Buckling of non-Lévy-type rectangular thick plates:New benchmark solutions in the symplectic framework

Abstract

The third-order shear deformation theories (TSDTs) are frequently employed to enhance the accuracy of mechanical behavior characterization for thick plates. However, the analytic buckling solutions based on the TSDTs are rare due to the major challenge in mathematical treatments. This study introduces an analytic symplectic superposition method to derive new benchmark buckling solutions of TSDT-based rectangular thick plates with non-Lévy-type boundary conditions (BCs), which are inaccessible using conventional analytic approaches. The governing equations are formulated in the Hamiltonian system. The symplectic framework-based mathematical techniques are manipulated, which shapes the characteristic of the method that a rational derivation is realized without any predetermined solution forms. The comprehensive buckling load factors and mode shapes of fully clamped plates and their variations are given, all of which are verified through comparison with the finite element method as well as literature results. Utilizing the obtained solutions, a comprehensive parametric analysis is conducted to elucidate the effects of BC, thickness-to-width ratio, and aspect ratio on critical buckling load factors. A comparison study is made between the results by the TSDT and those by the Kirchhoff theory and the first-order shear deformation theory, which demonstrates the superior accuracy of the former. The proposed rigorous framework offers a rational route to obtaining more benchmark buckling solutions.