Abstract
This paper describes a parametric optimization technique for shape and topology optimization. The proposed method is a generalization of the classical method of level sets which are represented with discrete grids. In using radial basis functions (RBFs), the proposed formulation projects the geometric motion of the level sets of an implicit function onto its parametric representation. The resulting method provides a set of new capabilities for general shape and topology optimization, particularly treating it as a parameter problem with the RBF implicit models. Numerical examples are presented in the paper, suggesting the potential of the method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. Allaire, Shape Optimization by the Homogenization Method, Springer, New York (2001).
G. Allaire, F. Jouve and A.-M. Toader, Structural optimization using sensitivity analysis and a level-set method, Journal of Computational Physics, 194, 363–393 (2004).
T. Belytschko, S.P. Xiao and C. Parimi, Topology optimization with implicit functions and regularization, International Journal for Numerical Methods in Engineering, 57(8), 1177–1196 (2003).
M.P. Bendsøe and N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering, 71, 197–224 (1988).
M.P. Bendsøe and O. Sigmund, Topology Optimization: Theory, Methods and Applications, Springer-Verlag, Berlin (2003).
M.D. Buhmann, Radial Basis Functions: Theory and Implementations, Cambridge Monographs on Applied and Computational Mathematics, Vol. 12, Cambridge University Press, New York (2004).
M. Burger, B. Hackl and W. Ring, Incorporating topological derivatives into level set methods, Journal of Computational Physics, 194, 344–362 (2004).
S. Osher and J.A. Sethian, Front propagating with curvature dependent speed: Algorithms based on hamilton-jacobi formulations, Journal of Computational Physics, 78, 12–49 (1988).
S.J. Osher and R.P. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Springer-Verlag, New York (2002).
J.A. Sethian, Level Set Methods and Fast Marching Methods, 2nd edition, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge, UK (1999).
M.Y Wang and X. Wang, PDE-driven level sets, shape sensitivity and curvature flow for structural topology optimization, Computer Modeling in Engineering & Sciences, 6(4), 373–395 (2004).
M.Y. Wang, X. Wang and D. Guo, A level set method for structural topology optimization, Computer Methods in Applied Mechanics and Engineering, 192, 227–246 (2003).
M.Y. Wang and P. Wei, Topology optimization with level set method incorporating topological derivative, in 6th World Congress on Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil (2005).
S.Y. Wang and M.Y. Wang, Radial basis functions and level set method for structural topology optimization, International Journal for Numerical Methods in Engineering, in press, doi:10.1002/nme.1536 (2005).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this paper
Cite this paper
Wang, M.Y., Wang, S. (2006). Parametric Shape and Topology Optimization with Radial Basis Functions. In: Bendsøe, M.P., Olhoff, N., Sigmund, O. (eds) IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials. Solid Mechanics and Its Applications, vol 137. Springer, Dordrecht . https://doi.org/10.1007/1-4020-4752-5_2
Download citation
DOI: https://doi.org/10.1007/1-4020-4752-5_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-4729-9
Online ISBN: 978-1-4020-4752-7
eBook Packages: EngineeringEngineering (R0)