Second order topological sensitivity analysis

International Journal of Solids and Structures

Volumn 44, Issue 14-15, 2007, Pages 4958-4977

  de Faria, J Rocha ^a   Novotny, A A ^a   Feijoo R A ^a   Taroco, E ^a   Padra, C ^b  

^a LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

^b CENTRO ATÓMICO BARILOCHE   (Argentina)

Author keywords

First order topological derivative; Second order topological derivative; Topological asymptotic expansion

Indexed keywords

ASYMPTOTIC ANALYSIS; COST FUNCTIONS; OPTIMIZATION; POISSON EQUATION; POTENTIAL ENERGY; TOPOLOGY;

ASYMPTOTIC EXPANSION; FINITE SIZE; FIRST ORDER TOPOLOGICAL DERIVATIVE; SECOND ORDER TOPOLOGICAL DERIVATIVE;

SENSITIVITY ANALYSIS;

EID: 33947672863     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2006.12.013     Document Type: Article

References (25)

1. Amstutz S. The topological asymptotic for the Navier-Stokes equations. ESAIM Journal of Control Optimization and Calculus of Variations 11 3 (2005) 401-425
2. Amstutz S., Horchani I., and Masmoudi M. Crack detection by the topological gradient method. Control and Cybernetics 34 1 (2005) 81-101
3. Céa J., Garreau S., Guillaume P.h., and Masmoudi M. The shape and topological optimizations connection. Computational Methods in Applied Mechanical Engineering 188 (2000) 713-726
4. Céa, J. 1981. Problems of shape optimal design. In: Haug & J. Céa (1981).
5. Eschenauer H.A., and Olhoff N. Topology optimization of continuum structures. A Review Applied Mechanics Review 54 (2001) 331-390
6. Eschenauer H.A., Kobelev V.V., and Schumacher A. Bubble method for topology and shape optimization of structures. Structural Optimization 8 (1994) 42-51
7. Eshelby J.D. The elastic energy-momentum tensor. Journal of Elasticity 5 (1975) 321-335
8. Feijóo R.A., Novotny A.A., Taroco E., and Padra C. The topological derivative for the Poisson's problem. Mathematical Models and Methods in Applied Sciences 13 12 (2003) 1825-1844
9. Feijóo, R.A., Novotny, A.A., Taroco, E., Padra, C., in press. The topological-shape sensitivity method and its application in 2D elasticity. Journal of Computational Methods in Science and Engineering.
10. Garreau S., Guillaume P.h., and Masmoudi M. The topological asymptotic for PDE systems: the elasticity case. SIAM Journal on Control and Optimization 39 (2001) 1756-1778
11. Guillaume P.h., and Sid Idris K. The topological asymptotic expansion for the Dirichlet problem. SIAM Journal on Control and Optimization 41 4 (2002) 1042-1072
12. Gurtin M.E. An Introduction to Continuum Mechanics Mathematics in Science and Engineering vol. 158 (1981), Academic Press
13. Gurtin M.E. Configurational Forces as Basic Concept of Continuum Physics Applied Mathematical Sciences vol. 137 (2000), Springer-Verlag
14. Haug, E.J., Céa, J., 1981. Proceedings: Optimization of Distributed Parameters Structures, Iowa, EUA.
15. Kozlov V.A., Maz'ya V.G., and Movchan A.B. Asymptotic Analysis of Fields in Multi-Structures (1999), Clarendon Press, Oxford
16. Lewinski T., and Sokolowski J. Energy change due to the appearance of cavities in elastic solids. International Journal of Solids and Structures 40 (2003) 1765-1803
17. Maz'ya W.G., Nazarov S.A., and Plamenevskii B.A. Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains vols. 1-2 (2000), Birkhäuser Verlag, Basel
18. Murat, F., Simon, J., 1976. Sur le Contrôle par un Domaine Géométrique. Ph.D. Thesis, Université Pierre et Marie Curie, Paris VI, France.
19. Novotny, A.A., 2003. Análise de Sensibilidade Topológica. Ph.D. Thesis, LNCC-MCT, Petrópolis, Brazil.
20. Novotny A.A., Feijóo R.A., Padra C., and Taroco E. Topological sensitivity analysis. Computational Methods on Applied Mechanical Engineering 192 (2003) 803-829
21. Novotny A.A., Feijoó R.A., Padra C., and Taroco E. Topological derivative for linear elastic plate bending problems. Control and Cybernetics 34 1 (2005) 339-361
22. Samet B., Amstutz S., and Masmoudi M. The topological asymptotic for the Helmholtz equation. SIAM Journal on Control and Optimization 42 5 (2003) 1523-1544
23. Sokolowski J., and Żochowski A. On the topological derivative in shape optimization. SIAM Journal on Control and Optimization 37 4 (1999) 1251-1272
24. Taroco E., and Feijóo R.A. Shape sensitivity analysis and the energy momentum tensor for the kinematic and static models of torsion. International Journal of Solids and Structures 43 (2006) 1908-1927
25. Zolésio, J.P. 1981. The material derivative (or speed) method for shape optimization. In: Haug & J. Céa (1981).