Contribuição aos métodos de redução de modelos de sistemas dinâmicos não lineares estocásticos

Abstract

This work is devoted to the deterministic and stochastic finite element modeling of thin flat plates under large displacements and subjected to geometric and discrete non-linearities. In order to solve the resulting non-linear equations of motion in the time-domain, the non-linear Newmark strategy combined with the Newton-Raphson method has been used herein. With the aim of reducing the computational cost required to solve the non-linear problems, especially for the cases in which the uncertainties are considered, the modal method based on the construction of an enriched reduction basis and an improved version of the combined approximations technique have been retained in the present study. With regard to the insertion of uncertainties in the deterministic model opted by the construction of a stochastic model of the system with no distributed linearity, using for this the Karhunen-Loève expansion technique in bi-dimensional form. In order to generate the envelopes of the dynamic responses of the non-linear systems in time-domain, it has been used the so-called Hyper-Cube-Latino. Based on the numerical simulations with plate structures subjected to various levels of excitation and boundary conditions it is possible to illustrate the methodology presented in this work. In particular, it can be concluded about the efficiency and necessity of performing efficient and accurate model reduction methods to deal with non-linear systems. Finally, it is also important to discuss about the interest in considering uncertainties in the analysis and design of non-linear systems in order to deal with more realistic non-linear situations