Abstract:

Algorithms for solving three classes of reliability-based optimal structural design problems are developed. The first class of problems is to minimize the cost of the design, subject to failure probability and structural constraints. The second class is to minimize the failure probability of the design, subject to cost and structural constraints. The third class of problems is to minimize the initial cost plus the expected cost of failure, subject to failure probability and structural constraints. The failure probabilities can describe component failures or series structural system failures. The third class of problems is further extended to the optimal design of a portfolio of structures.

Based on a first-order approximation to the failure probability, we construct approximating problems that can be solved repeatedly to obtain approximations to the solutions of the original design problems. The approximating problems are made dependent on a set of parameters that can be adjusted to improve the accuracy of the first-order approximations. The adjustment of the parameters is based on separate evaluations of the failure probability. In special cases, we show that the approximating problems are identical to the original ones. We develop a set of parameter-adjustment rules that, together with subroutines for solving the approximating problems, composes the collection of new algorithms for solving reliability-based optimal structural design problems. Effectively, the new algorithms solve a sequence of first-order approximating problems that are constructed as the computations progress. It is observed in a set of numerical design examples that the parameter-adjustment rules are efficient tools for improving the accuracy of the first-order approximations.

The reliability-based optimal structural design algorithms developed in this study present significant departures from the state-of-the-art. In particular, careful attention is given to the underlying assumptions and approximations to ensure a rigorous mathematical foundation for the algorithms. This, together with the fact that first-, or second-order reliability methods, Monte Carlo Simulation, or any other computational reliability method can be employed, makes the algorithms efficient, robust and versatile tools for solving reliability-based optimal structural design problems.