A complementary-energy based criterion for the stability analysis of geometrically exact framed structures

Stability analysis is a crucial aspect of structural design, particularly for beam type structures. This paper addresses the development of a complementary-energy based (dual) stability criterion for the quasi-static analysis of three-dimensional framed structures modeled using the so-called geometrically exact (Reissner–Simo) beam theory. The criterion is derived from the well known primal stability criterion based on the condition of minimum total potential energy. This is accomplished by resorting to the Lagrangian multiplier method together with the Legendre transformation. Several numerical benchmark problems are analyzed. The analyses are carried out using two dual finite element models and their corresponding stability criteria, namely, the traditional two-node displacement/rotation-based model with the primal stability criterion, and a recently introduced equilibrium-based model with the proposed dual stability criterion.