Análise de fadiga de sistemas estocásticos incorporando materiais viscoelásticos

Abstract

This work proposes a new probabilistic approach for the Sine’s fatigue criterion in the frequency-domain to investigate the fatigue damage of a viscoelastically-damped system with uncertainties. In this case, the finite element method has been used in conjunction with the Karhunen-Loève expansion method to discretize the Gaussian random fields and to construct the stochastic elementary FE matrices for a three-layer sandwich plate element. To incorporate the frequency- and temperature-dependent behavior of the 3M ISD112 viscoelastic material adopted here, it is considered the complex modulus approach, which is used in the computation of the frequency response functions and the stress responses of the viscoelastic system. These responses are required in the estimation of the Sine’s global criterion. A natural extension of the modeling capability presented here is the use of optimization techniques with the aim of reducing the time to perform a fatigue analysis of viscoelastic systems. Within this context, it has been used the well-known NSGA optimization technique. However, due to the large number of exact evaluations of the objective functions for the robust multiobjective optimization strategy proposed in the present contribution, it is suggested a model reduction method to deal with viscoelastic systems. It is based on the construction of a frequency- and temperature-independent basis which is further enriched by static residues due to the external excitations and viscoelastic damping forces in a iteratively way. The main goal is to approximate the stress responses of the viscoelastic system and to reduce the computational time required to compute the optimal-robust solutions. The numerical examples with a three-layer sandwich plate incorporating viscoelastic damping illustrate the developments of the methodology proposed herein and the necessity of considering the uncertainties in the optimization process of more realistic viscoelastically-damped systems with the aim of increasing their fatigue life.