Generalized plane deformation of electromagnetic thermoelastic solids I. Correspondence and invariance shifts

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 455, Issue 1984, 1999, Pages 1283-1299

  Zheng, Q S ^a   Chen, T ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Complete invariance shifts; Correspondence relations; Electromagnetic thermoelasticity; Fibrous composites; Generalized plane deformation; Invariance of fields

Indexed keywords

EID: 0004541691     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1999.0361     Document Type: Article

References (21)

1. Chen, T. 1995 Further results on invariant properties of the stress in plane elasticity and its extension to piezoelectricity. Mech. Res. Commun. 22, 251-256.
2. Chen, T. 1998 Further correspondences between plane piezoelectricity and generalized plane strain in elasticity. Proc. R. Soc. Lond. A 454, 873-884.
3. Chen, T. & Lai, D. 1997 An exact correspondence between plane piezoelectricity and generalized plane strain in elasticity. Proc. R. Soc. Lond. A 453, 2689-2713.
4. Cherkaev, A. V., Lurie, K. A. & Milton, G. W. 1992 Invariant properties of the stress in plane elasticity and equivalence classes of composites. Proc. R. Soc. Lond. A 438, 519-529.
5. Day, A. R., Snyder, K. A., Garboczi, E. J. & Thorpe, M. F. 1992 The elastic moduli of a sheet containing circular holes. J. Mech. Phys. Solids 40, 1031-1051.
6. Dundurs, J. 1967 Effect of elastic constants on stress in a composite under plane deformation. J. Composite Mater. 1, 310-322.
7. Dundurs, J. & Markenscoff, X. 1993 Invariance of stresses under a change in elastic compliances. Proc. R. Soc. Lond. A 443, 289-300.
8. Eringen, A. C. 1980 Mechanics of continua. Huntington, New York: R. E. Krieger.
9. Bringen, A. C. & Maugin, G. A. 1990 Electrodynamics of continua, vol. I. New York: Springer.
10. Hahn, T. 1987 Space-group symmetry. In International tables for crystallography, vol. A, 2nd edn. Dordrecht: D. Reidel.
11. Hashin, Z. & Shtrikman, S. 1963 A Variational approach to the theory of the elastic behavior of multiphase material. J. Mech. Phys. Solids 11, 127-140.
12. He, Q.-C. 1998 More on stress invariance conditions for the traction boundary value problem of plane linear elasticity. Int. J. Solids & Struct. 35, 3519-3537.
13. Hill, R. 1964 Theory of mechanical properties of fibre-strengthened materials. I. Elastic behaviour. J. Mech. Phys. Solids 12, 199-212.
14. Lekhnitskii, S. G. 1981 Theory of elasticity of an anisotropic body (translated from the revised 1977 Russian edition). Moscow: Mir.
15. Milton, G. W. 1997 Composites: a myriad of microstructurc independent relations. In Theoretical and applied mechanics 1996 (ed. T. Tatsumi, E. Watanabe & T. Kambe), pp. 443-459. Amsterdam: North-Holland.
16. Moran, B. & Gosz, M. 1994 Stress invariance in plane anisotropic elasticity. Modelling Simul. Mater. Sci. Engng 2, 677-688.
17. Muskhelishvili, N. I. 1953 Some basic problems of the mathematical theory of elasticity (translated by J. R. M. Radok). Groningen: Noordhoff.
18. Nye, J. F. 1985 Physical properties of crystals. Their representation by tensors and matrices. Oxford University Press.
19. Thorpe, M. F. & Jasiuk, I. 1992 Discussion of some exact results in the theory of elasticity for two-dimensional composites. Proc. R. Soc. Lond. A 438, 531-544.
20. Zheng, Q.-S. 1994 Theory of representations for tensor functions-a unified invariant approach to constitutive equations. Appl. Mech. Rev. 47, 545-587.
21. Zheng, Q.-S. & Chen, T. 1999 Generalized plane deformation of electromagnetic thermoelastic solids. II. Further results on invariance shifts and reduced dependences. Proc. R. Soc. Lond. A 455, 1301-1314. (Following paper.)