LETTERS TO THE EDITOR FATIGUE ANALYSIS OF NON-LINEAR STRUCTURES WITH

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 ishigh, the non-linear behavior of the structural system has signi"cant e!ect on the fatiguedamage. However, when the system is non-linear, the fatigue analysis becomes veryinvolved[5}7].Inan earlierstudy,wehavedevelopedacomputationallypracticalmethodfor predicting the fatigue life of non-linear structures under random excitations [7]. Themethod consists of an application of equivalent linearization combined with Monte Carlosimulationsinadecoupledlinearmodalspace,andcane$cientlygeneratetimehistoriesofthestressesofthestructureforthefatiguecalculation.Inthatpaper,themaximumstressofaplateinoneparticulardirectionwasusedinthefatiguecalculation,althoughtheplatewasclearly in multi-axial stress state. Recently, the well-known von Mises stress has been usedtoestimatethefatiguedamageofstructuresinthemulti-axialstressstate[8}12].Theworkreportedinthesepapersdidnotattackthenonlinearanalysisofstructures.Inthispaper,weshall extend the method developed in reference [7] to study the fatigue damages innon-linear structures by using the equivalent von Mises stress proposed in [9}12].We shall use a non-linear rectangular von KaHrmaHn plate to demonstrate the analysis[13}17]. In the fatigue study, we can use the linear accumulative damage theory inconjunction with the