Elastoplastic postbuckling analysis of moderately thick rectangular plates using the variational differential quadrature method

In this research, the elastoplastic postbuckling response of moderately thick rectangular plates subjected to in-plane loadings is analyzed by a novel numerical approach. The influence of transverse shear deformation is taken into account via the first-order shear deformation theory (FSDT). Also, the elastoplastic behavior is captured based on two theories of plasticity including the incremental theory (IT) (with the Prandtl-Reuss constitutive relations) and the deformation theory (DT) (with the Hencky constitutive relation). Moreover, it is assumed that the material of plate obeys the Ramberg-Osgood (RO) elastoplastic stress-strain relation. First, the matrix formulations of strain rates and constitutive relations are derived. In the next step, according to Hamilton's principle, the weak form of governing equations is derived which is then directly discretized using the variational differential quadrature (VDQ) technique. The discretization process is performed by accurate matrix derivative and integral operators of VDQ. Plates with various boundary conditions under uniaxial and equibiaxial compressions are considered. It is first indicated that the present results are in excellent agreement with the analytical solutions existing in the open literature. Thereafter, the influences of geometrical properties, boundary conditions, elastic modulus-to-nominal yield stress ratio and value of power c in the RO relation on the elastoplastic postbuckling paths of plates are studied. Furthermore, several comparisons are made between the predictions of IT and DT. (C) 2019 Elsevier Masson SAS. All rights reserved.