Single Variable Thick Plate Buckling Problems Using Double Finite Sine Transform Method

Abstract

The double finite sine transform method was utilized to obtain exact buckling solutions for thick plate problems • The method simplified the problem to algebraic ones since the sinusoidal function satisfies the boundary conditions • The buckling solutions aligned with exact solutions for thick plates This paper derives buckling solutions for single variable thick plate buckling problems using the double finite sine transform method (DFSTM). The problem governing partial differential equation (GPDE), originally formulated by Shimpi and others, uses a refined plate theory (RPT) and accounts for transverse shear deformations, rendering it applicable to thick plates. The thick plate is simply supported and subjected to (i) uniform uniaxial compressive load in the x direction. (ii) uniform biaxial compressive load in the x and y axes. The DFSTM was applied to the GPDE, and the problem transformed into an algebraic equation, which was simpler in this case due to the Dirichlet boundary conditions satisfied by the sinusoidal kernel of the DFSTM. Analytical buckling solutions were determined for the two considered cases of uniaxial and biaxial compressive loads in terms of the buckling modes, Poisson's ratio (µ), and thickness (h) to least dimension (a) ratio. Critical buckling loads (Pcr) determined at the first buckling modes agreed with previously obtained Navier solutions for Mindlin, Reddy, and Refined plates. Pcr calculated for ratios of h/a equal to 0.01 converged to the solutions obtained using Kirchhoff-Love plate theory (KLPT), illustrating the applicability of the GPDE to thin and thin plate buckling.

Galerkin-Kantorovich variational method for solving saint venant torsion problems of rectangular bars

“…Ike and Oguaghamba [14] used the double finite sine transform method (DFSTM) for the closed form analysis of unrestrained torsion of rectangular bars. The problem was expressed using Prandtl stress function as an inhomogeneous Laplace equation of the Poisson type; and the DFSTM converted the problem to an algebraic one in the transformed space.…”