Generalized thermoelastic-piezoelectric problem by hybrid laplace transform-finite element method

International Journal for Computational Methods in Engineering Science and Mechanics

Volumn 8, Issue 3, 2007, Pages 137-147

  Aouadi, Moncef ^a  

^a Rustaq Faculty of Education   (Oman)

Author keywords

Finite element method; Laplace transform; Piezoelectricity; Thermoelasticity

Indexed keywords

LAPLACE TRANSFORMS; PIEZOELECTRICITY; PROBLEM SOLVING; THERMOELASTICITY;

HEAT PROPAGATION; NUMERICAL LAPLACE INVERSION; PIEZOELECTRIC PLATES; THERMAL SHOCK PROBLEMS;

FINITE ELEMENT METHOD;

EID: 34147214423     PISSN: 15502287     EISSN: 15502295     Source Type: Journal    
DOI: 10.1080/15502280701252404     Document Type: Article

References (32)

1. R. D. Mindlin, On the equations of motion of piezoelectric crystals, in: N. I. Muskelishvili (Ed.), Mechanics, 70th Birthday Volume, pp. 282-290, SIAM, Philadelphia, 1961.
2. R. D. Mindlin, Equation of high frequency of thermo-piezoelectric crystals Plates, in Interactions in Elastic Solids, Springer, Wein, 1979.
3. W. Nowacki, Foundation of linear piezoelectricity, in H. Parkus (Ed.), Electromagnetic Interactions in Elastic Solids, chap. 1, Springer, Wein, 1979.
4. W. Nowacki, Some general theorems of thermo-piezoelectricity, Journal of Thermal Stresses, vol. 1, pp. 171-182, 1978.
5. W. Nowacki, New problems in mechanics of continua, in Mathematical Modes of Phenomenological Piezoelectricity, pp. 29-49, University of Waterloo Press, ON, Canada, 1983.
6. D. S. Chandrasekharaiah, A temperature rate dependent theory of piezoelectricity, Journal of Thermal Stresses, vol. 7, pp. 293-306, 1984.
7. D. S. Chandrasekharaiah, A generalized linear thermoelasticity theory of piezoelectric media, Acta Mechanica, vol. 71, pp. 39-49, 1988.
8. H. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech. Phys., vol. 15, pp. 299-309, 1967.
9. A. E. Green and K. A. Lindsay, Thermoelasticity, J. Elasticity, vol. 2, pp. 1-7, 1972.
10. D. Y. Tzou, A unified approach for heat conduction from macro to microscales, J. of Heat Transfer, vol. 117, pp. 8-16, 1995.
11. D. S. Chandrasekharaiah, Hyperbolic thermoelasticity, a review of recent literature, Appl. Mech. Rev., vol. 51, pp. 705-729, 1998.
12. D. D. Joseph and L. Preziosi, Heat waves, Rev. Mod. Phys., vol. 61, pp. 41-73, 1989.
13. D. D. Joseph and L. Preziosi, Addendum to the paper: Heat waves, Rev. Mod. Phys., vol. 62, pp. 375-391, 1990.
14. R. B. Hetnarski and J. Ignaczak, Generalized thermoelasticity, J. Thermal Stresses, vol. 22, pp. 451-476, 1999.
15. T. C. Chen and C. I. Weng, Coupled transient thermoelastic response in an axisymmetric circular cylinder by Laplace transform-finite method, Comput. Struct., vol. 33, pp. 533-542, 1989.
16. T. C. Chen and C. I. Weng, Generalized coupled transient thermoelastic plane problems by Laplace transform-finite method, J. Appl. Mech., vol. 55, pp. 377-382, 1988.
17. H. Tianhu, S. Yapeng, and T. Xiaogeng, Two-dimensional generalized thermal shock problem for a half-space in electromagneto-thermoelasticity, Int. J. Eng. Sci., vol. 42, pp. 809-823, 2004.
18. J. Awrejcewicz and V. A. Krysko, Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells, Springer Verlag, Berlin, 2003.
19. J. N. Sharma and M. Pal, Propagation of Lamb waves in a transversely isotropic piezothermoelectric plate, J. Sound Vibr., vol. 270, pp. 587-610, 2004.
20. M. Aouadi, Generalized thermo-piezoelectric problems with temperature-dependent properties, Int. J. Solids Structures, vol. 43, pp. 6347-6358, 2006.
21. G. Honig and U. Hirdes, A method for the numerical inversion of the Laplace transform, J. Comp. Appl. Math., vol. 10, pp. 113-132, 1984.
22. F. Durbin, Numerical inversion of Laplace transforms: an effective improvement of Dubner and Abate's method, Comput. J., vol. 17, pp. 371-376, 1973.
23. M. Aouadi, Discontinuities in an axisymmetric generalized thermoelastic problem, Int. J. Math. Math. Sci., vol. 7, pp. 1015-1029, 2005.
24. M. Aouadi, Generalized three dimensional heat source problem for small time, Int. J. Comput. Meth. Eng. Sci. Mech., vol. 7, pp. 59-67, 2006.
25. M. Aouadi, Variable electrical and thermal conductivity in the theory of generalized thermoelastic diffusion, Z. Angew. Math. Phys., vol. 57, pp. 350-366, 2006.
26. M. Aouadi, Hybrid Laplace transform-finite element method to a generalized electromagneto-thermoelastic problem, Appl. Math. Modelling, vol. 31, pp. 712-726, 2007.
27. J. D. Achenbach, Wave Propagation in Elastic Solids, North-Holland, Amsterdam, 1973.
28. M. Chester, Second sounds in solids, Phys. Rev., vol. 131, pp. 2013-2015, 1963.
29. A. Nayfeh and S. N. Nasser, Thermoelastic waves in solids with thermal relaxation, Acta Mechanica, vol. 12, pp. 53-69, 1971.
30. R. E. Peiers, Quantum Theory of Solids, Oxford University Press, London, 1955.
31. R. K. Bhangale and N. Ganesan, Free vibration of functionally graded nonhomogeneous magneto-electro-elastic cylindrical shell," International Journal for Computational Methods in Engineering Science and Mechanics, vol. 7, pp. 191-200, 2006.
32. J. N. Reddy, Theory and Analysis of Elastic Plates and Shells, 2nd ed., Taylor and Francis, Philadelphia, 2007.