Bending of variable thickness rectangular thin plates resting on a double-parameter foundation: integral transform solution

Abstract

Purpose

The purpose of this study is to propose a generalized integral transform technique (GITT) to investigate the bending behavior of rectangular thin plates with linearly varying thickness resting on a double-parameter foundation.

Design/methodology/approach

The bending of plates with linearly varying thickness resting on a double-parameter foundation is analyzed by using the GITT for six combinations of clamped, simply-supported and free boundary conditions under linearly varying loads. The governing equation of plate bending is integral transformed in the uniform-thickness direction, resulting in a linear system of ordinary differential equations in the varying thickness direction that is solved by a fourth-order finite difference method. Parametric studies are performed to investigate the effects of boundary conditions, foundation coefficients and geometric parameters of variable thickness plates on the bending behavior.

Findings

The proposed hybrid analytical-numerical solution is validated against a fourth-order finite difference solution of the original partial differential equation, as well as available results in the literature for some particular cases. The results show that the foundation coefficients and the aspect ratio b/a (width in the y direction to height of plate in the x direction) have significant effects on the deflection of rectangular plates.

Originality/value

The present GITT method can be applied for bending problems of rectangular thin plates with arbitrary thickness variation along one direction under different combinations of loading and boundary conditions.

Citation

Fu, G., Tuo, Y., Sun, B., Shi, C. and Su, J. (2022), "Bending of variable thickness rectangular thin plates resting on a double-parameter foundation: integral transform solution", Engineering Computations, Vol. 39 No. 7, pp. 2689-2704. https://doi.org/10.1108/EC-11-2021-0692