Análise de fadiga de sistemas estocásticos submetidos a carregamentos aleatórios multiaxiais

Abstract

This work is devoted to the proposition of numerical and computational studies of the multiaxial Sines' criterion for fatigue analyses of structural systems such as rectangular plates, taking into account the parametric uncertainties and subjected to stationary random loads. In this context, the Stochastic Finite Elements Method is used in such a way that the design parameters to be considered as random variables are factored out of the mass and stiffness matrices. In the simulations, the random variables are modeled as homogeneous Gaussian random fields and discretized according to the so-called Karhunen-Loève expansion. Thus, the stochastic mass and stiffness matrices are generated due to the modification of the integration process by the covariance functions. In the sequence, a numerical strategy is implemented in order to estimative the mean of the second invariant of stress tensor in the frequency domain to compute the fatigue criterion based on the use of the Sines' damage criterion. With the aim of reducing the computational burden evolved in the estimation process of the multiaxial damage criterion, a model reduction technique is implemented for the stochastic system based on the construction of a constant reduction basis formed by the modes of the nominal systems enriched by static residues due to the external forces. The numerical results obtained are presented in terms of the envelopes of frequency response functions, stress responses and fatigue indexes. Through the obtained results it is possible to conclude about the interest in considering the uncertainties on the fatigue analyses of engineering systems for more realistic situations and put in evidence that the methodology is a useful tool for the fatigue analysis of stochastic systems.