Mixed variational methods for finite element analysis of geometrically non-linear, inelastic Bernoulli-Euler beams

Bernoulli-Euler beam theory has long been the standard for the analysis of reticulated structures. The need to accurately compute the non-linear (material and geometric) response of structures has renewed interest in the application of mixed variational approaches to this venerable beam theory. Recent contributions in the literature on mixed methods and the so-called (but quite related) non-linear flexibility methods have left open the question of what is the best approach to the analysis of beams. In this paper we present a consistent computational approach to one-, two-, and three-field variational formulations of non-linear Bernoulli-Euler beam theory, including the effects of non-linear geometry and inelasticity. We examine the question of superiority of methods through a set of benchmark problems with features typical of those encountered in the structural analysis of frames. We conclude that there is no clear winner among the various approaches, even though each has predictable computational strengths. cr 2003 John Wiley and Sons, Ltd.