flexibility method of structural analysis examples

Further, we show that this nonlinear flexibility method is essentially identical, with some subtle algorithmic differences, to a two-field (Hellinger-Reissner) variational principle when the stress interpolation is exact (which is possible for this class of problems).

There is no need for h refinement to improve accuracy. The method does not involve interpolation of the displacement field and the accuracy of the method is limited only by the numerical scheme used to perform element integrals.

We show in this paper that, because the equations of equilibrium and kinematics are directly integrable, a nonlinear flexibility method (in the spirit of those presented in the literature) can be derived without appeal to variational principles. Some of them even seem not to be variationally consistent. Although most of these methods appeal to variational principles, the exact variational basis of these methods has not been entirely clear. These methods appear to perform very well compared to classical stiffness approaches for problems with constitutive nonlinearities. There have been a number of contributions to the literature on a class of structural analysis methods referred to as nonlinear flexibility methods.

Flexibility method of structural analysis examples