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Stress and fatigue constrained topology optimization
Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.
2013 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns structural optimization in conceptual design stages, for which constraints that are adapted to industrial requirements have been developed for topology optimization problems. The objective of the project has been to identify and solve problems that today prevent structural optimization from being used in a broader sense in the avionic industry; the main focus has been on stress and fatigue constraints in topology optimization.

The thesis consists of two parts. The rst part gives an introduction to topology optimization and describes the developed methods for stress and fatigue constraints. In the second part, two papers are included, where the stress and fatigue constraints are evaluated, respectively.

In the rst paper, a clustered approach is presented, where stress constraints are applied to stress clusters, rather than points on the structure. This allows for a trade-o between computational time and accuracy, as the number of clusters and thus constraints can be varied. Dierent approaches for how to sort stress evaluation points into clusters and how to update the clusters, such that the results are suciently accurate for conceptual designs, are developed and evaluated. The two-dimensional examples conrm the theoretical discussions and the designs that are obtained have managed to avoid large stress concentrations, even for problems with an initial stress singularity. Compared to the traditional stiness based designs, the stress constrained designs are considered to be closer to a nal design, which will decrease the total product development time.

The second paper uses the methodology developed in the rst paper and applies it to high-cycle fatigue constraints. Using loads described by a variable load spectrum and material data from fatigue tests, the tensile principal stresses are constrained by a limit that is determined such that fatigue failure will not occur. In the examples, where the mass is minimized subjected to fatigue and static stress constraints, simple topologies are obtained and the structural parts are sized with respect to the critical fatigue stress and the yield limit. Stress concentrations are again avoided, for example by the creation of a radius around an internal corner. A comparison between static stress constraints based on the von Mises criterion and the highest tensile principal stresses is given and the examples clearly show the characteristics of the two formulations.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2013. , 47 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1571
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-88094Local ID: LIU-TEK-LIC-2013:5ISBN: 978-91-7519-703-6 (print)OAI: oai:DiVA.org:liu-88094DiVA: diva2:601670
Presentation
2013-02-08, A35, A-huset, Campus Valla, Linköpings universitet, Linköping, 13:15 (Swedish)
Opponent
Supervisors
Available from: 2013-01-30 Created: 2013-01-30 Last updated: 2017-05-15Bibliographically approved
List of papers
1. Stress constrained topology optimization
Open this publication in new window or tab >>Stress constrained topology optimization
2013 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 48, no 1, 33-47 p.Article in journal (Refereed) Published
Abstract [en]

This paper develops and evaluates a method for handling stress constraints in topology optimization. The stress constraints are used together with an objective function that minimizes mass or maximizes stiffness, and in addition, the traditional stiffness based formulation is discussed for comparison. We use a clustering technique, where stresses for several stress evaluation points are clustered into groups using a modified P-norm to decrease the number of stress constraints and thus the computational cost. We give a detailed description of the formulations and the sensitivity analysis. This is done in a general manner, so that different element types and 2D as well as 3D structures can be treated. However, we restrict the numerical examples to 2D structures with bilinear quadrilateral elements. The three formulations and different approaches to stress constraints are compared using two well known test examples in topology optimization: the L-shaped beam and the MBB-beam. In contrast to some other papers on stress constrained topology optimization, we find that our formulation gives topologies that are significantly different from traditionally optimized designs, in that it actually manage to avoid stress concentrations. It can therefore be used to generate conceptual designs for industrial applications.

Keyword
Topology optimization, Stress constraints, Clusters, SIMP, MMA
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-88092 (URN)10.1007/s00158-012-0880-7 (DOI)000320865900003 ()
Available from: 2013-01-30 Created: 2013-01-30 Last updated: 2017-12-06Bibliographically approved
2. Fatigue constrained topology optimization
Open this publication in new window or tab >>Fatigue constrained topology optimization
2014 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 50, no 2, 207-219 p.Article in journal (Refereed) Published
Abstract [en]

We present a contribution to a relatively unexplored application of topology optimization: structural topology optimization with fatigue constraints. A probability based high-cycle fatigue analysis is combined with principal stress calculations in order to find the topology with minimal mass that can withstand prescribed loading conditions for a specific life time. This allows us to generate optimal conceptual designs of structural components where fatigue life is the dimensioning factor.

We describe the fatigue analysis and present ideas that makes it possible to separate the fatigue analysis from the topology optimization. The number of constraints is kept low as they are applied to stress clusters, which are created such that they give adequate representations of the local stresses. Optimized designs constrained by fatigue and static stresses are shown and a comparison is also made between stress constraints based on the von Mises criterion and the highest tensile principal stresses.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2014
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:liu:diva-88093 (URN)10.1007/s00158-014-1054-6 (DOI)000339944100003 ()
Available from: 2013-01-30 Created: 2013-01-30 Last updated: 2017-12-06Bibliographically approved

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