Generating optimal topologies in structural design using a homogenization method

doi:10.1016/0045-7825(88)90086-2

Computer Methods in Applied Mechanics and Engineering

Volume 71, Issue 2, November 1988, Pages 197-224

https://doi.org/10.1016/0045-7825(88)90086-2 Get rights and content

Abstract

Optimal shape design of structural elements based on boundary variations results in final designs that are topologically equivalent to the initial choice of design, and general, stable computational schemes for this approach often require some kind of remeshing of the finite element approximation of the analysis problem. This paper presents a methodology for optimal shape design where both these drawbacks can be avoided. The method is related to modern production techniques and consists of computing the optimal distribution in space of an anisotropic material that is constructed by introducing an infimum of periodically distributed small holes in a given homogeneous, isotropic material, with the requirement that the resulting structure can carry the given loads as well as satisfy other design requirements. The computation of effective material properties for the anisotropic material is carried out using the method of homogenization. Computational results are presented and compared with results obtained by boundary variations.

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Generating optimal topologies in structural design using a homogenization method

Abstract

Comput. Meths. Appl. Mech. Engrg.

Comput. Meths. Appl. Mech. Engrg.

Internat. J. Solids and Structures

Internat. J. Solids and Structures

Internat. J. Numer. Meths. Engrg.

Mech. Struct. Mach.

Comm. Pure Appl. Math.

Comm. Pure Appl. Math.

Comm. Pure Appl. Math.

AIAA J.

Optimal Shape Design for Elliptic Systems

An optimization procedure for stress concentration by the finite element technique

Internat. J. Numer. Meths. Engrg.

Adaptive finite element methods for shape optimization of linearly elastic structures

Comput. Meths. Appl. Mech. Engrg.

On the optimum shape of a fillet in a flat bar with restrictions

Shape optimization of three-dimensional folded-plate structures

AIAA J.

Shape optimal design using B-splines

Comput. Meths. Appl. Mech. Engrg.

Shape design sensitivity analysis of elastic structures

J. Structural Mech.

A domain method for shape design sensitivity analysis of built-up structures

Comput. Meths. Appl. Mech. Engrg.

Design sensitivity analysis in structural mechanics, III. Effects of shape variation

J. Structural Mech.

The material derivative (or speed) method for shape optimization

Differentiation with respect to the domain in boundary value problems

Numer. Funct. Anal. Optim.

A new variational approach to structural shape design sensitivity analysis

On the existence of a solution in a domain identification problem

J. Math. Anal. Appl.

Quelques Resultat sur l'identification de domaines

Estimation de coefficients homogeneises

Generalized plate models and optimal design

Shape optimal design using $B- splines$