Generating optimal topologies in structural design using a homogenization method
Martin P. Bendsøe,Noboru Kikuchi +1 more
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In this article, the authors present a methodology for optimal shape design based on homogenization, which 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, i.i.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, i~otropic 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.read more
Citations
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Optimal shape design as a material distribution problem
TL;DR: In this article, various ways of removing this discrete nature of the problem by the introduction of a density function that is a continuous design variable are described. But none of these methods can be used for shape optimization in a general setting.
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A level set method for structural topology optimization
TL;DR: A new approach to structural topology optimization that represents the structural boundary by a level set model that is embedded in a scalar function of a higher dimension that demonstrates outstanding flexibility of handling topological changes, fidelity of boundary representation and degree of automation.
Journal ArticleDOI
Structural optimization using sensitivity analysis and a level-set method
TL;DR: A new numerical method based on a combination of the classical shape derivative and of the level-set method for front propagation, which can easily handle topology changes and is strongly dependent on the initial guess.
Journal ArticleDOI
Material interpolation schemes in topology optimization
Martin P. Bendsøe,Ole Sigmund +1 more
TL;DR: In this article, the authors analyze and compare the various approaches to this concept in the light of variational bounds on effective properties of composite materials, and derive simple necessary conditions for the possible realization of grey-scale via composites, leading to a physical interpretation of all feasible designs as well as the optimal design.
Journal ArticleDOI
A simple evolutionary procedure for structural optimization
Yi Min Xie,Grant P. Steven +1 more
TL;DR: In this paper, a simple evolutionary procedure is proposed for shape and layout optimization of structures, where low stressed material is progressively eliminated from the structure during the evolution process, and various examples are presented to illustrate the optimum structural shapes and layouts achieved by this procedure.
References
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Asymptotic Analysis of Periodic Structures
Book
Asymptotic analysis for periodic structures
TL;DR: In this article, the authors give a systematic introduction of multiple scale methods for partial differential equations, including their original use for rigorous mathematical analysis in elliptic, parabolic, and hyperbolic problems, and with the use of probabilistic methods when appropriate.
Book
Non-Homogeneous Media and Vibration Theory
TL;DR: In this article, a spectral perturbation of spectral families and applications to self-adjoint eigenvalue problems are discussed, as well as the Trotter-Kato theorem and related topics.
Book
Design Sensitivity Analysis of Structural Systems
TL;DR: In this paper, the mathematical and engineering foundations of sensitivity analysis of structural systems are examined with a broad range of applications to structural components and structural systems, including finite element models, design distribution of material described by functions and shape, and built-up structures that are composed of interconnected components.
Book
Optimal Shape Design for Elliptic Systems
TL;DR: The techniques of the calculus of variation and of optimization proved to be successful for several optimal shape design problems however these remain expensive both in the qualification of the engineers required to understand the method and in computing time.