Topology design of plates considering different volume control methods
Abstract
Purpose
The purpose of this paper is to compare between two methods of volume control in the context of topological derivative-based structural optimization of Kirchhoff plates.
Design/methodology/approach
The compliance topology optimization of Kirchhoff plates subjected to volume constraint is considered. In order to impose the volume constraint, two methods are presented. The first one is done by means of a linear penalization method. In this case, the penalty parameter is the coefficient of a linear term used to control the amount of material to be removed. The second approach is based on the Augmented Lagrangian method which has both, linear and quadratic terms. The coefficient of the quadratic part controls the Lagrange multiplier update of the linear part. The associated topological sensitivity is used to devise a structural design algorithm based on the topological derivative and a level-set domain representation method. Finally, some numerical experiments are presented allowing for a comparative analysis between the two methods of volume control from a qualitative point of view.
Findings
The linear penalization method does not provide direct control over the required volume fraction. In contrast, through the Augmented Lagrangian method it is possible to specify the final amount of material in the optimized structure.
Originality/value
A strictly simple topology design algorithm is devised and used in the context of compliance structural optimization of Kirchhoff plates under volume constraint. The proposed computational framework is quite general and can be applied in different engineering problems.
Keywords
Acknowledgements
The authors would like to thank Professor Samuel Amstutz for helpful discussions on this paper. This research was partly supported by CNPq (Brazilian Research Council) and FAPERJ (Research Foundation of the State of Rio de Janeiro), under grants 470597/2010-0 and E-26/102.204/2009, respectively. D.E. Campeão was supported by CNPq. S.M. Giusti was partially supported by CONICET (National Council for Scientific and Technical Research) and PID-UTN (Research and Development Program of the National Technological University) of Argentina under grant no. 1420. The support of these agencies are gratefully acknowledged.
Citation
Esteves Campeão, D., Miguel Giusti, S. and Antonio Novotny, A. (2014), "Topology design of plates considering different volume control methods", Engineering Computations, Vol. 31 No. 5, pp. 826-842. https://doi.org/10.1108/EC-10-2012-0244
Publisher
:Emerald Group Publishing Limited
Copyright © 2014, Emerald Group Publishing Limited