Elastoplastic buckling analysis of porous thin plates by symplectic superposition method

Abstract

The elastoplastic buckling behavior of porous metallic rectangular thin plates is investigated accounting for pressure dependency of the material in plastic regime. The constitutive equations of two competitive theories including incremental theory (IT) and deformation theory (DT) of plasticity are proposed. To this end, related representative volume element of such materials with different porosities is constructed based on micromechanical averaging technique. The derived model is employed to study buckling of the plates with complex boundary conditions (BCs) under uniaxial and biaxial loading conditions. The current analytical solutions are restricted to the plates under Levy-type BCs. In this paper, a Hamiltonian system-based variational principle is reformulated for porous thin plates in the symplectic space. Three typical non-Levy-type BCs are studied for each of which two sub-problems are solved analytically using variable separation and symplectic eigen expansion methods. The results are validated against published literature. Comprehensive studies on the effects of plate’s aspect ratios, porosity factor and plasticity model on the buckling load and mode shapes have been carried out. It can be seen that the critical buckling load obtained from IT and DT are divergent especially for upper values of thicknesses. Also, the plastic buckling paradox is identified in which a significant disparity is observed between the DT and IT in calculating buckling loads for relatively thick plates.