Closed form solutions of axisymmetric bending of circular plates having non-linear variable thickness

A new analytical method for evaluation of elastic stresses and deformations in axisymmetric plates having variable thickness according to a power of a linear function, either solid or annular, subjected to symmetrical bending due to lateral loads either distributed on upper surface or distributed al...

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Bibliographic Details
Published in:International journal of mechanical sciences 2010-09, Vol.52 (9), p.1234-1252
Main Authors: Vivio, Francesco, Vullo, Vincenzo
Format: Article
Language:English
Subjects:
Annular
Axisymmetric
Bending load
Circular plate
Circular plates
Differential equations
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematical models
Non-linear variable thickness plate
Nonlinearity
Physics
Plates
Solid mechanics
Static elasticity (thermoelasticity...)
Stress analysis
Structural and continuum mechanics
Variable thickness
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Summary:A new analytical method for evaluation of elastic stresses and deformations in axisymmetric plates having variable thickness according to a power of a linear function, either solid or annular, subjected to symmetrical bending due to lateral loads either distributed on upper surface or distributed along the inner or the outer edges. The proposed procedure is based on two independent integrals of the hypergeometric differential equation describing the rotation field and constitutes the generalization of the one found in the literature. This method allows to study a wide range of plates, be they solid or annular, converging or diverging with linear or non-linear thickness function, convex, concave or linear tapered, without the restrictions of the known procedures. Analytical results obtained by using this method utterly match both theoretical results which may be obtained in the specific case known (constant-thickness circular plate, linear variable thickness annular circular plate) and numerical results obtained by using FEA.
ISSN:0020-7403
1879-2162
DOI:10.1016/j.ijmecsci.2010.05.011