Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Topology Optimization of Fatigue-Constrained Structures
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0002-0748-2853
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.
Series
TRITA-MAT-A, 2015:04
Keyword [en]
topology optimization, fatigue constraints, stress constraints, density filters, restriction methods, weakest link theory, critical plane criteria
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-163575ISBN: 978-91-7595-509-4 (print)OAI: oai:DiVA.org:kth-163575DiVA: diva2:805142
Public defence
2015-05-22, F3, Lindstedtsvägen 26, Kungl Tekniska Högskolan, Stockholm, 14:00
Opponent
Supervisors
Funder
Swedish Research Council, 2010-4172
Note

QC 20150504

Available from: 2015-05-04 Created: 2015-04-08 Last updated: 2015-05-04Bibliographically approved
List of papers
1. Density filters for topology optimization based on the Pythagorean means
Open this publication in new window or tab >>Density filters for topology optimization based on the Pythagorean means
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.

Keyword
Topology optimization, Regularization, Density filters
National Category
Computer Science Mathematics
Identifiers
urn:nbn:se:kth:diva-136500 (URN)10.1007/s00158-013-0938-1 (DOI)000326718800001 ()2-s2.0-84889102604 (Scopus ID)
Funder
Swedish Research Council
Note

QC 20131209

Available from: 2013-12-09 Created: 2013-12-05 Last updated: 2017-12-06Bibliographically approved
2. Interior value extrapolation: a new method for stress evaluation during topology optimization
Open this publication in new window or tab >>Interior value extrapolation: a new method for stress evaluation during topology optimization
2015 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 51, no 3, 613-629 p.Article in journal (Refereed) Published
Abstract [en]

This article presents a new method for evaluating stresses in the jagged structures that arise when using a fixed finite element mesh to optimize the topology of a structure. The new method, Interior Value Extrapolation, IVE, exploits the fact that in the interior of the structure, the stresses calculated by the finite element method are more accurate than at the boundary. The jagged nature of the mesh makes stresses at the boundary oscillate. Therefore, stresses at the boundary are instead extrapolated from results in the interior, resulting in a more stable and accurate stress measure. A restriction method in the form of a non linear density filter is also proposed, tailored to be used in conjunction with the new stress evaluation method. The new method is evaluated for accuracy using example geometries, for which the stresses are known. It is shown that IVE improves the accuracy of the stress calculation. Optimization examples are thereafter solved with and without IVE, and the results are discussed. It is shown that the change in stress evaluation can in fact cause changes in the solution of a typical stress minimization problem.

Keyword
Stress evaluation, Finite element methods, Topology design
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-163573 (URN)10.1007/s00158-014-1171-2 (DOI)000352705400005 ()
Funder
Swedish Research Council, 2010-4172
Note

QC 20150410

Available from: 2015-04-08 Created: 2015-04-08 Last updated: 2017-12-04Bibliographically approved
3. Using the weakest link model of fatigue in topology optimization
Open this publication in new window or tab >>Using the weakest link model of fatigue in topology optimization
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this work, a method for incorporating fatigue failure in topology op- timization problems is presented. The method is based on the weakest link model of failure, developed by Weibull. The model is based on an assumption on the failure probability of a volume element, as a function of the applied stress. Given some assumptions, the total failure probability of the structure may be calculated as an integral over all elements. In this paper, it is shown that the weakest link model for failure takes a form that is very suitable for topology optimization. In fact, it is shown that the expression for failure probability according to Weibull under some circumstances is very similar to the much used p-norm of stresses. In the paper, the weakest link model is explained in detail, and adaptations to make it suitable for topology optimization are made. Suggestions on how to choose the parameters of the model are given, and the effects of different parameter choices are evaluated using examples. 

Keyword
stress, fatigue, topology optimization
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-163574 (URN)
Funder
Swedish Research Council, 2010-4172
Note

QS 2015

Available from: 2015-04-08 Created: 2015-04-08 Last updated: 2015-05-04Bibliographically approved
4. A branch and bound algorithm for evaluation of the Findley fatigue criterion
Open this publication in new window or tab >>A branch and bound algorithm for evaluation of the Findley fatigue criterion
2015 (English)In: International Journal of Fatigue, ISSN 0142-1123, E-ISSN 1879-3452, Vol. 73, 27-38 p.Article in journal (Refereed) Published
Abstract [en]

In this manuscript, a new algorithm for evaluation of the Findley fatigue criterion is proposed. The algorithm uses a branch and bound technique to limit the number of investigated planes in the search for the critical one. The algorithm has two major advantages over currently existing methods. Firstly, for a given tolerance on the error of the evaluation, it needs to investigate fewer planes on average, thereby reducing the execution time compared to state of the art methods. Secondly, the algorithm is guaranteed to give results within a tolerance of the global maximum, and this tolerance may be freely chosen by the analyst.

Keyword
Critical plane, Multiaxial fatigue, Mathematical analysis, Global optimization
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-161086 (URN)10.1016/j.ijfatigue.2014.11.008 (DOI)000349272300003 ()2-s2.0-84916896494 (Scopus ID)
Funder
Swedish Research Council, 2010-4172
Note

QC 20150325

Available from: 2015-03-25 Created: 2015-03-09 Last updated: 2017-12-04Bibliographically approved

Open Access in DiVA

Thesis(729 kB)405 downloads
File information
File name FULLTEXT01.pdfFile size 729 kBChecksum SHA-512
c496636e654cfa69e7075ed459e356956c597da506777fd54e4d98b1c811fd5e8efbf9328c0d1644099cbc2e2965b5aed0c325df19a9041eba22edfe4bce13ef
Type fulltextMimetype application/pdf

Authority records BETA

Svärd, Henrik

Search in DiVA

By author/editor
Svärd, Henrik
By organisation
Optimization and Systems Theory
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 405 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 771 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf