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

Abstract

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.

A semi-analytical model on the critical buckling load of perforated plates with opposite free edges

“…In box girders and some load-bearing spars, cutouts are made for special purposes, for example, material saving and weight reduction, access for installation and inspections. [1][2][3][4] Generally, plates with cutouts have a relatively lower structural strength in comparison with those without, and the buckling behaviour is one of the most critical considerations in safety and reliability of these structures. The buckling analysis of a plate with cutouts is more complicated than that of an intact plate.…”

Buckling and free vibration characteristics of embedded inhomogeneous functionally graded elliptical plate in hygrothermal environment

“…The vibration characteristic of super elliptical plate was investigated by Hasrati et al. 21 Zhong et al. 22 employed the triangular DQM for analyzing the flexural response of the elliptical Reissner–Mindlin plate supported by Pasternak foundation.…”

“…Bellifa et al 20 investigated the bending and vibration of FGP by employing the neutral surface technique with SDT. The vibration characteristic of super elliptical plate was investigated by Hasrati et al 21 Zhong et al 22 employed the triangular DQM for analyzing the flexural response of the elliptical Reissner-Mindlin plate supported by Pasternak foundation. Kamrafard et al 23 used Hamilton principle for the vibration and buckling analysis of annular porous plate.…”