Static and dynamic analysis of material and geometrically nonlinear frame-like structures with softening

In the present work, a framework is proposed for the static and dynamic analysis of spatial frame-like structures with geometric and material nonlinearities. The formulation is based on a velocity-based finite-element approach that takes into account nonlinear material properties with the localization of deformations. The distinguishing characteristic of our approach is the interpolation of velocities and angular velocities, which are taken as primary unknowns for the quasi-static and dynamic formulations. Special attention is dedicated to the evaluation of strains using the kinematic compatibility equation. The nonlinear fiber-based stress-strain constitutive law is considered at the level of cross-sections taking into account also plasticity and softening. The proposed methodology is consistent, computationally efficient and robust, and shows excellent performance even in the neighborhood of critical points and in the presence of strong nonlinearities. The performance of the proposed methodology is demonstrated using several numerical examples.