Plastic buckling of Mindlin plates

Abstract

This thesis is concerned with the plastic bifurcation buckling of thick plates of arbitrary shapes that are defined by polynomial functions. The plates may be subjected to in-plane normal and/or shear stresses and the edges may take on any combination of boundary conditions. The effect of transverse shear deformation, which is significant in thick plates, is taken into account by adopting the Mindlin plate theory. In order to capture the plastic behaviour of the plates, two widely used plasticity theories are considered. They are the incremental theory (IT) of plasticity and deformation theory (DT) of plasticity.The Ritz method is automated for the first time for such plastic buckling analysis. This automation is made possible by employing Ritz functions comprising the product of mathematically complete, two-dimensional polynomials and boundary equations raised to appropriate powers that ensure the satisfaction of the geometric boundary conditions a priori. The Ritz formulations are coded for use in MATHEMATICA for three types of coordinate systems, namely Cartesian, skew and polar coordinate systems so as to better suit the plate shapes considered. The treatments of the presence of complicating effects such as internal line/points/curved/loop supports, elastically restrained boundary conditions, elastic foundations, internal line hinges and intermediate in-plane loads in the formulations and solution techniques are also presented. In addition to the Ritz method, a new analytical method is featured for handling the asymmetric plastic buckling problems of circular and annular Mindlin plates. The correctness of Ritz formulations and the developed analytical method are verified by comparing the results with some limited elastic and plastic solutions found in the open literature. Extensive plastic buckling data for various plate shapes, boundary and loading conditions are, for the first time, generated and compiled in one volume. The vast buckling data allows one to examine the effects of transverse shear deformation and geometrical parameters such as aspect ratios, thickness-to-width ratios.It is worth noting that the presented Ritz program codes can be used to study not only the plastic buckling of plates but also the elastic buckling of plates. One can calculate the elastic buckling stress parameter based on the classical thin plate theory by setting the thickness-to-width ratio to a small value. If one wish to calculate the elastic buckling stress parameter based on Mindlin plate theory, it can be easily done by setting the tangent modulus and secant modulus equal to Younga??s modulus.