Equilibrium Based Iterative Solutions for the Nonlinear Beam Problem

The paper describes a procedure for the non-linear analysis of structures which are an assemblage of beams with material non-linearities of general type; the approach uses the equilibrium integrals and a consistent iterative formulation at the element level, within the general framework of the displacement method for the solution of the global structural problem. The application of dierent approaches to the non-linear beam problem is presented and discussed including the traditional stiness and exibility approach and some mixed formulations. The proposed equilibrium-based approach is shown to be more accurate and more robust than the traditional compatibility-based approach, on which most of the non-linear beam elements available today are based. Similar advantages are also found with respect to an approach based on the three-eld mixed assumed strain method.