Journal ArticleDOI
Slope constrained topology optimization
Joakim Petersson,Ole Sigmund +1 more
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This article is published in International Journal for Numerical Methods in Engineering.The article was published on 1998-04-30. It has received 337 citations till now. The article focuses on the topics: Topology optimization.read more
Citations
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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
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
Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima
Ole Sigmund,Joakim Petersson +1 more
TL;DR: The current knowledge about numerical instabilities such as checkerboards, mesh-dependence and local minima occurring in applications of the topology optimization method are summarized and the methods with which they can be avoided are listed.
Journal ArticleDOI
Morphology-based black and white filters for topology optimization
TL;DR: In this article, the physical stiffness of an element is based on a function of the design variables of the neighboring elements, and a new class of morphology-based restriction schemes that work as density filters is introduced.
Journal ArticleDOI
On the Design of Compliant Mechanisms Using Topology Optimization
TL;DR: In this paper, the authors present a method for optimal design of compliant mechanism topologies based on continuum-type topology optimization techniques and find the optimal mechanism topology within a given design domain and a given position and direction of input and output forces.
References
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Book
The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
TL;DR: The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.
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.
Book
Optimization of structural topology, shape, and material
TL;DR: The method presented in this book has been developed by Martin Bendsoe in co-operation with other researchers and can be considered as one of the most effective approaches to the optimization of layout and material design as discussed by the authors.
Journal ArticleDOI
A new Approach to Variable-Topology Shape Design Using a Constraint on the Perimeter
TL;DR: The perimeter method as mentioned in this paper allows the designer to control the number of holes in the optimal design and to establish their characteristic length scale, thus eliminating the need for relaxation, thereby circumventing many of the complexities and restrictions of other approaches to topology design.
Journal ArticleDOI
An optimal design problem with perimeter penalization
Luigi Ambrosio,Giuseppe Buttazzo +1 more
TL;DR: In this paper, the optimal design problem of finding the minimal energy configuration for a mixture of two conducting materials when a perimeter penalization of the unknown domain is added is studied and it is shown that in this situation an optimal domain exists and that, under suitable assumptions on the data, it is an open set.
Related Papers (5)
Generating optimal topologies in structural design using a homogenization method
Martin P. Bendsøe,Noboru Kikuchi +1 more
Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima
Ole Sigmund,Joakim Petersson +1 more