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Dynamical systems and 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.
2010 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 42, no 2, 179-192 p.Article in journal (Refereed) Published
Abstract [en]

This paper uses a dynamical systems approach for studying the material distribution (density or SIMP) formulation of topology optimization of structures. Such an approach means that an ordinary differential equation, such that the objective function is decreasing along a solution trajectory of this equation, is constructed. For stiffness optimization two differential equations with this property are considered. By simple explicit Euler approximations of these equations, together with projection techniques to satisfy box constraints, we obtain different iteration formulas. One of these formulas turns out to be the classical optimality criteria algorithm, which, thus, is receiving a new interpretation and framework. Based on this finding we suggest extensions of the optimality criteria algorithm. A second important feature of the dynamical systems approach, besides the purely algorithmic one, is that it points at a connection between optimization problems and natural evolution problems such as bone remodeling and damage evolution. This connection has been hinted at previously but, in the opinion of the authors, not been clearly stated since the dynamical systems concept was missing. To give an explicit example of an evolution problem that is in this way connected to an optimization problem, we study a model of bone remodeling. Numerical examples, related to both the algorithmic issue and the issue of natural evolution represented as bone remodeling, are presented.

Place, publisher, year, edition, pages
Springer Science Business Media , 2010. Vol. 42, no 2, 179-192 p.
Keyword [en]
Topology optimization; Optimality criteria; Dynamical systems
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-58356DOI: 10.1007/s00158-010-0479-9ISI: 000278742800002OAI: diva2:343342
The original publication is available at Anders Klarbring and Bo Torstenfelt, Dynamical systems and topology optimization, 2010, Structural and multidisciplinary optimization, (42), 2, 179-192. Copyright: Springer Science Business Media Available from: 2010-08-13 Created: 2010-08-11 Last updated: 2010-08-19

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