ABSTRACT
This chapter presents an overview of the finite element method, to review selected finite element analysis techniques as applied to determining the nonlinear postbuckling and collapse response of elastic structures, and to describe selected application problems. The basic equilibrium equations are described first, followed by a discussion of the constitutive equations, then the strain-displacement relations, and finally the compatibility relations. For problems associated with postbuckling and collapse of elastic structures considered herein, a Lagrangian formulation is used wherein the deformations are referenced to the original configuration and differentiation and integration is performed relative to the original configuration. The chapter discusses the problems related to the buckling, vibration, postbuckling and collapse of plate and shell structure. The slightly higher collapse load and different postbuckling response obtained using the 9LAG element is attributed to the inherent weaknesses of elements developed using uniformly-reduced integration. Details of nonlinear solution algorithms for postbuckling, collapse problems were examined in detail and implementation details provided.
