A Modified Volumetric Penalization Method for Gray Elements Suppression


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The volumetric penalization approach is an important method for gray elements suppression in topology optimization. With the volumetric penalization approach, the topology optimization problem is consistent and regularized, and topology description is unambiguous. Considering the fact that an unreasonable topological form of structure is sometimes resulted with the traditional volumetric penalization function, a modified function is proposed. By utilizing the modified function, the gray elements are compelled to be 0 or 1, and the efficiency of optimization solving is also improved. To verify the validity of the modified method, it is compared with the famous volumetric penalization method, SINH method, through a typical example. Simultaneously, its numerical instabilities are also analyzed.



Edited by:

Yuning Zhong




M. Li and W. C. Tang, "A Modified Volumetric Penalization Method for Gray Elements Suppression", Applied Mechanics and Materials, Vol. 235, pp. 25-29, 2012

Online since:

November 2012




[1] M. Wang, S. Zhou, H. Ding: Struct Multidisc Optim, Vol. 28 (2004), p.262–276.

[2] O. Sigmund: Struct Multidisc Optim, Vol. 33 (2007), p.401–424.

[3] A.A. Groenwold, L.F.P. Etman: Struct and Multidisc Optim, Vol. 39 (2009) No. 3, pp.217-225.

[4] K. Long, H.W. Zhao: Journal of Computer-Aided Design & Computer Graphics, Vol. 22 (2010) No. 12, pp.2197-2201.

[5] T.E. Bruns: Struct Multidisc Optim, Vol. 30 (2005) No. 6, pp.428-436.

[6] M. Zhou, G. Rozvany: Comp. Meth. Appl. Mech. Eng. Vol. 40 (1991), p.1–26.

[7] J.M. Guedes, J.E. Taylor: Struct Optim. Vol. 14 (1997), p.193–199.

[8] E.L. Cardoso, J.S.O. Fonseca: J Braz Soc Mech Sci Eng, Vol. XXV (2003) No. 3, p.293–301.

[9] T.E. Bruns: Computer Methods in Applied Mechanics and Engineering, Vol. 196 (2007), pp.4430-4443.

[10] T.E. Bruns: International Journal of Heat and Mass Transfer, Vol. 50 (2007), pp.2859-2873.

[11] M.P. Bendson: Optimization of structural topology, shape and material (Springer-Verlag Telos, Inc. New York, 1995).

[12] E.J. Haug, K.K. Choi, V. Komkov: Design Sensitivity Analysis of Structural Systems (Academic Press, Inc. New York, 1986).

[13] T.E. Bruns, D.A. Tortorelli: Comput Methods Appl Mech Eng, Vol. 190 (2001), p.3443–3459.

[14] X.D. Huang, Y.M. Xie: Struct Multidisc Optim, Vol. 41 (2010) No. 5, pp.671-683.