Generalization of Plane Stress and Plane Strain States to Elastic Plates of Finite Thickness

This paper presents a novel method to establish a general solution for an isotropic homogeneous elastic plate of finite thickness. Under the assumption of vanishing out-of-plane shear stresses, a necessary condition of solvability of elastic problems is obtained. Moreover, a general solution depende...

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Bibliographic Details
Published inJournal of elasticity Vol. 140; no. 2; pp. 243 - 256
Main Authors Li, Xian-Fang, Hu, Zhen-Liang
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.08.2020
Springer Nature B.V
Subjects
Automotive Engineering
Biharmonic equations
Classical Mechanics
Elastic plates
Physics
Physics and Astronomy
Plane strain
Plane stress
Shear stress
Stress functions
Stress state
Thickness
74G05
Plane stress state
74B05
Three-dimensional elastic problems
Elasticity solution
Plane strain state
74A99
74A10
Elastic plate
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Summary:This paper presents a novel method to establish a general solution for an isotropic homogeneous elastic plate of finite thickness. Under the assumption of vanishing out-of-plane shear stresses, a necessary condition of solvability of elastic problems is obtained. Moreover, a general solution dependent on the thickness-wise coordinate is derived, where the unknown function is still governed by a two-dimensional biharmonic equation. In terms of the two-dimensional Airy stress function or the classical solution in plane strain state, exact elastic stresses in an elastic plate of finite thickness are given. The solution for plane strain state can be a special case of the present, whereas that classic plane stress state is reduced by letting thickness approach zero. A comparison of the results between the present paper and plane stress state is made.
ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-020-09768-7