Space-variant finite element reliability analysis Original Research Article

Of interest in this paper are reliability problems where the failure event is defined over a spatial domain, e.g. the excursion of a measure of damage above an allowable threshold anywhere within the body of a structure. The uncertainties in the problem may arise from the stochastic nature of the material, the loading, or the geometry and boundary conditions of the structure. The finite element approach, together with the first-order reliability method, are used to derive approximate solutions of the space-variant failure probability. The paper also introduces a new limit formula for the mean crossing density of a random field. Two examples are used to demonstrate the method and its accuracy.