Journal ArticleDOI
Material interpolation schemes in topology optimization
Martin P. Bendsøe,Ole Sigmund +1 more
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TLDR
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.Abstract:
In topology optimization of structures, materials and mechanisms, parametrization of geometry is often performed by a grey-scale density-like interpolation function. In this paper we analyze and compare the various approaches to this concept in the light of variational bounds on effective properties of composite materials. This allows us to 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. Thus it is shown that the so-called artificial interpolation model in many circumstances actually falls within the framework of microstructurally based models. Single material and multi-material structural design in elasticity as well as in multi-physics problems is discussed.read more
Citations
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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
A 99 line topology optimization code written in Matlab
TL;DR: It is shown that only 49 Matlab input lines are required for solving a well-posed topology optimization problem and by adding three additional lines, the program can solve problems with multiple load cases.
Journal ArticleDOI
Topology optimization approaches: A comparative review
Ole Sigmund,Kurt Maute +1 more
TL;DR: An overview, comparison and critical review of the different approaches to topology optimization, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.
Journal ArticleDOI
Topology optimization of non-linear elastic structures and compliant mechanisms
T.E. Bruns,Daniel A. Tortorelli +1 more
TL;DR: In this paper, the material density field is filtered to enforce a length scale on the field variation and is penalized to remove less effective intermediate densities to resolve the non-existent solution to the solid void topology problem.
Journal ArticleDOI
A survey of structural and multidisciplinary continuum topology optimization: post 2000
TL;DR: Topology optimization is the process of determining the optimal layout of material and connectivity inside a design domain this paper, which is the same as the problem of finding the optimal configuration of a set of components.
References
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Journal ArticleDOI
Generating optimal topologies in structural design using a homogenization method
Martin P. Bendsøe,Noboru Kikuchi +1 more
TL;DR: 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.
Journal ArticleDOI
A variational approach to the theory of the elastic behaviour of multiphase materials
Zvi Hashin,S. Shtrikman +1 more
TL;DR: In this paper, the authors derived upper and lower bounds for the effective elastic moduli of quasi-isotropic and quasi-homogeneous multiphase materials of arbitrary phase geometry.
Journal ArticleDOI
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.
Journal ArticleDOI
The COC algorithm, Part II: Topological, geometrical and generalized shape optimization
Ming Zhou,George I. N. Rozvany +1 more
TL;DR: In this paper, the COC algorithm is applied to the simultaneous optimization of the topology and geometry of trusses with many thousand potential members, and numerical results obtained are shown to be in close agreement with analytical results.
Book
Shape optimization by the homogenization method
TL;DR: In this article, a relaxed formulation for shape optimization in the context of shape optimization is presented, where the authors seek minimizers of the sum of the elastic compliance and of the weight of a solid structure under specified loading.