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Topology and shape optimization as a tool for mechanical optimal design
Linköping University, Department of Mechanical Engineering. Linköping University, The Institute of Technology.
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: urn:nbn:se:liu:diva-24790Local ID: 7053OAI: oai:DiVA.org:liu-24790DiVA: diva2:245113
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2012-12-03
In thesis
1. Multi-parameter topology optimization in continuum mechanics
Open this publication in new window or tab >>Multi-parameter topology optimization in continuum mechanics
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:nbn:se:liu:diva-24801 (URN)7065 (Local ID)91-85297-71-2 (ISBN)7065 (Archive number)7065 (OAI)
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

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Thellner, Mikael

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