Journal ArticleDOI
The interior solution for linear problems of elastic plates
R. D. Gregory,Frederic Y. M. Wan +1 more
TLDR
In this paper, boundary conditions for the interior solution of circular plate problems with edgewise nonuniform boundary data are discussed in detail and then applied to two specific problems, one of them is concerned with a circular plate compressed by two equal and opposite point forces at the plate rim.Abstract:
1 Necessary conditions have been established recently for the prescribed data along the cylindrical edge(s) of an elastic flat plate to induce only an exponentially decaying elastostatic state. The present paper describes how these conditions may be used to determine the interior solution (or its various thin and thick plate theory approximations) of plate problems. The results in turn show that the necessary conditions for a decaying state are also sufficient conditions. Boundary conditions for the interior solution of circular plate problems with edgewise nonuniform boundary data are discussed in detail and then applied to two specific problems. One of them is concerned with a circular plate compressed by two equal and opposite point forces at the plate rim. The solution process for this problem illustrates for the first time how the stretching action in the plate interior induced by transverse loads can be I properly analyzed.read more
Citations
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The concentration of stress and strain in finite thickness elastic plate containing a circular hole
TL;DR: In this article, the elastic stress and strain fields of a large plate containing a hole are systematically investigated using 3D finite element method, and it is found that the maximum and strain concentration factors of the finite thickness plate are different even if the plate is in elasticity state except at notch root of plate surface.
Journal ArticleDOI
Three-dimensional stress constraint in an elastic plate with a notch
Andrei Kotousov,Chun H. Wang +1 more
TL;DR: In this article, the authors presented analytical solutions for the three-dimensional stress distribution around typical stress concentrators in an isotropic plate of arbitrary thickness, which is a pre-requisite to analyzing the effect of plate thickness on the elastic-plastic deformation at a notch root.
Journal ArticleDOI
On Timoshenko-Reissner type theories of plates and shells
TL;DR: In this paper, linear Timoshenko-Reissner theories of isotropic plates and shells are discussed and the main subject under consideration is the construction of these theories by the asymptotic method and related error estimates for static and dynamic problems.
Journal ArticleDOI
Effect of vertex singularities on stress intensities near plate free surfaces
TL;DR: In this article, the authors proposed a theoretical model for the SIF distribution along the front of a through-the-thickness crack and demonstrated that the asymptotic behavior of SIF near the surface is governed by the difference in the strength of the corner and edge singularities.
Journal ArticleDOI
The general form of the three-dimensional elastic field inside an isotropic plate with free faces
TL;DR: In this paper, the authors gave a rigorous proof that the most general state of stress % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2cf9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x%
References
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Journal ArticleDOI
Decaying states of plane strain in a semi-infinite strip and boundary conditions for plate theory +
TL;DR: In this paper, the classical plate theory of Kirchhoff is the leading term of the outer expansion solution (in a small thickness parameter) for the linear elasto-statics of thin, flat, isotropic bodies.
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Derivation of an approximate theory of bending of a plate by the method of asymptotic integration of the equations of the theory of elasticity
TL;DR: In this article, the authors considered the possibility of making more exact the theory of plates based on Kirchhoff's hypothesis, and formulated the problem of bending a plate as a three-dimensional problem of elasticity which can be solved by an iteration process.
Journal ArticleDOI
On plate theories and Saint-Venant's principle
R. D. Gregory,Frederic Y. M. Wan +1 more
TL;DR: In this article, the authors derived the correct set of boundary conditions for arbitrarily prescribed admissible edge data (without an explicit solution of the inner (or boundary layer) solution) for a number of special cases of general interest, including cases with displacement edge-data.