Semi-analytical optimal solution for maximum buckling load of simply supported orthotropic plates

Abstract

The buckling characteristic of rectangular orthotropic plates under axial compression with simply supported boundary has been extensively studied. To enhance the structural efficiency, the stacking sequence of laminate should be optimized to maximize the critical buckling load. In this study, the discrete stiffness parameters are employed to yield the theoretical optimal ply orientation corresponding to the maximum critical buckling load at a layer level, and the buckling mode shapes are calculated analytically. Subsequently, the derivation is performed based on optimal ply orientation to derive the optimal stacking sequence of the laminate, in which a sign vector is adopted to minimize the bending-twisting coupling effects. As a result, two laminate optimal design problems are solved: maximizing critical buckling load with fixed thickness, as well as minimizing the thickness with buckling constraint. Two numerical examples are adopted to verify the yielded optimal solutions. Lastly, the theoretical optimal ply orientations exhibiting different load ratios and aspect ratios are presented.