RELIABILITY-BASED OPTIMAL STRUCTURAL AND MECHANICAL DESIGN.

Abstract

Structural reliability technology provides analytical tools for management of uncertainty in all relevant design factors in structural and mechanical systems. Generally, the goal of analysis is to compute probabilities of failure in structural components or system having single or multiple failure mode. Alternately, modern optimization methods provide efficient numerical algorithms for locating optima, particularly in large-scale systems having prescribed deterministic constraints. Optimization procedure can accommodate random variables either directly in its objective function or as one of the primary constraints. The combination of elementary optimization and probabilistic design techniques is the subject of this study. Presented herein is a general strategy for optimization when the design factors are random variables and some or all of the constraints are probability statements. A literature review has indicated that optimization technology in a reliability context has not been fully explored for the general case of nonlinear performance functions and nonnormal variates associated multiple failure modes. This research focuses upon development of the theory to address this general problem. Because analysis algorithms are complicated, a computer code, program RELOPT, is constructed to automate the analysis. The objective function to be minimized is arbitrary, but would generally be the total expected lifetime costs including all initial costs as well as all costs associated with failure. Uncertainty is assumed to be possible in all design factors (including the factors to be determined), and they are modeled as random variables. In general, all of the constraints can be probability statements. The generalized reduce gradient (GRG) method was used for optimization calculations. Options for point probability calculations are first order reliability analysis using the Rackwitz-Fiessler (R-F) or advanced reliability analysis using Wu/FPI. For system reliability analysis either the first order Cornell's bounds or the second order Ditlevsen's bounds can be specified. Several examples are presented to illustrate the full range of capabilities of RELOPT. The program is validated by checking with independent and exact solutions. An example is provided which demonstrates that the cost of running RELOPT can be substantial as the size of the problem increases.