Topological derivatives for contact problems

Free and Moving Boundaries: Analysis, Simulation and Control

Volumn , Issue , 2007, Pages 309-320

  Sokołowski, Jan ^a,b   Zochowski, Antoni ^b  

^a UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

^b SYSTEMS RESEARCH INSTITUTE   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85057400306     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (22)

1. M.O. Bašeleĭšvili, An analog of the Poisson formula in elasticity (Georgian, with Russian abstract), Trudy Wyčislitelnovo Centra AN Gruzinskoĭ SSR, 1 (1960), 97–101.
2. T. Lewinski and J. Sokolowski, Optimal shells formed on a sphere. The topological derivative method. RR-3495, INRIA-Lorraine, 1998.
3. T. Lewinski and J. Sokolowski, Energy change due to appearing of cavities in elastic solids, Int. J. Solids & Structures, 40 (2003), 1765–1803.
4. T. Lewinski, J. Sokolowski, A. Zochowski, Justification of the bubble method for the compliance minimization problems of plates and spherical shells, CDRom, 3rd World Congress of Structural and Multidisciplinary Optimization (WCSMO-3) Buffalo/Niagara Falls, New York, May 17–21, 1999.
5. W. G. Mazja, S. A. Nazarov, and B. A. Plamenevskii, Asymptotic theory of elliptic boundary value problems in singularly perturbed domains, Vols. 1 and 2, Birkhäuser, Basel, 2000.
6. S. A. Nazarov and B. A. Plamenevsky, Elliptic problems in domains with piecewise smooth boundaries, De Gruyter Exposition in Mathematics 13, Walter de Gruyter, Berlin, 1994.
7. S. A. Nazarov and J. Sokołowski, Asymptotic analysis of shape functionals, Journal de Mathématiques pures et appliquées, 82, 2 (2003), 125–196.
8. S. A. Nazarov and J. Sokołowski, Self-adjoint extensions for the Neumann Laplacian in application to shape optimization, Les prépublications de l’Institut Élie Cartan 9/2003; http://www.iecn.u-nancy.fr/Preprint/publis/preprints-2003.html
9. S. A. Nazarov and J. Sokołowski, The topological derivative of the Dirichlet integral due to formation of a thin ligament, Siberian Math. J., 45, 2 (March–April 2004), 341–355.
10. S. A. Nazarov and J. Sokołowski, Self-adjoint extensions of differential operators in application to shape optimization, Comptes Rendus Mecanique, 331, 10 (October 2003), 667–672.
11. S. A. Nazarov and J. Sokołowski, Techniques of asymptotic analysis in shape optimization, French–Russian A.M. Liapunov Institute for Applied Mathematics and Computer Science Transactions, 4 (2003), 49–57.
12. S. A. Nazarov and J. Sokołowski, Self-adjoint extensions for elasticity system in application to shape optimization, to appear in Bulletin of the Polish Academy of Sciences—Mathematics.
13. S. A. Nazarov, A.S. Slutskij, and J. Sokołowski, Topological derivative of the energy functional due to formation of a thin ligament on the spatial body, Les prépublications de l’Institut Élie Cartan 14/2004; http://www.iecn.u-nancy.fr/Preprint/publis/index.html
14. M. Rao and J. Sokołowski, Non-linear balayage and applications, Illinois J. Math., 44 (2000), 310–328.
15. M. Rao and J. Sokołowski, Tangent sets in Banach spaces and applications to variational inequalities, Les prépublications de l’Institut Élie Cartan, 42, 2000.
16. J. Sokołowski and J-P. Zolésio, Introduction to shape optimization. Shape sensitivity analysis, Springer-Verlag, Heidelberg, 1992.
17. J. Sokołowski and A. Zochowski, On topological derivative in shape optimisation, INRIA-Lorraine, Rapport de Recherche No. 3170, 1997.
18. J. Sokołowski and A. Zochowski, On topological derivative in shape optimization, SIAM Journal on Control and Optimization, 37, 4 (1999), 1251–1272.
19. J. Sokołowski and A. Zochowski, Topological derivative for optimal control problems, Control and Cybernetics, 28, 3 (1999), 611–626.
20. J. Sokołowski and A. Zochowski, Topological derivatives for elliptic problems, Inverse Problems, 15, 1 (1999), 123–134.
21. J. Sokołowski and A. Zochowski, Topological derivatives of shape functionals for elasticity systems, Mechanics of Structures and Machines, 29 (2001), 333–351.
22. J. Sokołowski and A. Zochowski, Optimality conditions for simultaneous topology and shape optimization, SIAM Journal on Control and Optimization, 42, 4 (2003), 1198–1221.