LETTERS TO THE EDITOR: FATIGUE ANALYSIS OF NON-LINEAR STRUCTURES WITH VON MISES STRESS

Fatigue analysis of vibrating structures subject to random excitations due to earthquakes, wind loadings, or ocean waves is an important subject [1}4]. When the excitation level is high, the non-linear behavior of the structural system has signi"cant e!ect on the fatigue damage. However, when the system is non-linear, the fatigue analysis becomes very involved [5}7]. In an earlier study, we have developed a computationally practical method for predicting the fatigue life of non-linear structures under random excitations [7]. The method consists of an application of equivalent linearization combined with Monte Carlo simulations in a decoupled linear modal space, and can e$ciently generate time histories of the stresses of the structure for the fatigue calculation. In that paper, the maximum stress of a plate in one particular direction was used in the fatigue calculation, although the plate was clearly in multi-axial stress state. Recently, the well-known von Mises stress has been used to estimate the fatigue damage of structures in the multi-axial stress state [8}12]. The work reported in these papers did not attack the nonlinear analysis of structures. In this paper, we shall extend the method developed in reference [7] to study the fatigue damages in non-linear structures by using the equivalent von Mises stress proposed in [9}12]. We shall use a non-linear rectangular von KaH rmaH n plate to demonstrate the analysis [13}17]. In the fatigue study, we can use the linear accumulative damage theory in conjunction with the S}N curve of the material [1, 18, 19]. Since the plate considered here has multiple resonant modes, the response will be broadband. It is well known that the Rain-Flow cycle counting scheme is well suited to a broadband process [2, 18, 20]. The present approach carries out the stress analysis in the time domain, and then applies the Rain-Flow scheme to count stress cycles. This fatigue estimate has to be done in the time domain because the Rain-Flow scheme is di$cult to incorporate in a probabilistic formulation. The method of equivalent linearization is applied to solve for the response of the non-linear plate [6, 21}23]. The equivalent linearization method implies that the modal responses of the structure are Gaussian. We have shown that the estimated fatigue life of non-linear structures by the equivalent linearization method is in excellent agreement with the result obtained by direct numerical simulations [7, 24]. The remainder of the paper is organized as follows. In section 2, we present the method of equivalent linearization for calculating stresses of the non-linear plate. In section 3, we