Optimal shape design as a material distribution problem

Optimal shape design as a material distribution problem Shape optimization in a general setting requires the determination of the optimal spatial material distribution for given loads and boundary conditions. Every point in space is thus a material point or a void and the optimization problem is a discrete variable one. This paper describes various ways of removing this discrete nature of the problem by the introduction of a density function that is a continuous design variable. Domains of high density then define the shape of the mechanical element. For intermediate densities, material parameters given by an artificial material law can be used. Alternatively, the density can arise naturally through the introduction of periodically distributed, microscopic voids, so that effective material parameters for intermediate density values can be computed through homogenization. Several examples in two-dimensional elasticity illustrate that these methods allow a determination of the topology of a mechanical element, as required for a boundary variations shape optimization technique. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Structural and Multidisciplinary Optimization Springer Journals

Optimal shape design as a material distribution problem

, Volume 1 (4) – Apr 23, 2005
10 pages

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References (37)

Publisher
Springer Journals
Subject
Engineering; Theoretical and Applied Mechanics; Computational Mathematics and Numerical Analysis; Engineering Design
ISSN
1615-147X
eISSN
1615-1488
DOI
10.1007/BF01650949
Publisher site
See Article on Publisher Site

Abstract

Shape optimization in a general setting requires the determination of the optimal spatial material distribution for given loads and boundary conditions. Every point in space is thus a material point or a void and the optimization problem is a discrete variable one. This paper describes various ways of removing this discrete nature of the problem by the introduction of a density function that is a continuous design variable. Domains of high density then define the shape of the mechanical element. For intermediate densities, material parameters given by an artificial material law can be used. Alternatively, the density can arise naturally through the introduction of periodically distributed, microscopic voids, so that effective material parameters for intermediate density values can be computed through homogenization. Several examples in two-dimensional elasticity illustrate that these methods allow a determination of the topology of a mechanical element, as required for a boundary variations shape optimization technique.

Journal

Structural and Multidisciplinary OptimizationSpringer Journals

Published: Apr 23, 2005