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A SMOOTHING METHOD FOR SHAPE OPTIMIZATION: TRACTION METHOD USING THE ROBIN CONDITION

Department of Complex Systems Science, Graduate School of Information Science, Nagoya University, Furo-cho, Chigusa-ku, Nagoya City, Aichi Prefecture, 464-8601, Japan

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KENZEN TAKEUCHI

Quint Corporation, 1-14-1 Fuchu-cho, Fuchu, Tokyo, 183-0055, Japan

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https://doi.org/10.1142/S0219876206000709Cited by:79 (Source: Crossref)

Abstract

This paper presents an improved version of the traction method that was proposed as a solution to shape optimization problems of domain boundaries in which boundary value problems of partial differential equations are defined. The principle of the traction method is presented based on the theory of the gradient method in Hilbert space. Based on this principle, a new method is proposed by selecting another bounded coercive bilinear form from the previous method. The proposed method obtains domain variation with a solution to a boundary value problem with the Robin condition by using the shape gradient.

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References

H. Azegami, Trans. of Jpn. Soc. of Mech. Engs., Ser. A 60, 1479 (1994). Crossref, Google Scholar
H. Azegamiet al., Computer Aided Optimization Design of Structures IV, Structural Optimization, eds. S. Hernandez, M. El-Sayed and C. A. Brebbia (Computational Mechanics Publications, Southampton, 1995) pp. 51–58. Google Scholar
H. Azegami and Z. C. Wu, JSME International Journal, Ser. A 39, 272 (1996). Google Scholar
H. Azegamiet al., Computer Aided Optimization Design of Structures V, eds. S. Hernandez and C. A. Brebbia (Computational Mechanics Publications, Southampton, 1997) pp. 309–326. Google Scholar
H. Azegami, Inverse Problems in Engineering Mechanics II, eds. M. Tanaka and G. S. Dulikravich (Elsevier, Tokyo, 2000) pp. 277–284. Crossref, Google Scholar
H. Azegami, High Performance Structures and Materials II, eds. C. A. Brebbia and W. P. de Wilde (WIT Press, Southampton, 2004) pp. 589–598. Google Scholar
J. Cea, Optimization of Distributed Parameter Structures 2, eds. E. J. Haug and J. Cea (Sijthoff and Noordhoff, Alphen aan den Rijn, 1981) pp. 1005–1048. Crossref, Google Scholar
J. Cea, Optimization of Distributed Parameter Structures (1981) pp. 1049–1088. Crossref, Google Scholar
K. K. Choi and N. H. Kim , Structural Sensitivity Analysis and Optimization 1–2 ( Springer , New York , 2005 ) . Google Scholar
J. Hadamard, Mémoire des savants etragers. Oeuvres de J. Hadamard (CNRS, Paris, 1968) pp. 515–629. Google Scholar
E. J. Haug , K. K. Choi and V. Komkov , Design Sensitivity Analysis of Structural Systems ( Academic Press , Orland , 1986 ) . Google Scholar
M. H. Imam, Int. J. Num. Meth. Engrg. 18, 661 (1982). Crossref, Web of Science, Google Scholar
Jameson, A. [2003] Aerodynamic shape optimization using the adjoint method, citeseer.ist.psu.edu/jameson03aerodynamic.html . Google Scholar
B. Mohammadi and O. Pironneau , Applied shape optimization for fluids ( Clarendon Press , Oxford , 2001 ) . Google Scholar
O. Pironneau , Optimal Shape Design for Elliptic Systems ( Springer-Verlag , New York , 1984 ) . Crossref, Google Scholar
J. Sokolowski and J. P. Zolésio , Introduction to Shape Optimization: Shape Sensitivity Analysis ( Springer–Verlag , New York , 1991 ) . Google Scholar
J. P. Zolésio, Optimization of Distributed Parameter Structures 2, eds. E. J. Haug and J. Cea (Sijthoff and Noordhoff, Alphen aan den Rijn, 1981) pp. 1089–1151. Crossref, Google Scholar
J. P. Zolésio, Optimization of Distributed Parameter Structures (1981) pp. 1152–1194. Crossref, Google Scholar