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Multi-parameter topology optimization in continuum mechanics
Linköping University, Department of Mechanical Engineering. Linköping University, The Institute of Technology.
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns structural optimization in general, and topology optimization in particular. The discipline structural optimization deals with the optimal design of load-carrying structures. In topology optimization the problem consists in finding the optimal shape of the external and internal boundaries of the structure and the number of holes. Topology optimization was originally developed as a subdiscipline of structural optimization and has been the subject of an intense research for some 15 years. The development has reached some level of maturity and conceptual consistency which have lead to a unified methodology and to new applications outside the original applications within structural mechanics. The general goal of this research has been to extend and apply the idea of topology optimization methods in new areas.

Integrated topology and shape optimization is discussed. The goal is to use shape optimization to postprocess the often coarse layout which is the result of a topology optimization. Based on those ideas a new method for topology optimization with design-dependent loads is developed using simultaneous shape and topology variation. With a fixed design domain, on which the loads and constraints are specified, it is not possible to handle loads which depend on the design. Domain shape variation is therefore introduced, using techniques from shape optimization, simultaneously with topology optimization, to handle the design-dependent loads.

The topology optimization method has been extended to convection-diffusion problems based on previously developed methodologies for topology optimization of fluids in Stokes flow. The problem considered is the optimal layout of heat-exchanging designs. For optimal performance two objectives are considered: the weighted integral average of the temperature and the average pressure drop in the domain.

Engineering design often deals with multiple, possibly conflicting, objective functions or design criteria. The multidisciplinary aspect of engineering design has been introduced to topology optimization using a novel approach. Multidisciplinary topology optimization has been formulated in the game theory framework. The problem is solved as a noncooperative two player game and we determine a Nash equilibrium which is a computationally cheap alternative to Pareto optima. A coupled heat transfer-thermoelastic system has been studied for which a topology design approach is developed.

Place, publisher, year, edition, pages
Linköping: Linköpings Universitet , 2005. , 10 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 934
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-24801Local ID: 7065ISBN: 91-85297-71-2 (print)OAI: oai:DiVA.org:liu-24801DiVA: diva2:245124
Public defence
2005-04-29, Sal C3, Hus C, Campus Valla, Linköping, 10:15 (Swedish)
Opponent
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2012-12-03
List of papers
1. Topology and shape optimization as a tool for mechanical optimal design
Open this publication in new window or tab >>Topology and shape optimization as a tool for mechanical optimal design
2002 (English)Report (Other academic)
Abstract [en]

This survey reviews different methods to integrate topology and shape optimization that are presented in the literature. Topology optimization was early recognized as an important tool for product development. The result of a topology optimization gives only a coarse layout of the boundaries of the structure. Shape optimization can be used for postprocessing t,o determine the final shape of the structure.

Integrated topology and shape optimization is a sequential process which can be divided into three steps: topology optimization, transition step a nd shape optimization. It is concluded in the survey that there are a number of well working methods for two dimensional integrated topology and shape optimization. For three dimensional integrated topology and shape optimization the transition step needs further work.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2002
Series
LITH-IKP-R, ISSN 0281-5001 ; 1366
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-24790 (URN)7053 (Local ID)7053 (Archive number)7053 (OAI)
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2012-12-03
2. Implementation and applications of simultaneous shape and thickness optimization
Open this publication in new window or tab >>Implementation and applications of simultaneous shape and thickness optimization
2002 (English)Report (Other academic)
Abstract [en]

This paper presents an implementation of simultaneous shape and thickness optimization of continuum structures in a general finite element software. The implementation facilitates a user-friendly and efficient use of simultaneous optimization. With simultaneous optimization the shape of the plane domain and the out-of-plane thickness of the structure arc simultaneously varied to obtain an optimal design. By this means it is possible to solve an essentiallythree dimensional optimization problem by only performing a two dimensional analysis. A numerical example is provided where simultaneous optimization is compared with other structural optimization problems.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2002
Series
LITH-IKP-R, ISSN 0281-5001 ; 1367
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-24793 (URN)7057 (Local ID)7057 (Archive number)7057 (OAI)
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2012-12-03
3. Topology optimization with design-dependant using simultaneous shape and topology variation
Open this publication in new window or tab >>Topology optimization with design-dependant using simultaneous shape and topology variation
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We present a new method for topology optimization with design-dependent loads. In traditional topology optimization a fixed design domain on which the loads and constraints are specified is used. Such an approach can not handle loads which depend on the design. Here we introduce domain shape variation. using techniques from shape optimization, simultaneously with topology optimization. For topology optimization we use the SIMP interpolation function together with a filter as restriction method. The stiffness of the structure is maximized given a limited alllount of material. Three numerical examples are presented which illustrates the proposed method.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-85922 (URN)
Available from: 2012-12-03 Created: 2012-12-03 Last updated: 2012-12-03
4. Topology optimization of convection-diffusion problems
Open this publication in new window or tab >>Topology optimization of convection-diffusion problems
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We have extended previously developed methodologies for topology optimization of solid structures and Stokes flow to convectiondiffusion problems. The problem considered here is the optimal layout of heat-exchanging designs. The goal is a uniform temperature distribution and the weighted sum of two objectives is minimized subject to a fluid volume constraint. The two objectives are the weighted integral average of the temperature and the average pressure dropin the domain. The optimization problem is solved using sequential convex programming. A filter is used as a restriction method to limit the minimum channel width. We present three numerical examples.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-85923 (URN)
Available from: 2012-12-03 Created: 2012-12-03 Last updated: 2012-12-03
5. Multidisciplinary topology optimization solved as a Nash game
Open this publication in new window or tab >>Multidisciplinary topology optimization solved as a Nash game
2004 (English)In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 61, no 7, 949-963 p.Article in journal (Refereed) Published
Abstract [en]

In the present work, multidisciplinary optimization is formulated in the game theory framework. We choose a coupled heat transfer—thermoelastic system as the case study for which a topology design approach is developed. The multidisciplinary optimization problem is solved as a non-cooperative game and we determine a Nash equilibrium. The game has two players and the parameterization of the design domain is such that the design variables describe the material density and a parameter which influences the heat flow by convection to the surrounding fluid. The first player controls the structure and the second player controls the temperature distribution in the structure. For the second player, we present mathematical proof of existence of a discrete valued optimal solution and it is concluded that no regularization of the suboptimization problem is needed. We present two numerical examples which illustrate the proposed methodology. One of the examples is also solved by weighting the objectives to a scalar valued objective function and the result is compared with the Nash game solution.

Keyword
Game theory, Heat transfer, Multidisciplinary optimization, Nash equilibrium, Thermoelasticity, Topology optimization
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-45599 (URN)10.1002/nme.1093 (DOI)
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13

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