Some Basic Principles of Reliability-Based Optimization (RBO) of Structures and Mechanical Components

Abstract

Particularly in view of the introduction of product liability, reliability-based design procedures, and for that matter optimization (RBO) receive increasing attention. The analysis deals with statistical uncertainties inherent in structural, material, damage parameters, etc., which are modeled by random variables. The mechanical representation of the structure and the component respectively is generally modeled by Finite Elements (FE). In this paper basic mathematical formulations of design objectives and restrictions including reliability measures are discussed. Based on these models structural reliability analyses provide information for design modification and selection of an optimal design solution. As generally minimization of the expected total cost of the structure including initial costs and costs due to failure, minimization of the overall probability of failure and weight minimization with respect to reliability constraints are considered. Design problems commonly denoted as multiobjective or multicriteria optimization problems are treated. For the reliability analysis numerical methods are utilized to estimate the reliability measures. These procedures are already cast in an easy-to-use-software, denoted as COSSAN (Computational Stochastic Structural Analysis). In this context a concept is discussed, which is based on the separation of the tasks of reliability analysis and nonlinear mathematical programming techniques for which pertinent applicable software is already available. The RBO procedure utilizes approximation techniques for estimating the reliability measures. In particular, the reliability analysis makes use of the well known Response Surface Method (RSM) in context with Advanced Monte Carlo Simulation techniques, while the reliability based optimization procedure itself is controlled by the well known NLPQL-algorithm. Finally a number of numerical applications are shown in order to exemplify the approach.