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REVIEW ARTICLES

Layout Optimization of Structures

[+] Author and Article Information
G. I. N. Rozvany

FB 10, Essen University, Postfach 10 37 64, D-45117 Essen, Germany

M. P. Bendso̸e

Mathematical Institute, Technical University of Denmark, Bldg. 303, DK-2800 Lyngby, Denmark

U. Kirsch

Department of Civil Engineering, Technion, Technion City, Haifa 32000, Israel

Appl. Mech. Rev 48(2), 41-119 (Feb 01, 1995) (79 pages) doi:10.1115/1.3005097 History: Online April 29, 2009

Abstract

Layout or topology optimization deals with the selection of the best configuration for structural systems and constitutes one of the newest and most rapidly expanding fields of structural design, although some of its basic concepts were established almost a century ago. While mathematically and computationally perhaps the most challenging, it is also economically the most rewarding design task. This review article is based on a unified formulation and covers in detail both exact, analytical methods and approximate, discretized methods of layout optimization. Although discretized solutions are unavoidable for most practical, real-world problems, only explicit analytical solutions provide (i) a reliable means for checking the validity and convergence of numerical methods and (ii) a basis for assessing the relative economy of other designs. Moreover, some of the most efficient new numerical methods of layout optimization are iterative versions of analytical methods. Particularly promising are recent extensions of the exact layout theory to multiload, multipurpose elastic systems.

Copyright © 1995 by The American Society of Mechanical Engineers
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