Plastic Buckling

Abstract

Plastic buckling has received a great deal of attention and its progress has been slow but steady. The chapter focuses on post-bifurcation and imperfection-sensitivity aspects of plastic buckling. A combination of model studies and analytical and numerical work has been drawn on to illustrate a wide range of behaviors. A simple two degree of freedom model is used to introduce post-bifurcation behavior and a second model brings out some of the features peculiar to the behavior of continuous solids and structures. Bifurcation criterion for a class of three-dimensional solids is provided and is applied to a widely used theory for plates and shells. Following specification of the bifurcation criterion, a detailed commentary is provided on the extent to which bifurcation predictions for plates and shells depend on the plasticity theory used with particular focus on the differences between predictions based on the simplest deformation and incremental theories. The chapter presents a general treatment of the initial post-bifurcation behavior of plates and shells within the context of the Donnell-Mushtari-Vlasov theory (DMV-theory). The theory is illustrated by applications to several column and plate problems. A discussion of some of the effects of imperfections is also provided. The chapter concludes with a selection of numerical results for columns, plates, and shells. © 1974, Academic Press Inc.