Structural optimization using topological and shape sensitivity via a level set method

Control and Cybernetics

Volumn 34, Issue 1, 2005, Pages 59-81

  Allaire, Grégoire ^a   De Gournay, Frédéric ^a   Jouve, François ^a   Toader, Anca Maria ^b  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^b UNIVERSITY OF LISBON   (Portugal)

Author keywords

Level set method; Shape and topology optimization; Topological gradient

Indexed keywords

EID: 25844436983     PISSN: 03248569     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. ALLAIRE, G. (2001) Shape Optimization by the Homogenization Method. Springer Verlag, New York.
2. ALLAIRE, G. and JOUVE, F. (2005) A level-set method for vibration and multiple loads structural optimization. To appear in Comput. Methods Appl. Mech. Engrg.
3. ALLAIRE, G., JOUVE, F. and TOADER, A.-M. (2002) A level set method for shape optimization. C. R. Acad. Sci. Paris, Série I, 334, 1125-1130.
4. ALLAIRE, G., JOUVE, F. and TOADER, A.-M. (2004) Structural optimization using sensitivity analysis and a level set method, J. Comp. Phys. 194 (1), 363-393.
5. BENDSØE, M. (1995) Methods for Optimization of Structural Topology, Shape and Material. Springer Verlag, New York.
6. BENDSØE, M. and SIGMUND, O. (2003) Topology Optimization. Theory, Methods, and Applications. Springer Verlag, New York.
7. BURGER, M. (2003) A framework for the construction of level set methods for shape optimization and reconstruction. Interfaces and Free Boundaries 5, 301-329.
8. BURGER, M., HACKL, B. and RING, W. (2004) Incorporating topological derivatives into level set methods. J. Comp. Phys. 194 (1), 344-362.
9. CÉA, J., GARREAU, S., GUILLAUME, P. and MASMOUDI, M. (2000) The shape and topological optimizations connection. IV WCCM, Part II (Buenos Aires, 1998), Comput. Methods Appl. Mech. Engrg. 188, 713-726.
10. ESCHENAUER, H. and SCHUMACHER, A. (1994) Bubble method for topology and shape optimization of structures. Structural Optimization 8, 42-51.
11. GARREAU, S., GUILLAUME, P. and MASMOUDI, M. (2001) The topological asymptotic for PDE systems: the elasticity case. SIAM J. Control Optim. 39 (6), 1756-1778.
12. MOHAMMADI, B. and PIRONNEAU, O. (2001) Applied Shape Optimization for Fluids. Clarendon Press, Oxford.
13. MURAT, F. and SIMON, S. (1976) Etudes de problèmes d'optimal design. Lecture Notes in Computer Science 41, Springer Verlag, Berlin, 54-62.
14. NAZAROV, S.A. and SOKOŁOWSKI, J. (2004) The topological derivative of the Dirichlet integral under formation of a thin ligament. Siberian Math. J. 45, 341-355.
15. OSHER, S. and SANTOSA, F. (2001) Level set methods for optimization problems involving geometry and constraints: frequencies of a two-density inhomogeneous drum. J. Comp. Phys. 171, 272-288.
16. OSHER, S. and SETHIAN, J.A. (1988) Front propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comp. Phys. 78, 12-49.
17. PIRONNEAU, O. (1984) Optimal Shape Design for Elliptic Systems. Springer-Verlag, New York.
18. SETHIAN, J.A. (1999) Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision and Materials Science. Cambridge University Press.
19. SETHIAN, J. and WIEGMANN, A. (2000) Structural boundary design via level set and immersed interface methods. J. Comp. Phys. 163, 489-528.
20. SIMON, J. (1980) Differentiation with respect to the domain in boundary value problems. Num. Funct. Anal. Optimz. 2, 649-687.
21. SOKOŁOWSKI, J. and ŻOCHOWSKI, A. (1999) On the topological derivative in shape optimization. SIAM J. Control Optim. 37, 1251-1272.
22. SOKOŁOWSKI, J. and ŻOCHOWSKI, A. (2001) Topological derivatives of shape functionals for elasticity systems. Mech. Structures Mach. 29 (3), 331-349.
23. SOKOŁOWSKI, J. and ZOLESIO J.P. (1992) Introduction to Shape Optimization: Shape Sensitivity Analysis. Springer Series in Computational Mathematics 10, Springer, Berlin.
24. WANG, M.Y., WANG, X. and Guo, D. (2003) A level set method for structural topology optimization. Comput. Methods Appl. Mech. Engrg. 192, 227-246.
25. WANG, X., YULIN, M. and WANG, M.Y. (2004) Incorporating topological derivatives into level set methods for structural topology optimization. In: T. Lewinski et al., eds., in Optimal shape design and modeling, Polish Academy of Sciences, Warsaw, 145-157.