The prediction of fatigue life with system uncertainties to achieve high reliability and safety of engineering structures is an important task. Uncertainties a!ecting structural fatigue life come from three main sources [1, 2] : (a) structural parameter uncertainties due to geometry and material properties including density, Young's modulus, damping coe$cients, and Poisson ratio; (b) environmental factors including loads, boundary conditions, temperature, and humidity; (c) theoretical assumptions of the idealized modelling. Some uncertainties result in large variance in structural fatigue life while others may have little e!ect. Such a knowledge is valuable to design engineers. This paper intends to contribute to the accumulation of this knowledge by studying the e!ect of various uncertainties on structural fatigue life.
Dependent on the available information, the uncertainties can be modelled as an interval, a fuzzy set or a random variable [3}6]. This work will adopt the interval model of uncertainties. In the future, when more information becomes available, we shall consider random and fuzzy models.
Structural fatigue prediction involves two tasks: dynamic analysis and fatigue modelling. Many methods have been developed to study the dynamics of stochastic systems including Monte Carlo simulation, "nite element methods, weighted integral method and maximum entropy approach [1, 7}10]. With the wide availability of high-speed computers and e$cient algorithms for simulating stochastic processes, Monte Carlo simulation has become an increasingly powerful and popular method [11,12]. Many researchers believe that Monte Carlo simulation is currently the only universal method that can provide accurate solutions for stochastic mechanics problems involving system stochasticity, large variations of uncertain parameters, etc. [10]. This is the method we shall use in this work.
Fatigue is a topic of long history [13}15]. There are two broad classes of fatigue models: a fracture mechanics-based one and an S}N curve-based one [16}19]. Fatigue is typically a random process, particularly, when the structure is subject to random excitations. This random nature has promoted the probabilistic modelling of fatigue [15,19,20]. When the S}N model is adopted, cycle counting schemes are needed to identify fatigue damage events of a random stress history [21}23]. In this paper, we shall make use of the S}N model together with the popular rain#ow counting algorithm [14,24].
In the present paper, we shall consider the structural system with parameter uncertainties subject to Gaussian white noise excitations. The rest of the paper is organized as follows. In section 2, the temporal and spectral response of the stress of a beam is presented. Section 3