Classical plate buckling theory as the small-thickness limit of three-dimensional incremental elasticity

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 94, Issue 1-2, 2014, Pages 7-20

  Steigmann, D J ^a   Ogden, R W ^b,c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF ABERDEEN   (United Kingdom)

^c UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

Elastic stability.; Incremental elasticity; Plate buckling

Indexed keywords

EID: 84891751865     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.201200160     Document Type: Article

References (17)

1. H.L. Cox, The Buckling of Plates and Shells (Pergamon-McMillan, New York, 1963).
2. A.M.A. van der Heijden, W. T. Koiter's Elastic Stability of Solids and Structures (Cambridge University Press, Cambridge, 2009).
3. G. Fichera, Existence Theorems in Elasticity. In: Handbuch der Physik, Vol. VIa/2 edited by C. Truesdell, (Springer, Berlin, 1972), pp. 347-389.
4. R.W. Ogden, Non-linear Elastic Deformations (Dover, New York, 1997).
5. R.J. Knops and E.W. Wilkes, Theory of Elastic Stability. In: Handbuch der Physik, Vol. VIa/3 edited by C. Truesdell (Springer, Berlin, 1973), pp. 125-302.
6. R. Hill, On uniqueness and stability in the theory of finite elastic strain, J. Mech. Phys. Solids 5, 229-241 (1957).
7. W.T. Koiter, A Basic Open Problem in the Theory of Elastic Stability. Joint IUTAM/IMU Symposium on Applications of Methods of Functional Analysis to Problems in Mechanics, Sept. 1-6, Part XXIX, Marseille, 1975 (Springer, Berlin, Heidelberg, 1975).
8. Y.B. Fu, Perturbation Methods and Nonlinear Stability Analysis. In: Nonlinear Elasticity, Theory and Applications, edited by Y. B. Fu and R. W. Ogden, London Mathematical Society Lecture Note Series, 283 (Cambridge University Press, Cambridge, 2001).
9. D.J. Steigmann, Two-dimensional models for the combined bending and stretching of plates and shells based on three-dimensional linear elasticity, Int. J. Eng. Sci. 46, 654-76 (2008).
10. D.J. Steigmann, Refined theory for linearly elastic plates: laminae and laminates, Math. Mech. Solids (2012), doi: 10.1177/1081286511419971.
11. A.E. Green and W. Zerna, Theoretical Elasticity, 2nd edition (Oxford University Press, Oxford, 1968).
12. D.J. Steigmann, Applications of Polyconvexity and Strong Ellipticity to Nonlinear Elasticity and Elastic Plate Theory, in: CISM Course on Applications of Poly-, Quasi-, and Rank-One Convexity in Applied Mechanics, Vol. 516 edited by J. Schröder and P. Neff (Springer, Wien, New York, 2010), pp. 265-299.
13. M.G. Hilgers and A.C. Pipkin, The Graves condition for variational problems of arbitrary order, IMA. J. Appl. Math. 48, 265-269 (1992).
14. R.T. Shield, The rotation associated with large strain, SIAM J. Appl. Math. 25, 483-491 (1973).
15. R. Paroni, Theory of linearly elastic residually stressed plates, Math. Mech. Solids 11, 137-159 (2006).
16. D.J. Steigmann, Linear theory for the bending and extension of a thin, residually stressed, fiber-reinforced lamina, Int. J. Eng. Sci. 47, 1367-1378 (2009).
17. R.W. Ogden and B. Singh, Propagation of waves in an incompressible transversely isotropic solid with initial stress: Biot revisited, J. Mech. Mater. Struct. 6, 453-477 (2011).