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Density filters for topology optimization based on the Pythagorean means
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering.ORCID iD: 0000-0002-0748-2853
2013 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 48, no 5, 859-875 p.Article in journal (Refereed) Published
Abstract [en]

In topology optimization, restriction methods are needed to prohibit mesh dependent solutions and enforce length scale on the optimized structure. This paper presents new restriction methods in the form of density filters. The proposed filters are based on the geometric and harmonic means, respectively, and possess properties that could be of interest in topology optimization, for example the possibility to obtain solutions which are almost completely black and white. The article presents the new filters in detail, and several numerical test examples are used to investigate the properties of the new filters compared to filters existing in the literature. The results show that the new filters in several cases provide solutions with competitive objective function values using few iterations, but also, and perhaps more importantly, in many cases, different filters make the optimization converge to different solutions with close to equal value. A variety of filters to choose from will hence provide the user with several suggested optimized structures, and the new filters proposed in this work may certainly provide interesting alternatives.

Place, publisher, year, edition, pages
2013. Vol. 48, no 5, 859-875 p.
Keyword [en]
Topology optimization, Regularization, Density filters
National Category
Computer Science Mathematics
URN: urn:nbn:se:kth:diva-136500DOI: 10.1007/s00158-013-0938-1ISI: 000326718800001ScopusID: 2-s2.0-84889102604OAI: diva2:677271
Swedish Research Council

QC 20131209

Available from: 2013-12-09 Created: 2013-12-05 Last updated: 2015-05-04Bibliographically approved
In thesis
1. Topology Optimization of Fatigue-Constrained Structures
Open this publication in new window or tab >>Topology Optimization of Fatigue-Constrained Structures
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Fatigue, or failure of material due to repeated cyclic loading, is one of the most common causes of mechanical failures. The risk of fatigue in a load carrying component is often lowered by adding material, thereby reducing stresses. This increases the component weight, reducing the performance of the component and increasing its manufacturing cost. There is thus a need to design components to be as light as possible, while keeping the risk of fatigue at a low enough level, i.e. there is a need for optimization of the component subject to fatigue constraints

This thesis deals with design against fatigue using topology optimization, which is a form of structural optimization where an optimal design is sought by using mathematical programming to decide which parts of a design domain should be filled with material, and which should not. 

To predict fatigue, accurate representation of the geometry and accurate stress computation are of utmost importance. In this thesis, methods for imposing constraints such as minimum inner radii and minimum member sizes in the form of four new density filters are proposed. The filters are able to generate a very sharp representation of the structural boundary. A method for improving the accuracy of stress results at the structural boundary is also proposed, based on extrapolation of results from the interior of the structure. The method gives more accurate stresses, which affects the resulting structures when solving optimization problems. 

A formulation for fatigue constraints in topology optimization is proposed, based on the weakest link integral. The formulation avoids the problem of choosing between accurate but costly local constraints, and efficient but approximate aggregated constraints, and gives a theoretical motivation for using expressions similar to the p-norm of stresses. 

For verifying calculations of the fatigue probability of an optimized structure, critical plane criteria are commonly used. A new method for evaluating such criteria using optimization methods is proposed, and is proved to give results within a user given error tolerance. It is shown that compared to existing brute force methods, the proposed method evaluates significantly fewer planes in the search of the critical one.


Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. xii, 39 p.
TRITA-MAT-A, 2015:04
topology optimization, fatigue constraints, stress constraints, density filters, restriction methods, weakest link theory, critical plane criteria
National Category
Research subject
urn:nbn:se:kth:diva-163575 (URN)978-91-7595-509-4 (ISBN)
Public defence
2015-05-22, F3, Lindstedtsvägen 26, Kungl Tekniska Högskolan, Stockholm, 14:00
Swedish Research Council, 2010-4172

QC 20150504

Available from: 2015-05-04 Created: 2015-04-08 Last updated: 2015-05-04Bibliographically approved

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