Development of a Large Admissible Perturbations methodology for reliability of complex structures.

摘要

Satisfactory techniques exist in structural reliability to calculate (approximate) the probability of failure of a structure for which the failure domain has been defined. In the space of random material, geometry, and loading variables, the failure domain is defined as the union of all failure states with respect to all global failure equations. Calculation of the reliability of complex structures presents a challenging and long standing research problem because of the difficulty in defining the failure domain for such structures; i.e. providing global failure equations.;There are two major contributions in this dissertation: (1) A new methodology called Large Admissible Perturbations Approach to Reliability, is developed for reliability analysis and design of complex structures. The core of this new methodology is the development of the exact, piecewise continuous and strongly nonlinear implicit global failure equation for any type of failure criterion, provided that the corresponding structural analysis can be performed by FEM. This is achieved by relating the mean structural state to the most probable failure state through the Large Admissible Perturbation theory. A stochastic Large Admissible Perturbations algorithm is developed to identify the most probable failure state with only a few finite element analyses. Calculation of the probability of failure for complex structures is then achieved using mathematical tools of structural reliability theory. (2) The to-date illusive term redundancy is defined as an injective mapping relating the redundancy of the entire structure to that of all individual structural components in a way that can be used for design. The logical gap between redundancy and reliability is closed.;Several numerical applications are worked out to demonstrate the efficiency of the stochastic Large Admissible Perturbations algorithm and to allow comparisons with existing techniques. It is shown that the newly developed methodology has effectively solved the reliability analysis problem for complex structures and furthermore that it has the potential to solve the reliability design problem in the future.