Elasto-plastic analysis of plate bending using higher order shear deformation theory

Almost all structures have a capacity to resist large loads even when stressed beyond their elastic limit and this is more so in case of plates. This aspect leads to the investigation of the elasto-plastic behaviour of the plates. An accurate elastic bending theory is essential for pursuing an exact non-linear analysis. Higher order shear deformation theories (HOSDT) are considered to be most appropriate, because these are now well-established theories for accurate prediction of behaviour in the elastic range. In this paper, the HOSDT, proposed by Kant and later modified by Pandya and Kant, has successfully been applied for non-linear analysis of plate bending using an incremental finite element formulation. In the fnite element formulation, nine-noded heterosis element with the provision of different integration schemes has been used. A modified Newton-Raphson method has been used to solve the non-linear equations. Von-Mises yield criterion has been adopted to deal with yielding of the materials along with the isotropic hardening. A suitable computer program has been developed and a variety of plate bending problems have been solved with it. The results have been compared with existing standard or benchmark solutions. Comparisons clearly indicate the better performance of the theory in the non-linear analysis as well.