Plastic buckling of thin flat rectangular isotropic plates under uniaxial in-plane loads

Abstract

This study presents the analysis of plastic buckling of thin flat rectangular isotropic plates. To actualize this, the deformation theory of plasticity by Stowell’s approach is used in expressing the governing differential equation, and this equation is modified by adopting the method of work principle based on the principle of conservation of energy. Taylor-Maclaurin series functions truncated at the fifth term is used in estimating the deflection functions. The analyzed plates are subjected to uniform uniaxial in-plane compression and the direction of the loading is in the longitudinal direction (x-axis). The three plate boundary conditions considered in this study are: four simply supported edges (SSSS); four clamped edges (CCCC); and two clamped edges along the x-axis and two simply supported edges along the y-axis (CSCS). The Taylor-Maclaurin series formulation satisfied each of the plate boundary conditions and resulted to a distinct deflection function for each plate. These deflection functions are substituted into the governing equation to obtain the critical plastic buckling loads. Values of the buckling coefficient, k, which is derived from the critical plastic buckling load equation, are calculated for aspect ratios, p, ranging from 0.1 to 1.0 in steps of 0.1, using values of moduli ratio, E_t/E_s, equal to 0.6, 0.7, 0.8, and 0.9. The results are compared with those of a previous investigation. The percentage differences of k with plastic buckling solutions for the different values of p and E_t/E_s of the plates ranged from −4.685% to 6.276%. It is shown that the technique proposed in this study is an alternative approximate method for analyzing the plastic buckling of thin rectangular isotropic plates under uniform uniaxial in-plane loads.