Layout Optimization of Structures

TLDR

Layout or topology optimization selects the best configuration for structural systems, a rapidly expanding field whose basic concepts date back nearly a century; it is mathematically challenging but economically rewarding, and while discretized solutions are unavoidable for most practical problems, explicit analytical solutions provide a reliable means for checking validity and convergence, a basis for assessing relative economy, and recent efficient numerical methods often extend analytical methods to multiload, multipurpose elastic systems. This review aims to present a unified formulation that covers both exact analytical and approximate discretized methods of layout optimization. The review examines these methods in detail, comparing exact analytical solutions with approximate discretized approaches.

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.