Structural Optimization

Fundamentals and Applications

verfasst von: Prof. Uri Kirsch

Verlag: Springer Berlin Heidelberg

Enthalten in: Professional Book Archive

Einloggen, um Zugang zu erhalten

Über dieses Buch

This book was developed while teaching a graduate course at several universities in the United States. Europe and Israel. during the last two decades. The purpose of the book is to introduce the fundamentals and applications of optimum structural design. Much work has been done in this area recently and many studies have been published. The book is an attempt to collect together selected topics of this literature and to present them in a unified approach. It meets the need for an introductory text covering the basic concepts of modem structural optimization. A previous book by the author on this subject ("Optimum Structural Design". published by McGraw-Hill New York in 1981 and by Maruzen Tokyo in 1983). has been used extensively as a text in many universities throughout the world. The present book reflects the rapid progress and recent developments in this area. A major difficulty in studying structural optimization is that integration of concepts used in several areas. such as structural analysis. numerical optimization and engineering design. is necessary in order to solve a specific problem. To facilitate the study of these topics. the book discusses in detail alternative problem formulations. the fundamentals of different optimization methods and various considerations related to structural design. The advantages and the limitations of the presented approaches are illustrated by numerous examples.

Inhaltsverzeichnis

Frontmatter

1. Problem Statement

Abstract

The motivation of optimization is to exploit the available limited resources in a manner that maximizes utility. The object of optimal design is to achieve the best feasible design according to a preselected measure of effectiveness. A growing realization of scarcity of the raw materials resulted in a demand for light weight and low cost structures. This demand emphasizes the need for weight and cost optimization of structures.

Uri Kirsch

2. Optimization Methods

Abstract

Optimization problems discussed in this chapter can be formulated in the general form presented in Sect. 1.3.4, where the objective function and the constraints are nonlinear functions of the variables. The solution methods commonly used for obtaining the optimal design may be divided into several categories. One classification of solution methods considers specific versus general methods. Specific optimality criteria methods, used exclusively in structural optimization, will be presented in Sect. 4.3. In this chapter general-purpose mathematical programming (MP) methods, which are commonly applied to optimization problems in several fields, will be discussed. These methods have the advantage of wider applicability and base of resources. As a result, efficient and reliable algorithms are continually developed. Applying MP methods to structural design, a wide variety of problems can be considered, including:

Complex structural systems subject to different failure modes in each of several load conditions.

General design variables representing cross-sectional dimensions, the geometry or the topology of the structure.

Various constraints on the structural behavior and on the design variables.

A general objective function representing the cost or the weight of the structure.

Uri Kirsch

3. Approximation Concepts

Abstract

One of the main obstacles in the solution of optimal design problems is the high computational cost required for solving large scale problems. Applications of approximation concepts in structural optimization have been motivated by the following characteristics of the design problem:

The problem size (number of variables and constraints) is usually large. Each element involves at least one variable, and various failure modes under each of several load conditions must be considered.
The constraints are usually implicit functions of the design variables. That is, evaluation of the constraints for any given design involves solution of a set of simultaneous equations. In addition, it is often required to calculate constraint derivatives with respect to design variables.
In general, the solution of optimal design problems is iterative and consists of repeated analyses followed by redesign steps. The number of redesigns (or repeated analyses) is usually a function of the problem dimensionality.

Uri Kirsch

4. Design Procedures

Abstract

In establishing an optimal design procedure, the following steps should be taken:

The design problem is formulated. The design variables are chosen, the constraints and the objective function are defined and an analysis model is introduced. This step is of crucial importance for the solution process. A poor problem formulation might lead to incorrect results and/or prohibitive computational cost. Various formulations have been discussed in Chap. 1.
The optimization method is selected. One of the methods presented in Chap. 2 might be suitable for the solution process. In general, the reliability and ease of use of the method are more important than its computational efficiency. Since most of the cost of optimization is associated with the exact analysis and derivative calculations, efficiency of the method used to solve the problem is not a major consideration in choosing the method.
Approximations are introduced. It has been noted that approximations are essential in most practical design problems. Using linking and basis reduction methods, it is possible to reduce the number of independent design variables. Scaling of variables, constraint normalization and constraint deletion techniques (Sect. 1.3.4) are all intended to improve the solution efficiency. Approximate behavior models, discussed in Chap. 3, are often necessary in order to reduce the number of exact analyses during the solution process.
A design procedure is established. The problem formulation, the chosen optimization method and the approximation concepts are integrated to introduce an effective solution strategy. In this chapter, various design procedures demonstrate the solution methodology.

Uri Kirsch

Backmatter

Titel: Structural Optimization
verfasst von: Prof. Uri Kirsch
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-642-84845-2
Print ISBN: 978-3-540-55919-1
DOI: https://doi.org/10.1007/978-3-642-84845-2

Springer Professional

Über dieses Buch

Inhaltsverzeichnis

Frontmatter

1. Problem Statement

2. Optimization Methods

3. Approximation Concepts

4. Design Procedures

Backmatter