Work principle in inelastic buckling analysis of axially compressed rectangular plates

Abstract

Purpose The purpose of this paper is to analyze the inelastic buckling of a rectangular thin flat isotropic plate subjected to uniform uniaxial in-plane compression using a work principle, a deformation plasticity theory and Taylor–Maclaurin series formulation. Design/methodology/approach The non-loaded longitudinal edges of the rectangular plate are clamped, whereas the loaded edges are simply supported (CSCS). Total work error function is applied to Stowell’s plasticity theory in the derivation of the inelastic buckling equation. Mathematical formulation of the Taylor–Maclaurin series deflection function satisfied the boundary conditions of the CSCS rectangular plate. The critical inelastic load of the plate is then derived by applying variational principles. Findings Values of the plate buckling coefficient are calculated using various values of moduli ratio for aspect ratios ranging from 0.1 to 1.0, in intervals of 0.1. The accuracy of the proposed technique is validated by comparing the results obtained in the present study with solutions from a previous investigation. The percentage differences in the values of the buckling coefficient ranged from −0.122 to −4.685 per cent. Originality/value The results indicate that the work principle approach can be used as an alternative approximate method for analyzing inelastic buckling of rectangular thin flat isotropic plates under uniform in-plane compressive loads.

Analysis of inelastic buckling of rectangular plates with a free edge using polynomial deflection functions

“…A work principle method was applied in [14] using a total work error function. For a single degree of freedom, the buckling load Eq.…”

“…A work principle technique [13] is an approximate method, which uses total work error functional and requires minimisation. The technique is applicable to deflection functions with multiple degrees of freedom and seems to have more effective convergence than the Raleigh-Ritz technique [14]. The work principle is combined with Taylor's series to form the deflection function of rectangular plates.…”

“…The work principle is combined with Taylor's series to form the deflection function of rectangular plates. The Taylor's series is more useful than the trigonometric series in formulating deflection functions of various boundary condition arrangements whose solutions are difficult to solve [14].…”