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Thin Plates. Kirchhoff Theory

2013
This chapter introduces the study of structures formed by “thin surfaces” such as plates and shells. Plates will be studied in this and the two following chapters. Shell structures formed by assembly of flat plates will be considered in Chapter 8. Axisymmetric shells will be treated in Chapter 9.
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Nonlinear Boundary Conditions in Kirchhoff-Love Plate Theory

Journal of Elasticity, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Iosifescu, Oana, Licht, Christian, Michaille, Gérard   +2 more
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From Kirchhoff to Mindlin plate elements

Communications in Applied Numerical Methods, 1988
AbstractA procedure to generalize Kirchhoff thin plate finite elements so that they can be used for solving thick Mindlin plates is presented. Two typical discrete Kirchhoff elements, a triangular one and a quadrilateral one, are modified. Numerical results for a clamped circular plate show that the accuracy of the new Mindlin elements is the same as ...
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Bending Solutions of Sectorial Mindlin Plates from Kirchhoff Plates

Journal of Engineering Mechanics, 2000
This study presents exact relationships between the bending solutions of sectorial plates based on the Kirchhoff (or classical thin) plate theory and the Mindlin plate theory. While the former plate theory neglects the effect of transverse shear deformation, the latter theory allows for this effect, which becomes significant when dealing with thick ...
Wang, C. M., Lim, G. T.
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Decomposition of plate displacements via Kirchhoff-Love displacements

Mathematical Methods in the Applied Sciences, 2023
In this paper, we show that any displacement of a plate is the sum of a Kirchhoff-Love displacement and two terms, one for shearing and one for warping. Then, the plate is loaded in order to obtain that the bending and shearing contribute the same order of magnitude to the fiber rotations.
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Simply Supported Polygonal Mindlin Plate Deflections Using Kirchhoff Plates

Journal of Engineering Mechanics, 1995
This study presents a derivation of an exact relationship between the deflection values of a simply supported Mindlin plate and the corresponding simply supported Kirchhoff plate. The relationship is valid for any polygonal plate shape and transverse loading condition.
C. M. Wang, W. A. M. Alwis
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Iterative nonlocal elasticity for Kirchhoff plates

International Journal of Mechanical Sciences, 2015
Abstract Recently, the nonlocal elasticity theories have been used in studying the different behaviors of micro/nanostructures. However, there is a complicity in applying the natural boundary conditions in the context of the nonlocal differential elasticity models.
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A NEW FINITE ELEMENT METHOD FOR KIRCHHOFF PLATES

Applied and Industrial Mathematics in Italy II, 2006
Based on the ideas from [1] and [2] we present a new finite element method for the Kirchhoff plate bending model [3]. The method uses C 0 basis functions for the deflection and the rotation, i.e. the same approach as used for the Reissner-Mindlin model. To account for the effective shear force at the free boundary a stabilization term is added.
Beirao da Veiga L, Niiranen J, Stenberg R   +2 more
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A Hybridizable Discontinuous Galerkin Method for Kirchhoff Plates

Journal of Scientific Computing, 2018
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Huang, Jianguo, Huang, Xuehai
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Interface crack between isotropic Kirchhoff plates

Meccanica, 2012
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