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Stress constrained topology optimization
Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.
Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.ORCID iD: 0000-0001-8460-0131
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.

Place, publisher, year, edition, pages
2013. Vol. 48, no 1, 33-47 p.
Keyword [en]
Topology optimization, Stress constraints, Clusters, SIMP, MMA
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-88092DOI: 10.1007/s00158-012-0880-7ISI: 000320865900003OAI: oai:DiVA.org:liu-88092DiVA: diva2:601666
Available from: 2013-01-30 Created: 2013-01-30 Last updated: 2017-12-06Bibliographically approved
In thesis
1. Stress and fatigue constrained topology optimization
Open this publication in new window or tab >>Stress and fatigue constrained topology optimization
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:nbn:se:liu:diva-88094 (URN)LIU-TEK-LIC-2013:5 (Local ID)978-91-7519-703-6 (ISBN)LIU-TEK-LIC-2013:5 (Archive number)LIU-TEK-LIC-2013:5 (OAI)
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
2. Topology optimization considering stress, fatigue and load uncertainties
Open this publication in new window or tab >>Topology optimization considering stress, fatigue and load uncertainties
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This dissertation concerns structural topology optimization in conceptual design stages. The objective of the project has been to identify and solve problems that prevent structural topology optimization from being used in a broader sense in the avionic industry; therefore the main focus has been on stress and fatigue constraints and robustness with respect to load uncertainties.

The thesis consists of two parts. The first part gives an introduction to topology optimization, describes the new contributions developed within this project and motivates why these are important. The second part includes five papers.

The first paper deals with stress constraints and a clustered approach is presented where stress constraints are applied to stress clusters, instead of being defined for each point of the structure. Different approaches for how to create and update the clusters, such that sufficiently accurate representations of the local stresses are obtained at a reasonable computational cost, are developed and evaluated.

High-cycle fatigue constraints are developed in the second paper, where loads described by a variable-amplitude load spectrum and material data from fatigue tests are used to determine a limit stress, for which below fatigue failure is not expected. A clustered approach is then used to constrain the tensile principal stresses below this limit.

The third paper introduces load uncertainties and stiffness optimization considering the worst possible loading is then formulated as a semi-definite programming problem, which is solved very efficiently. The load is due to acceleration of point masses attached to the structure and the mass of the structure itself, and the uncertainty concerns the direction of the acceleration. The fourth paper introduces an extension to the formulated semi-definite programming problem such that both fixed and uncertain loads can be optimized for simultaneously.

Game theory is used in the fifth paper to formulate a general framework, allowing essentially any differentiable objective and constraint functions, for topology optimization under load uncertainty. Two players, one controlling the structure and one the loads, are in conflict such that a solution to the game, a Nash equilibrium, is a design optimized for the worst possible load.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2016. 63 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1730
National Category
Applied Mechanics
Identifiers
urn:nbn:se:liu:diva-123008 (URN)10.3384/diss.diva-123008 (DOI)978-91-7685-883-7 (ISBN)
Public defence
2016-01-15, C3, C-huset, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2015-12-01 Created: 2015-12-01 Last updated: 2017-05-15Bibliographically approved

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