Asymmetric/Axisymmetric buckling of circular/annular plates under radial load first-order shear deformation

This paper proposes a mathematical method for the asymmetric buckling analysis of homogeneous and isotropic circular/annular plates under radial load based on the first-order shear deformation theory and nonlinear von Karman relations. The buckling load is presented for different combinations of the free, clamped, and simply supported boundary conditions at the plate outer edges and different aspect ratios. The equilibrium equations which are five coupled nonlinear partial differential equations are extracted using the principle of virtual work and they are solved analytically using the perturbation technique. The stability equations which are a system of coupled linear partial differential equations with variable coefficients are obtained by employing the adjacent equilibrium criterion. The differential quadrature method is utilized to find the buckling load which is the eigenvalue of the stability equations. Also, the buckling load is examined using the classical plate theory as well. The sensitivity analysis investigates the effect of geometrical parameters on the buckling load. The results are compared with the obtained results from the classical plate theory, finite elements, and the results were reported in the other references.