On the dynamic deformation of porous Cosserat linear-thermoelastic shells

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 88, Issue 1, 2008, Pages 74-78

  Bîrsan, Mircea ^a  

^a ALEXANDRU IOAN CUZA UNIVERSITY OF IASI   (Romania)

Author keywords

Cosserat surfaces; Existence of solution; Porous thermoelastic shells

Indexed keywords

EID: 38749097458     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.200610361     Document Type: Article

References (19)

1. P.A. Zhilin, Mechanics of deformable directed surfaces, Int. J. Solids Struct. 12, 635 (1976).
2. R. Kienzler, H. Altenbach, and I. Ott, Theories of shells and plates: critical review and new applications, Lecture Notes in Applied and Computational Mechanics Vol. 16 (Springer, Berlin, 2004).
3. J. W. Nunziato and S. C. Cowin, A nonlinear theory of elastic materials with voids, Arch. Ration. Mech. Anal. 72, 175 (1979).
4. S. C. Cowin and J. W. Nunziato, Linear elastic materials with voids, J. Elast. 13, 125 (1983).
5. D. Iesan, A theory of thermoelastic materials with voids, Acta Mech. 60, 67 (1986).
6. P. M. Naghdi, The Theory of Shells and Plates, in: Handbuch der Physik Vol. VIa/2, edited by W. Flügge (Springer-Verlag, Berlin, 1972), pp. 425-640.
7. M. B. Rubin, Cosserat Theories: Shells, Rods, and Points (Kluwer Academic Publishers, Dordrecht, 2000).
8. A. E. Green and P. M. Naghdi, On thermodynamics and the nature of the second law, Proc. R. Soc. Lond. A 357, 253 (1977).
9. A. E. Green and P.M. Naghdi, On thermal effects in the theory of shells, Proc. R. Soc. Lond. A 365, 161 (1979).
10. M. Bîrsan, On the theory of elastic shells made from a material with voids, Int. J. Solids Struct. 43, 3106 (2006).
11. M. Bîrsan, On a thermodynamic theory of porous Cosserat elastic shells, J. Therm. Stresses 29, 879 (2006).
12. M. B. Rubin and Y. Benveniste, A Cosserat shell model for interphases in elastic media, J. Mech. Phys. Solids 52, 1023 (2004).
13. M. Bîrsan, Inequalities of Korn's type and existence results in the theory of Cosserat elastic shells, J. Elast., DOI: 10.1007/s 10659-007-9140-2 (in print, 2007).
14. C. Davini, Existence of weak solutions in linear elastostatics of Cosserat surfaces, Meccanica (Italy) 10, 225 (1975).
15. M. Bîrsan, Existence and uniqueness of weak solutions in the linear theory of elastic shells with voids, Libertas Math. 20, 95 (2000).
16. P. Neff, A geometrically exact Cosserat shell-model including size effects, avoiding degeneracy in the thin shell limit. Part I: Formal dimensional reduction for elastic plates and existence of minimizers for positive Cosserat couple modulus, Contin. Mech. Thermodyn. 16, 577 (2004).
17. P. Neff, A geometrically exact planar Cosserat shell-model with microstructure: existence of minimizers for zero Cosserat couple modulus, Math. Models Methods Appl. Sci. 17, 363 (2007).
18. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Series in Applied Mathematical Sciences Vol.44 (Springer-Verlag, New York, 1983).
19. I.I. Vrabie, Co-Semigroups and Applications, Series in Mathematics Studies Vol. 191 (North-Holland, Elsevier, Amsterdam, 2003).