STRUCTURAL ANALYSIS OF FRAMES WITH MIXED VARIATIONAL AND FLEXIBILITY METHODS

Abstract eng:
The need to accurately compute the nonlinear response of structural frames has sparked an interest in the application of mixed variational and flexibility-based methods to the formulation of beam finite elements. The socalled Nonlinear Flexibility Methods, notwithstanding the fact that they have not been extended for geometrically nonlinear problems, appear to perform well compared to classical stiffness methods for inelastic beams (Neuenhofer and Filippou 1997). Flexibility-based methods do not involve interpolation of the displacement field and hence, there is no need for mesh refinement to improve the accuracy of the results. Although, most of these methods appeal to the variational principles (Spacone et al. 1996), their exact variational basis has not been made entirely clear. We show that, because the equations of equilibrium and kinematics can be integrated directly, a nonlinear flexibility method, in the spirit of those presented in the literature, can be derived without appealing to variational principles. The formulation can be implemented as a classical displacement-based finite element method. Furthermore, it can be shown that this nonlinear flexibility method can be interpreted algorithmically, as an optimal two-field (Hellinger-Reissner) variational principle, with minor subtleties.

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