Structural Optimization: Fundamentals and Applications by Uri Kirsch

By Uri Kirsch

This publication was once built whereas instructing a graduate path at a number of universities within the usa. Europe and Israel. over the last twenty years. the aim of the ebook is to introduce the basics and functions of optimal structural layout. a lot paintings has been performed during this region lately and lots of reviews were released. The ebook is an try to acquire jointly chosen subject matters of this literature and to offer them in a unified strategy. It meets the necessity for an introductory textual content protecting the elemental options of modem structural optimization. a prior publication via the writer in this topic ("Optimum Structural Design". released via McGraw-Hill big apple in 1981 and by means of Maruzen Tokyo in 1983). has been used largely as a textual content in lots of universities through the global. the current ebook displays the speedy development and up to date advancements during this quarter. a huge hassle in learning structural optimization is that integration of strategies utilized in a number of parts. similar to structural research. numerical optimization and engineering layout. is important on the way to clear up a particular challenge. To facilitate the learn of those issues. the e-book discusses intimately substitute challenge formulations. the basics of other optimization tools and numerous concerns with regards to structural layout. the benefits and the restrictions of the awarded methods are illustrated through various examples.

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Weight is the most commonly used objective function due to the fact that it is readily quantified, although most optimization methods are not limited to weight minimization. The weight of the structure is often of critical importance, but the minimum weight is not always the cheapest. Cost is of wider practical importance than weight, but it is often difficult to obtain sufficient data for the construction of a real cost function. A general cost function may include the cost of materials, fabrication, transportation, etc.

The following relations have been assumed for the cross sections: 54 1 Problem Statement 100 Fig. 19. 0. The constraints are related to the stresses in sections A, B, C, D and the objective function represents the volume of the beam. The modulus of elasticity is 30,000. B. 8 assume the force method of analysis. Formulate the optimal design problem: a. 64)]; b. 62)]; c. 69). 2, assuming N I and N z =redundant force in member 4. 3, assuming NI = bending moment over the interior support under PI' and N z bending moment over the interior support underPz· = X, ~ I: Fig.

4 Typical Problem Formulations 45 Simultaneous Analysis and Design. 50). 58) Kr=R C1=Sr In this formulation the analysis equality constraints are included in the problem formulation. These constraints are satisfied at the optimum but not necessarily at intermediate designs. before the optimum is reached. Since the stresses are given explicitly in terms of the displacements. it is not necessary to consider C1 as independent variables. Substituting the explicit stress-displacement relations into the stress constraints.

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