A relook at Reissner’s theory of plates in bending Authors K. Vijayakumar Department of Aerospace Engineering Indian Institute of Science Original

First Online: 08 February 2011 Received: 13 January 2010 Accepted: 24 January 2011 DOI :
10.1007/s00419-011-0513-4

Cite this article as: Vijayakumar, K. Arch Appl Mech (2011) 81: 1717. doi:10.1007/s00419-011-0513-4
Abstract Shear deformation and higher order theories of plates in bending are (generally) based on plate element equilibrium equations derived either through variational principles or other methods. They involve coupling of flexure with torsion (torsion-type) problem and if applied vertical load is along one face of the plate, coupling even with extension problem. These coupled problems with reference to vertical deflection of plate in flexure result in artificial deflection due to torsion and increased deflection of faces of the plate due to extension. Coupling in the former case is eliminated earlier using an iterative method for analysis of thick plates in bending. The method is extended here for the analysis of associated stretching problem in flexure.

Keywords Plates Bending Isotropy Elasticity This work is dedicated to Eric Reissner (1913–1996) whose works on plate theories have inspired several investigators on development of higher order theories of plates.

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