Reflections on the Theory of Elastic Plates

[+] Author and Article Information
Eric Reissner

University of California at San Diego, La Jolla CA 92093

Appl. Mech. Rev 38(11), 1453-1464 (Nov 01, 1985) (12 pages) doi:10.1115/1.3143699 History: Online June 12, 2009


We depart from a three-dimensional statement of the problem of small bending of elastic plates, for a survey of approximate two-dimensional theories, beginning with Kirchhoff’s fourth-order formulation. After discussing various variational statements of the three-dimensional problem, we describe the development of two-dimensional sixth-order theories by Bollé, Hencky, Mindlin, and Reissner which take account of the effect of transverse shear deformation. Additionally, we report on an early analysis by Lévy, on a direct two-dimensional formulation of sixth-order theory, on constitutive coupling of bending and stretching of laminated plates, on higher than sixth-order theories, and on an asymptotic analysis of sixth-order theory which leads to a fourth-order interior solution contribution with first-order transverse shear deformation effects included, as well as to a sequentially determined second-order edge zone solution contribution.

Copyright © 1985 by American Society of Mechanical Engineers
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