Explicit Local Buckling Analysis of Rotationally- and Vertically-restrained Orthotropic Plates Under Uniaxial Compression

In this paper, explicit local buckling analysis of orthotropic plates subjected to uniaxial compression with two loaded edges simply-supported and two unloaded edges supported by combined vertical and rotational restraining springs is presented. Based on the total potential energy function, the eigenvalue problem is formulated by treating the buckled shape functions as the admissible functions that satisfy the boundary conditions of the rectangular plates. Closed-form and approximate local buckling solutions of the combined rotationally- and vertically-restrained orthotropic plates, as well as explicit formulas for the critical buckling load and critical aspect ratio under the uniform compression, are obtained. By adjusting the stiffness of the rotational and vertical restraining springs, explicit local buckling solutions are established for eight simple cases of boundary conditions. To verify the explicit solutions, numerical analyses of orthotropic plates using the exact transcendental and finite element methods are conducted, for which reasonable agreement has been obtained between the explicit and numerical solutions, particularly for the simplified cases. The explicit solution obtained in this study can be used to facilitate the buckling analysis of composite laminated structures with different boundary conditions or joint connections as parts of stiffened and thin-walled structures by treating them as discrete plates with restrained boundary conditions.