Journal ArticleDOI
Solutions to shape and topology eigenvalue optimization problems using a homogenization method
TLDR
In this article, a solution strategy to find the shape and topology of structures that maximize a natural frequency is presented, based on a homogenization method and the representation of the shape of the structure as a material property.Abstract:
A solution strategy to find the shape and topology of structures that maximize a natural frequency is presented. The methodology is based on a homogenization method and the representation of the shape of the structure as a material property. The problem is formulated as a reinforcement problem in which a given structure is reinforced using a prescribed amount of material. Two dimensional, plane elasticity problems are considered. Examples are presented for illustration.read more
Citations
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Journal ArticleDOI
Topology optimization of continuum structures: A review*
Hans A. Eschenauer,Niels Olhoff +1 more
Journal ArticleDOI
A critical review of established methods of structural topology optimization
TL;DR: In this paper, the authors evaluate and compare established numerical methods of structural topology optimization that have reached the stage of application in industrial software, and they hope that their text will spark off a fruitful and constructive debate on this important topic.
Journal ArticleDOI
Topology optimization of continuum structures with local stress constraints
Pierre Duysinx,Martin P. Bendsøe +1 more
TL;DR: In this paper, the authors introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria for porous composite materials, initially by studying the stress states of the so-called rank 2 layered materials, then, on the basis of the theoretical study of the rank 2 microstructures, they propose an empirical model that extends the power penalized stiffness model (also called SIMP for Solid Isotropic Microstructure with Penalization for intermediate densities).
Journal ArticleDOI
A topology optimization method based on the level set method incorporating a fictitious interface energy
TL;DR: In this paper, the authors proposed a new topology optimization method, which can adjust the geometrical complexity of optimal configurations, using the level set method and incorporating a fictitious interface energy derived from the phase field method.
Journal ArticleDOI
Topological design for vibrating structures
TL;DR: In this article, the topological optimization technique using micro-scale voids with the homogenization method has been applied to solve stiffness maximization problem with success, and an extended optimization algorithm is also derived to maximize a set of eigenvalues as well as to identify the topology design for specified eigen values to characterize forced vibration of a structure.
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
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.
Book
Elements of Structural Optimization
TL;DR: In this article, the authors present an approach for the optimization of structural components of a ten-bar truss and a twenty-five-bar trestle in the context of structural optimization.
Journal ArticleDOI
A homogenization method for shape and topology optimization
Katsuyuki Suzuki,Noboru Kikuchi +1 more
TL;DR: In this paper, shape and topology optimization of a linearly elastic structure using a modification of the homogenization method introduced by Bendsoe and Kikuchi together with various examples which may justify validity and strength of the present approach for plane structures are discussed.
Journal ArticleDOI
On optimal orientation of orthotropic materials
TL;DR: In this paper, the optimal orientation of an anisotropic material with respect to the actual strain condition was investigated and complete analytical results were derived, including local as well as global maxima and minima.