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

Abstract

PurposeThe 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/approachThe 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.FindingsThe 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/valueThe 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.

Static Elastic Bending Analysis of a Three-Dimensional Clamped Thick Rectangular Plate using Energy Method

“…The parametric data for the trigonometric stiffness coefficient, kx, kxy, ky, kz, k2z and kq for CCCC shape functions are presented in Table 1. This data was obtained by substituting Equation 58 into Equations 30,31,32,33,34 and 35 as presented in the Figure 5. This stiffness coefficients were used to obtain the value of the shape functions and displacement and rotation of the plate material when subjected to a uniformly distributed transverse load under the same boundary conditions.…”

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