A framework for nonlinear shells based on generalized stress and strain measures

International Journal of Solids and Structures

Volumn 34, Issue 13, 1997, Pages 1609-1632

  Hackl, Klaus ^a  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTOPLASTICITY; MATHEMATICAL MODELS; STRAIN RATE; STRESS CONCENTRATION; THERMOELASTICITY; VARIATIONAL TECHNIQUES; YIELD STRESS;

BIORTHOGONAL FUNCTION SYSTEM; NEO HOOKEAN MATERIAL; SHELL THEORY; VON MISES YIELD CONDITION;

SHELLS (STRUCTURES);

EID: 0031146111     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(96)00109-6     Document Type: Article

References (21)

1. Antman, S. S. (1995). Nonlinear Problems of Elasticity. Applied Mathematical Sciences. Vol. 107, Springer, New York.
2. Ciarlet, P. G. (1980). A justification of the von Kármán equations. Arch. Rat. Mech. Anal. 73, 349-389.
3. Ciarlet, P. G. (1988). Mathematical Elasticity, Vol. 1: Three-Dimensional Elasticity, North-Holland, Amsterdam.
4. Crisfield, M. A. (1991). Non-linear Finite Element Analysis of Solids and Structures. Vol. 1, John Wiley and Sons. New York.
5. Davet, J. L. (1986). Justification de modèles de plaques non linéaires pour des lois de comportement générales. Modelisation Math. Anal. Num. 20, 225-249.
6. Destuynder, P. and Nguyen, Q. S. (1985). Derivation of the inelastic behavior of plates and shells from the three dimensional models and extensions. In Inelastic Behavior of Plates and Shells. IUTAM Symposium, Rio de Janeiro, Brazil (eds L. Bevilacqua, R. Feijóo and R. Valid), pp. 49-67, Springer, New York.
7. Dikmen, M. (1982). Theory of Thin Elastic Shells, Pitman, London.
8. Fox, D. D., Raoult, A. and Simo, J. C. (1993). A justification of non-linear properly invariant plate theories. Arch. Rat. Mech. Anal. 124, 157-199.
9. Gilbert, R. P. and Hackl. K. (1995). The elastic-plastic plate. In Asymptotic Theories for Plates and Shells (eds R. P. Gilbert and K. Hackl), pp. 55-66, Pitman Research Notes in Mathematics Series 319, Longman, UK.
10. Gilbert, R. P. and Hackl, K. (1995). The two-dimensional, linear thermoelastic plate. In Asymptotic Theories for Plates and Shells (eds R. P. Gilbert and K. Hackl), pp. 67 80. Pitman Research Notes in Mathematics Series 319, Longman, UK.
11. Hackl, K. (1995). Generalized standard media and variational principles in classical and finite strain elasto-plasticity. Prepared for publication.
12. Lee, E. H. (1969). Elastic-plastic deformation at finite strains. J. Appl. Mech. 36, 1-6.
13. Marsden, J. E. and Hughes, T. J. R. (1983). Mathematical Foundations of Elasticity, Prentice-Hall. Englewood Cliffs, NJ.
14. Mukherjee, S. and Kollmann, F. G. (1985). A new rate principle suitable for analysis of inelastic deformation of plates and shells. J. Appl. Mech. 107, 533-535.
15. Naghdi, M. (1972). The theory of shells. In Handbuch der Physik Bd. Vla/2 (ed. C. Truesdell), Springer, Berlin.
16. Rockafellar, R. T. (1974). Conjugate Duality and Optimization. CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 16. SIAM, Philadelphia.
17. Simo, J. C. and Fox, D. D. (1989). On a stress resultant geometrically exact shell model. Part I. Formulation and optimal parametrization. Computer Meths. Appl. Mech. Engng 72, 267-304.
18. Simo, J. C. and Kennedy, J. G. (1992). On a stress resultant geometrically exact shell model. Part V. Nonlinear plasticity: formulation and integration algorithms. Computer Meths. Appl. Mech. Engng 96, 133-171.
19. Simo, J. C. and Miehe, C. (1992). Associative coupled thermoplastichy at finite strains: formulation, numerical analysis and implementation. Computer Meths. Appl. Mech. Engng 98, 41-104.
20. Truesdell, C. and Noll, W. (1965). The nonlinear field theories of mechanics. In Handbuch der Physik Bd. III/3 (ed. S. Fluegge), Springer, Berlin.
21. Zienkiewicz, O. C. and Taylor, R. L. (1991). The Finite Element Method, Vol. 1. McGraw-Hill, UK, fourth edition.