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doi:10.1016/0045-7949(94)00572-K 
Copyright © 1995 Published by Elsevier Science Ltd.
Finite elements for post-buckling analysis. I—The W-formulation
Received 3 February 1994.
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Abstract
This paper presents a convenient formulation 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 formulation 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 formulation 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.
