The new approach is applied to the design of a simple structure. Both methods are robust to a satisfactory degree. The results are compared to those obtained by the safety index approach without integrating the analysis and design processes. The new methods substantially reduce the computational cost of optimization, which indicates that integrated analysis and design has the potential of removing a major obstacle, which is the excessive computational cost, in applying stochastic optimization to real life structural design. AcknowledgementsAcknowlcdgcments iii;"- Introduction Structural optimization has seen remarkable progress in recent years and is now recognized as a practical design tool. The development of the above method was associated with the advancement in several other areas like:• Establishment of finite element methods.• Advancement in computer technology.• Creation of new, more efficient and robust optimization algorithms.• Development of semi-analytical procedures for sensitivity analysis. By semi-analytical we mean that the expressions developed, involved terms, that had to be calculated numerically.Introduction l I-Iowever, it is generally recognized that structural problems are often non-deterministic and, consequently, decisions have to be made in the presence of uncertainties. That gave birth, in the last one-two decades to systematic procedures for decision making under uncertainties, through the concept of reliability.In general, a stochastic programming problem is an optimization problem in.which some or all of the parameters are described by random variables rather than by deterministic quantities. The basic idea of all stochastic programming methods is to convert the probabilistic problem into an equivalent deterministic one.One of the first publications dealing with reliability based optimization design was published by F. Moses and D.E. Kinser [1]. There, techniques for tinding the minimum weight design of a multi-load, multi-element structure with a prescribed level of safety have been described. Any form of frequency distribution for loads and strengths can be treated, but the probabilistic analysis is applicable only to conventional structures, for which there is a valid structural analysis. It was also demonstrated that an overall level of structural safety can be prescribed in terms of a rational criterion, like the probability of failure, and minimum weight structures can be designed to meet the prescribed safety level.Thoft-Christensen and Sorensen [2,3], established a procedure for system reliability based optimization for framed structures, using the beta-unzippinng method for estimating system reliability. Sensitivity derivatives of the safety index of each failure element of the system were calculated using semi-analytical Introduction 2formulas. Feng and Moses [4], derived an optimality criterion for sizing the components of framed structures, that satisfy a system reliability constraint. This criterion, which is a special case of the Kuhn-Tucker conditions, states tha...
This paper describes an application of genetic algorithms to deterministic and probabilistic (reliability-based) optimization of damping augmentation for a truss structure. The probabilistic formulation minimizes the probability of exceeding upper limits on the magnitude of the dynamic response of the structure due to uncertainties in the properties of the damping devices. The corresponding deterministic formulation maximizes a safety margin with respect to these limits. Because this work was done in the context of an experimental comparison of the reliabilities of the resulting designs, antioptimization was used to maximize the contrast between the probabilities of failure of the two designs. This contrast maximization was also performed with a genetic algorithm. The paper describes the genetic algorithm used for the optimization and antioptimization, and a number of modifications to the antioptimization formulation intended to reduce the computational expense to an acceptable level. Optimal designs are obtained for both formulations. The probabilistic design shows a very significant improvement in reliability.
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