4th edn., McGraw-Hill, London.