A numerical approach to the elastic/plastic axisymmetric buckling analysis of circular and annular plates resting on elastic foundation

Presented herein is the elastic/plastic axisymmetric buckling analysis of circular and annular plates resting on elastic foundation under radial loading based on a variational numerical method named as variational differential quadrature. To accomplish this aim, a first-order shear deformable plate model is developed in the context of incremental theory of plasticity (IT) (with the Prandtl-Reuss constitutive equations) and the deformation theory of plasticity (DT) (with the Hencky constitutive equations). It is considered that the material of plates exhibits strain hardening characterized by the Ramberg-Osgood relation. Also, the Winkler and Pasternak models are employed in order to formulate the elastic foundation. To implement the variational differential quadrature method, the matrix formulations of strain rates and constitutive relations are first derived. Then, based upon Hamilton's principle and using the variational differential quadrature derivative and integral operators, the discretized energy functional of the problem is directly obtained. Selected numerical results are presented to study the effects of various parameters including thickness-to-radius ratio, elastic modulus-to-nominal yield stress ratio, power of the Ramberg-Osgood relation and parameters of elastic foundation on the elastic/plastic buckling of circular and annular plates subject to different boundary conditions. Moreover, several comparisons are provided between the results of two plasticity theories, i.e. IT and DT. The effect of transverse shear deformation is also highlighted.