Elastic Buckling Analysis of SSCF and SSSS Rectangular Thin Plates using the Single Finite Fourier Sine Integral Transform Method

Abstract

The analysis of the stability problem of plate subjected to inplane compressive load is important due to the relatively poor capacity of plates in resisting compressive forces compared to tensile forces. It is also significant due to the nonlinear, sudden nature of buckling failures. This study presents the elastic buckling analysis of SSCF and SSSS rectangular thin plates using the single finite Fourier sine integral transform method. The considered plate problems are (i) rectangular thin plate simply supported on two opposite edges, clamped on one edge and free on the fourth edge; (ii) rectangular thin plate simply supported on all edges. The plates are subject to uniaxial uniform compressive loads on the two simply supported edges. The governing domain equation is a fourth order partial differential equation (PDE). The problem solved is a boundary value problem (BVP) since the domain PDE is subject to the boundary conditions at the four edges. The single finite sine transform adopted automatically satisfies the Dirichlet boundary conditions along the simply supported edges. The transform converts the BVP to an integral equation, which simplifies upon use of the linearity properties and integration by parts to a system of homogeneous ordinary differential equations (ODEs) in terms of the transform of the unknown buckling deflection. The general solution of the system of ODEs is obtained using trial function methods. Enforcement of boundary conditions along the y = 0, and y = b edges (for the SSCF and SSSS plates considered) results in a system of four sets of homogeneous equations in terms of the integration constants. The characteristic buckling equation in each case considered is found for nontrivial solutions as a transcendental equation, whose roots are used to obtain the buckling loads for various values of the aspect ratio and for any buckling modes. In each considered case, the obtained buckling equation is exact and identical with exact expressions previously obtained in the literature using other solution methods. The buckling loads obtained by the present method are validated by the observed agreement with results obtained by previous researchers who used other methods.

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

“…The general solution of the integral equation is found for Cmn as Equation ( 25) which is expressible using integrals I1, I2, …, I8. Thus w(x, y) is determined as Equation (36). With the aid of bending moments-displacement equations, the bending moments are obtained in general as Equations ( 39) and (40).…”

“…Elastic stability problems involving rectangular Kirchhoff plates subjected to inplane compressive loads were investigated by authors in [32][33][34][35][36].…”

“…They obtained for each considered case, closed form solution that satisfies the boundary conditions and domain equation. In [36], the authors performed and obtained stability solutions for rectangular thin SSCF and SSSS plates using the single finite Fourier sine integral transform method. They obtained for the studied problems, exact solutions that satisfied the deformation and force equations at the restrained boundaries and the governing field equation.…”

Kirchhoff-Love Plate Theory: First-Order Analysis, Second-Order Analysis, Plate Buckling Analysis, and Vibration Analysis Using the Finite Difference Method

“…Both conventional and staggered equispaced stencils for first and second derivatives were considered. Onyia et al [7] presented the elastic buckling analysis of rectangular thin plates using the single finite Fourier sine integral transform method. Pisacic et al…”

Bending Analysis of Isotropic Rectangular Kirchhoff Plates Subjected to a Thermal Gradient Using the Fourier Transform Method<strong> </strong>

“…Sayyad et al [8] assessed a trigonometric plate theory for the static bending analysis of plates resting on Winkler elastic foundation; the theory considered the effects of transverse shear and normal strains. Onyia et al [9] presented the elastic buckling analysis of rectangular thin plates using the single finite Fourier sine integral transform method. Ike [10] presented the double Fourier cosine series method for solving the flexural problem of Kirchhoff plates resting on an elastic foundation of the Winkler type.…”