Closed-form approximate solution for linear buckling of Mindlin plates with SRSR-boundary conditions

Abstract The present work deals with the buckling analysis of rectangular Mindlin plates consisting of laminated composites with symmetrical, balanced lay-up or isotropic materials. Along the longitudinal edges the plate is rotationally restrained by springs. The transversal edges are simply supported. In agreement with common notation, the boundary conditions are abbreviated as follows: simply supported (S), rotationally restrained (R), and fully clamped (C). As loading situation axial compression is considered. Aiming at high computational efficiency the problem is solved by the Rayleigh-Ritz-method. Since well suited shape functions for deflection and rotations with very few variables are used, closed-form approximate solutions for the buckling load can be obtained. For verification exact transcendental solutions and/or high fidelity finite element analyses are employed. Additionally, results are compared to those of existing closed-form approximate solutions. Apart from the special case of simply supported longitudinal edges where all methods yield exact or nearly exact results, the present method shows clear advantages: 1. Due to the type of shape functions it is able deal with unsymmetrical boundary conditions. 2. For the case of both longitudinal edges fully clamped where all closed-form approximate solutions show the greatest deviations the present method is significantly more accurate.