Estudo de algoritmos de integração elemento por elemento para análise dinâmica não linear de estruturas

Abstract

The topic of structural dynamics involves an ample actuation field since the most of nature actions are time dependent. The analyses of structures in aerospace engineering, offshore engineering, civil engineering and others might be realized including the inertial effects since they have important role in reliability and safety of them. Due to the various nonlinearities that can be present in the dynamic analysis, the preview of the dynamic behavior of a structure can become a complex task. That analysis is generally executed using computational numeric algorithms improved for spatial and temporal discretization where computational requirements are excessive. Techniques based on element-by-element concept have gained recognition due to its increasing efficiency caused by the recent development of parallel computers. This work is focused on time integration algorithms for nonlinear dynamic problems formulated by the finite element approach. Besides, the considered algorithms have been prepared to be used, in the future, on parallel computational architectures. The main algorithms for nonlinear structural dynamics and alternatives of implementation of the element-by-element techniques are studied. The software MATLAB has been used for implementation of some algorithms, whose features are analyzed by examples. Some characteristics as computational cost, number of iterations and solutions quality are observed for nonlinear quasistatic and dynamic problems, adopting several spatial and temporal discretization levels.