A relook at Reissner’s theory of plates in bending
 K. Vijayakumar
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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 (torsiontype) 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.
 Reissner, E. (1944) On the theory of bending of elastic plates. J. Math. Phys. 23: pp. 184191
 Reissner, E. (1985) Reflections on the theory of elastic plates. Appl. Mech. Rev. 38: pp. 14531464 CrossRef
 Lo, K.H., Christensen, R.M., Wu, E.M. (1977) A higherorder theory of plate deformation. J. Appl. Mech. 44: pp. 663676 CrossRef
 Lo, K.H., Christensen, R.M., Wu, E.M. (1978) Stress determination for higherorder plate theory. Int. J. Solids Struct. 14: pp. 655662 CrossRef
 Lewinski, T. (1986) A note on recent developments in the theory of elastic plates with moderate thickness. Eng. Trans. 34: pp. 531542
 Lewinski, T. (1987) On refined plate models based on kinematical assumptions. Ingenieur Arch. 57: pp. 133146 CrossRef
 Blocki, J. (1992) A higherorder linear theory for isotropic platesi, theoretical considerations. Int. J. Solids Struct. 29: pp. 825836 CrossRef
 Kienzler, R. (2002) On consistent plate theories. Arch. Appl. Mech. 72: pp. 229247 CrossRef
 Batista, M. (2010) The derivation of the equations of moderately thick plates by the method of successive approximations. Acta Mech. 210: pp. 159168 CrossRef
 Reissner, E. (1945) The effect of transverse shear deformations on the bending of elastic plates. J. Appl. Mech. 12: pp. A69A77
 Reissner, E. (1947) On bending of elastic plates. Q. Appl. Math. 5: pp. 5568
 Reissner, E. (1950) On a variational theorem in elasticity. J. Math. Phys. 29: pp. 9095
 Vijayakumar, K. (1988) Poisson–Kirchhoff paradox in flexure of plates. AIAA J. 26: pp. 247249 CrossRef
 Vasiliev, V.V. (2000) Modern conceptions of plate theory. Compos. Struct. 48: pp. 3948 CrossRef
 Love, A.E.H. (1934) A Treatise on Mathematical Theory of Elasticity. Cambridge University Press, Cambridge
 Vijayakumar, K. (2009) A new look at Kirchhoff’s theory of plates. AIIA J. 47: pp. 10451046 CrossRef
 Preusser, G. (1984) Eine systematische Herleitung verbesserter Plattengleichungen. Ingenieur Arch. 54: pp. 5161 CrossRef
 Krenk, S. (1981) Theories for elastic plates via orthogonal polynomials. Trans. ASME 48: pp. 900904 CrossRef
 Krishna Murthy, A.V. (1988) Higherorder theory of homogeneous plate flexure. AIIA J. 26: pp. 719725 CrossRef
 Reddy, J.N. (1984) A simple higher order theory for laminated composite plates. J. Appl. Mech. 51: pp. 745752 CrossRef
 Reissner, E. (1983) A twelvth order theory of transverse bending of transversely isotropic plates. ZAMM 63: pp. 285289 CrossRef
 Lewinski, T. (1990) On the twelthorder theory of elastic plates. Mech. Res. Commun. 17: pp. 375382 CrossRef
 Reissner, E. (1991) A mixed variational equation for a twelfthorder theory of bending of nonhomogeneous transversely isotropic plates. Comput. Mech. 7: pp. 355360 CrossRef
 Cheng, S. (1979) Elasticity theory of plates and a refined theory. J. Appl. Mech. 46: pp. 644650 CrossRef
 Wang, W., Shi, M.X. (1997) Thick plate theory based on general solutions of elasticity. Acta Mech. 123: pp. 2736 CrossRef
 Gao, Y., Zhao, B.S. (2009) A refined theory of elastic thick plates for extensional deformation 79: pp. 518
 Gol’denveizer, A.L., Kolos, A.V. (1965) On the derivation of twodimensional equations in the theory of thin elastic plates. PMM 29: pp. 141155
 Touratier, M. (1991) An efficient standard plate theory. Int. J. Eng. sci. 29: pp. 901916 CrossRef
 Title
 A relook at Reissner’s theory of plates in bending
 Journal

Archive of Applied Mechanics
Volume 81, Issue 11 , pp 17171724
 Cover Date
 20111101
 DOI
 10.1007/s0041901105134
 Print ISSN
 09391533
 Online ISSN
 14320681
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Plates
 Bending
 Isotropy
 Elasticity
 Industry Sectors
 Authors

 K. Vijayakumar ^{(1)}
 Author Affiliations

 1. Department of Aerospace Engineering, Indian Institute of Science, Bangalore, 560012, India