First-Excursion Probability and Response Peak Distribution of a Nonlinear Structure Under Non-Gaussian Non-Stationary Loadings

Abstract

Abstract Probabilistic methods have been used recently for the reliability assessment and design of ship structures because of the presence of various uncertainties in structural configuration, material properties, and environmental and operating conditions. Among these uncertainties, random dynamic loads induced by either sea waves or slamming play a significant role in reliability-based ship structural design. The present state-of-the-art probabilistic method for ship design is based on a linear structural response model subjected to stationary Gaussian random processes. However, under extreme operating conditions, the ship structural response may not be linear due to the initiation and evolution of multiple local damage, such as local plastic deformation, stiffener tripping, panel buckling, or fracture. In addition, the complexity of fluid-structure interaction phenomena may render the assumptions on the loading process (stationary and Gaussian) invalid. Under this study, we developed a simulation based probabilistic analysis framework for a nonlinear dynamic structural system under non-Gaussian non-stationary loadings. The general simulation based probabilistic analysis framework (SIMLAB) is formulated by integrating 1) random variable generating modules; 2) random process generation modules; and 3) user selected deterministic solver and limit state function. The developed random process simulation module is able to generate a Gaussian, non-Gaussian, stationary, or non-stationary process. To demonstrate the applicability of the developed tool for a structural dynamic system with random variables and random processes, a free-free beam subjected to a sea wave induced random process is solved by integrating a structural dynamics code, DYNA3D, with the developed probabilistic analysis framework. The limit state function is formulated based on the first crossing of a beam Von Mises stress at an integration point above a safe threshold. In order to validate the accuracy of SIMLAB, a linear beam structure subjected to a stationary Gaussian process is considered first and the simulated statistical distributions of peak and extreme response variables are compared with analytical predictions. The effect of material nonlinearity on probability of failure and peak statistics is explored by using an elastoplastic beam model subjected to a random excitation. Results on probability of failure and peak statistics are compared with the corresponding statistical models for a linear structure. The great versatility of the simulation based probabilistic analysis framework provides us a solid foundation for the development of more advanced probabilistic analysis tools for reliability-based ship design.