Buckling Analysis of Relatively Thick Plates using First Order Shear Deformation Plate Theory: Exact Solutions

Abstract

Critical buckling load determinations for thick plates are crucial for their analysis and design. This study presents first principles derivation of the governing partial differential equations of elastic stability (GPDEES) of relatively thick plates using equilibrium methods. The formulation considered transverse shear deformation effects and applies to relatively thick plates. The GPDEES were constructed using kinematics, constitutive and equilibrium equations as a coupled set of three partial differential equations (PDEs) in terms of rotational displacements  and  of the middle surface and transverse displacement w(x, y). The buckling solutions were derived using Double Fourier series method (DFSM) for simply supported plates under (i) uniaxial, compressive loads, (ii) biaxial compressive loads. The DFSM simplified the GPDEES to homogeneous algebraic system of equations in A_mn, B_mn and W_mn, the amplitudes of  and w(x, y) respectively. The conditions for nontrivial solutions gave the buckling equation. It was found that the present value for  for each case was identical with previous results. It was confirmed by comparison with thin plate buckling solutions that the present results gave safe solutions to the buckling problems of thick plates, and the thin plate theory significantly overestimates the  for thick plates.