Dominant Failure Modes for Structures with Stochastic Load Processes

Abstract

Modal Failure probability (MFP) has no unique definition in time-invariant analysis, and true MFPs cannot be obtained without information on load history. Knowledge of true MFPs of a structure is important for design, since different failure modes have different consequences. Therefore, dominant mode identification methods for structures with time-varying random loading are needed. To this end, a three-phase method based on the first passage probability is presented to identify systematically the dominant failure modes when loads and/or resistances are stochastic processes. In phase I, the modes with higher pseudo modal outcrossing rates are identified. In phase II, modes are chosen which refine the partial system state limit surface such that the total outcrossing rate of the modes selected in phase I is minimized. Modes selected in phases I and II with outcrossing rates below a tolerance level are discarded in phase III. A rigid-plastic frame structure is provided to illustrate the effectiveness of the method. Mathematical programming formulation based on the kinematic theorem for plasticity is used to carry out the maximization and minimization processes.