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Topology optimization in crashworthiness design
Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
Linköping University, Department of Management and Engineering, Energy Systems. Linköping University, The Institute of Technology.
2007 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 33, no 1, 1-12 p.Article in journal (Refereed) Published
Abstract [en]

Topology optimization has developed rapidly, primarily with application on linear elastic structures subjected to static loadcases. In its basic form, an approximated optimization problem is formulated using analytical or semi-analytical methods to perform the sensitivity analysis. When an explicit finite element method is used to solve contact–impact problems, the sensitivities cannot easily be found. Hence, the engineer is forced to use numerical derivatives or other approaches. Since each finite element simulation of an impact problem may take days of computing time, the sensitivity-based methods are not a useful approach. Therefore, two alternative formulations for topology optimization are investigated in this work. The fundamental approach is to remove elements or, alternatively, change the element thicknesses based on the internal energy density distribution in the model. There is no automatic shift between the two methods within the existing algorithm. Within this formulation, it is possible to treat nonlinear effects, e.g., contact–impact and plasticity. Since no sensitivities are used, the updated design might be a step in the wrong direction for some finite elements. The load paths within the model will change if elements are removed or the element thicknesses are altered. Therefore, care should be taken with this procedure so that small steps are used, i.e., the change of the model should not be too large between two successive iterations and, therefore, the design parameters should not be altered too much. It is shown in this paper that the proposed method for topology optimization of a nonlinear problem gives similar result as a standard topology optimization procedures for the linear elastic case. Furthermore, the proposed procedures allow for topology optimization of nonlinear problems. The major restriction of the method is that responses in the optimization formulation must be coupled to the thickness updating procedure, e.g., constraint on a nodal displacement, acceleration level that is allowed.

Place, publisher, year, edition, pages
2007. Vol. 33, no 1, 1-12 p.
Keyword [en]
Contact-impacts, Explicit finite element analysis, Nonlinear problems, Topology optimization
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-50018DOI: 10.1007/s00158-006-0040-zOAI: diva2:270914
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2012-12-07
In thesis
1. Structural optimization in vehicle crashworthiness design
Open this publication in new window or tab >>Structural optimization in vehicle crashworthiness design
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns the optimization of structures subjected to impact loading. Major applications can be found in the crashworthiness design of vehicles. There is an industrial interest in using optimization methods in the crashworthiness design process. However, strongly nonlinear responses, including high frequency components, make the Finite Element (FE) simulations computationally demanding. This fact restricts the number of possible optimization methods that can be applied.

In this work two optimization methods have been investigated: Response Surface Methodology (RSM) and Kriging. In both these methods the number of functional evaluations, i.e. here FE simulations, depends at least linearly on the number of design parameters. Thus, the number of design parameters is limited due to the computational effort. One objective of this work has been to reduce the total computational cost of the optimization process, or alternatively the possibility to use more design parameters at the same computational cost. When using RSM and Kriging, the number of functional evaluations in each iteration can be reduced, and/or the convergence of the optimization process can be improved. In many applications, RSM has been used with linear approximating response surfaces for robustness and efficiency reasons. Linear RSM may suffer from iterative oscillations, since the optimal design is often found on the boundary of the feasible design region. This oscillatory behaviour can be reduced if Kriging is used for the approximating response surfaces. However, it has been found that Kriging may have problems in fulfilling the constraints. In the initial design process of a structure very many alternative designs exist. At these early stages topology optimization is a mean of finding a structure that is optimal for the objective at hand. In this work a topology optimization approach is proposed for the design of crashworthiness structures. The resulting structure must still be subjected to an interpretation by engineers and also be improved by further optimization.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2005. 26 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 940
National Category
Engineering and Technology
urn:nbn:se:liu:diva-31403 (URN)17174 (Local ID)91-85297-78-X (ISBN)17174 (Archive number)17174 (OAI)
Public defence
2005-05-20, C3, C-huset, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2012-12-07Bibliographically approved

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