Buckling analysis of orthotropic plates with various boundary conditions using a new hyperbolic shear displacement model: an analytical approach

Purpose This paper introduces a closed-form solution for analyzing the buckling behavior of orthotropic plates using a refined plate theory with four variable parameters, leveraging a new hyperbolic shear displacement model. Design/methodology/approach The proposed theory incorporates a quadratic variation of transverse shear strains across the plate’s thickness and satisfies zero traction boundary conditions on both the upper and lower surfaces without employing shear correction factors. The governing equations are derived from the principle of minimum total potential energy. Closed-form solutions for rectangular plates, with two opposite edges simply supported and the remaining two edges subjected to arbitrary boundary conditions, are obtained using the state space approach to the Levy-type solution. Comparative studies are conducted to validate the accuracy of the obtained results. Findings The paper successfully examines and discusses in detail the effects of boundary conditions, loading conditions, variations in modulus ratio and thickness ratio on the critical buckling load of orthotropic plates. Originality/value This study presents a novel and precise method for evaluating the buckling behavior of orthotropic plates. The refined plate theory, without the need for shear correction factors, offers significant insights and improvements in understanding the critical buckling load under various conditions, contributing valuable knowledge to the field of structural analysis.