A Three-Variable Geometrically Nonlinear New First-Order Shear Deformation Theory for Isotropic Plates: Formulation and Buckling Analysis

This paper presents a displacement-based geometrically nonlinear first-order shear deformation theory for the analysis of shear deformable isotropic plates. Nonlinear strain–displacement relations as utilized by the von Kármán plate theory and linear stress–strain constitutive relations are used to formulate this theory. Governing equations of this theory are derived by utilizing equilibrium equations for an infinitesimal plate element. Commonly occurring plate edge boundary conditions are described based on the physical understanding of the plate deformation. As against other geometrically nonlinear first-order shear deformation plate theories reported in the literature, main contributions of this theory are that (1) it incorporates the rotation-free shear deformation plate kinematics of the first order; (2) this theory involves only three governing equations involving only three unknown functions; (3) expressions of governing equations of this theory have a striking resemblance to corresponding expressions of the von Kármán plate theory; (4) this theory describes two unique, physically meaningful plate clamped edge boundary conditions. Illustrative examples pertaining to the buckling of shear deformable isotropic Lévy-type plates and the comparison of the results obtained with the corresponding results reported in the literature demonstrate the efficacy of the proposed theory.