Spectral Method for Fatigue Damage Assessment of Structures with Uncertain Parameters

Abstract

This study presents a spectral method for fatigue damage evaluation of linear structures with uncertain-but-bounded parameters subjected to the stationary multi-correlated Gaussian IntroductionFatigue damage is one of the major factors in the failures of engineering structure and mechanical equipment. The traditional method on fatigue damage assessment usually can be divided into two groups, namely, time domain approach and spectral approach. For the former, the traditional method on fatigue damage assessment is the so-called nominal-stress approach [1], which uses numerical methods for cycle counting and damage accumulation stepwise. To compute the time histories of the stress or strain of critical points, time domain method is computationally very time-consuming, especially for large structures. For the spectral approach [2], the external loads are modeled as stationary Gaussian processes, and fatigue damage evaluation is derived from the power spectral density (PSD) function of the stress or strain process of critical points in frequency domain.The above two approaches always consider structural parameters like geometry, material properties, constitutive laws and boundary conditions as fixed values. However, it has been recently recognized that the model parameters are poorly known too, giving arise to structures with uncertain parameters. In these cases, the uncertain parameters are described by the following two methods, known as probabilistic and non-probabilistic approaches. For the first group, structural uncertain parameters are modeled as random variables or stochastic field, and structural generic response under external load is given by stochastic finite element method or Monte Carlo simulation method, and then the fatigue damage of the structure will be obtained based on the cumulative damage theory. However, the reliable probabilistic model requires a large amount of accurate sample data, which are sometimes difficult to get particularly in the preliminary design stage. Meanwhile, the characteristics of the structural uncertainty are not random. Therefore, nonprobabilistic model is more suitable than probabilistic model to define the structure with uncertain parameters.In the past decade, the non-probabilistic theory, which has made a considerable progress as a new method to describe the uncertainty, generally comprises convex set theory, fuzzy set theory and interval theory. Ben-Haim [3] first introduced

Damage Zone Size Limit During the Crack Propagation

“…The general formulation of a problem of interaction implies a propagation of a semi-infinite crack in a neighbouring zone called damage zone or process zone [16,17]. The stress and displacements components of a dislocation near the semi-infinite crack are formulated by employing the complexes potentials theory of the elasticity of Muskhelishvili [18].…”

Effect of Strengthening on the Fatigue Life of Construction Materials

“…Therefore, several hypotheses aiming to estimate the fatigue life of the structure under variable loads have been posited, including modified Miner's rule (MMR) and relative Miner's rule (RMR). The phenomenon of fatigue is described more and more accurately, for example, by the description as a stochastic process [8,9,10]. High accuracy may be obtained by taking into account the strengthening effect of load cycles below the fatigue limit (LALS).…”