Issues of computational efficiency in reliability-based structural optimization

This dissertation outlines new methodologies for computationally efficient reliability-based optimization (RBO) of structures. Specifically, new most probable failure point (MPP) approximations stemming from the Hasofer-Lind Rackwitz-Fiessler first-order reliability method (FORM) are introduced. Approximations are constructed during an RBO constraint assessment using the results of the MPP search employed by the FORM. The approximation is used in a subsequent constraint assessment to facilitate more rapid convergence of a new MPP search. To further reduce the computational cost of RBO, the approximations are implemented in a progressive RBO framework. The progressive framework is characterized by using a series of progressively more accurate reliability methods in the constraint analyses over the course of an RBO. The combination of the progressive framework and MPP approximation is shown to be more computationally efficient than a standard approach to RBO in several numerical examples.; The proposed RBO methodologies are implemented in structural test problems including truss structures and an aircraft engine turbine blade. The truss structures facilitate the testing of computationally intensive RBO methods and visualization of design spaces, while the turbine blade structure examines the applicability of RBO methods on a real-world problem. Several numerical examples are examined to provide a comparison of standard RBO approaches with the proposed methodologies. A discussion of the computational cost associated with the various RBO approaches is presented.; Lastly, methodologies for solving the discrete RBO (DRBO) problem are outlined. The DRBO problem is characterized by the presence of discrete design variables or discrete random variables, or both, in an RBO problem. The first DRBO technique explored uses a branch and bound (BB) method of discrete variable optimization to perform the design optimization and reliability analyses. The reliability analyses are performed using the FORM, where the BB algorithm is used to find the MPP. The second approach investigates the application of a genetic algorithm (GA) in both optimization tasks. The BB and GA techniques are tested on a truss structure to examine the effects of discretization. A discussion of implementation issues and optimization results is presented.