Design of Compliant Mechanisms of Distributed Compliance Using a Level-Set Based Topology Optimization Method

Abstract:

This paper presents a level set-based structural shape and topology optimization for the design of compliant mechanisms. The design boundary of the compliant mechanism is implicitly represented as the zero level-set of a higher-dimensional level set surface. A quadratic energy functional is introduced to augment the objective function in order to control the structural geometric size of the resulting mechanism. The optimization is thus changed to a numerical process that describes the design as a sequence of motions by updating the implicit boundaries until the optimized structure is achieved under specified constraints. A semi-implicit scheme with an additive operator splitting (AOS) algorithm is used to solve the Hamilton-Jacobi partial differential equation (PDE) in the level set method. In doing so, it is expected that numerical difficulties in most conventional level set methods can be eliminated. The final mechanism is characterized with strip-like members able to generate distributed compliance, and so that to resolve the hinge problem long sought-after in the design of compliant mechanisms. Typical numerical case is used to evidence the effectiveness of this method in the design of monolithic compliant mechanisms.

• Periodical: Applied Mechanics and Materials (Volumes 110-116)
• Pages: 2319-2323
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.110-116.2319
• Online since: October 2011
• Authors: Yu Wang, Zhen Luo
• Keywords: Compliant Mechanism, Level Set Method (LSM), Topology Optimization

References

[1] M.P. Bendsøe, O. Sigmund: Topology Optimization: Theory, Methods, and Applications (Springer, Berlin Heidelberg 2003).

[2] L.L. Howell: Compliant mechanisms (John Wiley & Sons, Inc., New York 2001).

[3] G.K. Ananthasuresh, and L.L. Howell: J. Mech. Des. Vol. 127 (2005), p.736.

[4] S. Osher, and J.A. Sethian: J. of Comput. Phys. Vol. 78 (1988), p.12.

[5] J.A. Sethian, and A. Wiegmann: J. of Comput. Phys. Vol. 163 (2000), p.489.

[6] S. Osher, and F. Santosa: J. of Comput. Phys. Vol. 171 (2001), p.272.

[7] M.Y. Wang, X.M. Wang, and D.M. Guo: Comput. Methods Appl. Mech. Eng. Vol. 192 (2003), p.227.

[8] G. Allaire, F. Jouve, and A.M. Toader: J. of Comput. Phys. Vol. 194 (2004), p.363.

[9] Z. Luo, L. Tong, M.Y. Wang, and et al: J. of Comput. Phys. Vol. 227 (2007), p.680.

[10] M. Rochery, I. Jermyn, and J. Zerubia: Int. J. Comput. Vision Vol. 69 (2006), p. 27O.

[11] J. Weickert, B.M. Romeny, and M. Viergever: IEEE Trans. Image Process. Vol. 7 (1998), p.398.

[12] Sigmund, and J. Petersson: Struct. Multidisc. Optim. Vol. 16 (1998), p.68.

[13] O. Sigmund: Mech. Struct. Machines Vol. 25 (1997), p.493.

[14] J. Luo, Z. Luo, S. Chen, and et al: Comput. Methods Appl. Mech. Eng. Vol 198 (2008), p.318.

[15] S. Chen, M. Y. Wang, and A. Q. Liu: Computer-Aided Design Vol. 40 (2008), p.951.

[16] M.Y. Wang, S. Chen, X. Wang, and et al: J. Mech. Des. Vol. 127 (2005), p.941.

[17] Z. Luo, L. Tong: Int. J. Numer Methods Eng. Vol 76 (2008), p.862.

[18] S. Osher, and R.P. Fedkiw: Level set methods and dynamic implicit surface (Springer-Verlag, New York 2002).

[19] J. Sokolowski, and J.P. Zolesio: Introduction to shape optimization: Shape sensitivity analysis (Springer, Berlin 1992).

DOI: 10.1007/978-3-642-58106-9_4

[20] J. Luo, Z. Luo, L. Chen, and et al: J. of Comput. Phys. Vol. 227 (2008), p.5561.

[21] Z. Luo, L. Tong, J. Luo, and et al: J. of Comput. Phys. Vol. 228 (2009), p.2643.