Finite Elements for Post - Buckling Analysis . I - the W - Formulation

This paper presents a convenient fonnulation for the stability analysis of structures using the finite element method. The main assumptions are linear elasticity, a linear fundamental path, and the existence of distinct critical loads (i.e. no coupling between buckling modes occurs). The fonnulation developed is known as W-formulation, in which the energy is written in terms of a sliding set of incremental coordinates measured with respect to the fundamental path. In the presentation developed here, the only ingredients required to carry out the analysis are the strain-displacement and the constitutive matrices at the element level. The present fonnulation is compared with the so called V-formulation, in which the displacements refer to the unloaded state. It is shown that under the present assumptions of linear fundamental path, the advantages of the V-formulation are lost and both approaches are similar. An example of a circular plate under in-plane loading illustrates the procedures. Part II of this paper deals with the application to the post buckling analysis of plate assemblies made of composite materials.