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Interior value extrapolation: a new method for stress evaluation during topology optimization
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0002-0748-2853
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.

Place, publisher, year, edition, pages
2015. Vol. 51, no 3, 613-629 p.
Keyword [en]
Stress evaluation, Finite element methods, Topology design
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-163573DOI: 10.1007/s00158-014-1171-2ISI: 000352705400005OAI: oai:DiVA.org:kth-163573DiVA: diva2:801283
Funder
Swedish Research Council, 2010-4172
Note

QC 20150410

Available from: 2015-04-08 Created: 2015-04-08 Last updated: 2017-12-04Bibliographically 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.
Series
TRITA-MAT-A, 2015:04
Keyword
topology optimization, fatigue constraints, stress constraints, density filters, restriction methods, weakest link theory, critical plane criteria
National Category
Mathematics
Research subject
Mathematics
Identifiers
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
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

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