Statistical prediction for nonlinear failure function of linear loads: application to plate buckling in ship structure

Abstract This study presents a practical method for calculating the probability of exceedance (PoE) of the nonlinear failure function of the linear loads randomly fluctuating in irregular waves. In general, obtaining the exact PoE of such nonlinear quantities requires sophisticated computational method that are not well-suited for practical design. In contrast, the author in a previous study proposed a practical formula of the PoE distribution for von Mises stresses by asymptotic approximation, which can be applied when the criterion surface is ellipsoid in the stochastic variable space. Following this, the present study shows a method for calculating the PoE for a more general function of which the isosurface is expressed as a combination of ellipsoids. As a specific example of its application, this paper takes the limit state of the plates in ship structures specified in the common structural rules (CSR) and presents the calculation procedure of direct numerical integration as well as asymptotic approximation approaches. Calculation of the 1/1000 maximum expected value of the evaluation function of plates in short-term sea states using 700 actual plates in a ship structure confirms that the proposed method, which does not require integration, is in good agreement with rigorous methods using numerical integration.