Tytuł artykułu
Treść / Zawartość
Pełne teksty:
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We consider Helmholtz problems in two and three dimensions. The topological sensitivity of a given cost function J(uɛ) with respect to a small hole Bɛ around a given point x0ɛ ∈ Bɛ ⊂ Ω depends on various parameters, like the frequency k chosen or certain material parameters or even the shape parameters of the hole Bɛ. These parameters are either deliberately chosen in a certain range, as, e.g., the frequencies, or are known only up to some bounds. The problem arises as to whether one can obtain a uniform design using the topological gradient. We show that for 2-d and 3-d Helmholtz problems such a robust design is achievable.
Czasopismo
Rocznik
Tom
Strony
227--248
Opis fizyczny
Bibliogr. 38 poz., rys.
Twórcy
autor
- FAU Senior Fellow of Applied Mathemathics, Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nüurnberg (FAU), Cauerstrasse 11, 91058 Erlangen, Germany
autor
- Laboratório Nacional de Computa,cão Cientifica, LNCC/MCTI, Coordena,cão de Métodos Mathemáticos e Computacionais, Av. Getúlio Vargas 333, 25651-075 Petrópolis – RJ, Brazil
autor
- Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warszawa, Poland
Bibliografia
- Allaire, G., Jouve, F. and Toader, A. M. (2004) Structural optimization using sensitivity analysis and a level-set method. Journal of Computational Physics, 194(1): 363–393.
- Amstutz, S. (2006) Sensitivity analysis with respect to a local perturbation of the material property. Asymptotic Analysis, 49(1-2): 87–108.
- Amstutz, S. (2022) An introduction to the topological derivative. Engineering Computations, 39(1): 3–33.
- Amstutz, S. and Novotny, A. A. (2010) Topological optimization of structures subject to von Mises stress constraints. Structural and Multidisciplinary Optimization, 41(3): 407–420.
- Assous, F., Ciarlet, P. and Labrunie, S. (2018) Mathematical Foundations of Computational Electromagnetism. Applied Mathematical Sciences. Springer Nature Switzerland.
- Barros, G., Filho, J., Nunes, L. and Xavier, M. (2022) Experimental validation of a topological derivative-based crack growth control method using digital image correlation. Engineering Computations, 39(1): 438–454.
- Baumann, Ph. and Sturm, K. (2022) Adjoint-based methods to compute higher-order topological derivatives with an application to elasticity. Engineering Computations, 39(1): 60–114.
- Bonnet, M. (2022) On the justification of topological derivative for wavebased qualitative imaging of finite-sized defects in bounded media. Engineering Computations, 39(1): 313–336.
- Bonnet, M. and Guzina, B. B. (2004) Sounding of finite solid bodies by way of topological derivative. International Journal for Numerical Methods in Engineering, 61(13): 2344–2373.
- Canelas, A. and Roche, J.R. (2022) Shape and topology optimal design problems in electromagnetic casting. Engineering Computations, 39(1): 147–171.
- Delfour, M.C. (2022) Topological derivatives via one-sided derivative of parametrized minima and minimax. Engineering Computations, 39(1): 34–59.
- Fernandez, L. and Prakash, R. (2022) Imaging of small penetrable obstacles based on the topological derivative method. Engineering Computations, 39(1): 201–231.
- Ferrer, A. and Giusti, S.M. (2022) Inverse homogenization using the topological derivative. Engineering Computations, 39(1): 337–353.
- Garreau, S., Guillaume, Ph. and Masmoudi, M. (2001) The topological asymptotic for PDE systems: the elasticity case. SIAM Journal on Control and Optimization, 39(6): 1756–1778.
- Guzina, B. B. and Chikichev, I. (2007) From imaging to material identification: a generalized concept of topological sensitivity. Journal of the Mechanics and Physics of Solids, 55(2): 245–279.
- Henrot, A. and Pierre, M. (2005) Variation et optimisation de formes. Mathématiques et applications, 48, Springer-Verlag, Heidelberg.
- Hintermüller, M. (2005) Fast level set based algorithms using shape and topological sensitivity. Control and Cybernetics, 34(1): 305–324.
- Hlavaček, I., Novotny, A. A., Sokolowski, J. and Żochowski, A.(2009) On topological derivatives for elastic solids with uncertain input data. Journal of Optimization Theory and Applications, 141(3): 569–595.
- Ilin, A. M. (1992) Matching of Asymptotic Expansions of Solutions of Boundary Value Problems. Translations of Mathematical Monographs. American Mathematical Society, 102, Providence, RI. Translated from Russian by V. V. Minachin.
- Kliewe, Ph., Laurain, A. and Schmidt, K. (2022) Shape optimization in acoustic-structure interaction. Engineering Computations, 39(1): 172–200.
- Le Louër, F. and Rapún, M.L. (2022a)Topological sensitivity analysis revisited for timeharmonic wave scattering problems. Part I: The free space case. Engineering Computations, 39(1):232–271.
- Le Louër, F. and Rapún, M.L. (2022b) Topological sensitivity analysis revisited for timeharmonic wave scattering problems. Part II: Recursive computations by the boundary integral equation method. Engineering Computations, 39(1):272–312.
- Masmoudi, M., Pommier, J. and Samet, B. (2005) The topological asymptotic expansion for the Maxwell equations and some applications. Inverse Problems, 21(2):547–564.
- Novotny, A. A. and Sokołowski, J. (2013) Topological Derivatives in Shape Optimization. Interaction of Mechanics and Mathematics. Springer-Verlag, Berlin, Heidelberg.
- Novotny, A. A. and Sokołowski, J. (2020) An Introduction to the Topological Derivative Method. Springer Briefs in Mathematics. Springer Nature Switzerland.
- Novotny, A. A., Sokołowski, J. and Żochowski, A. (2019) Applications of the Topological Derivative Method. Studies in Systems, Decision and Control. Springer Nature Switzerland.
- Novotny, A.A., Giusti, S.M. and Amstutz, S. (2022) Guest Editorial: On the topological derivative method and its applications in computational engineering. Engineering Computations, 39(1):1–2.
- Rakotondrainibe, L., Allaire, G. and Orval, P. (2022) Topological sensitivity analysis with respect to a small idealized bolt. Engineering Computations, 39(1):115–146.
- Romero, A. (2022) Optimum design of two-material bending plate compliant devices. Engineering Computations, 39(1):395–420.
- Samet, B., Amstutz, S. and Masmoudi, M. (2003) The topological asymptotic for the Helmholtz equation. SIAM Journal on Control and Optimization, 42(5): 1523–1544.
- Santos, R.B. and Lopes, C.G. (2022) Topology optimization of structures subject to selfweight loading under stress constraints. Engineering Computations, 39(1): 380–394.
- Schumacher, A. (1995) Topologieoptimierung von bauteilstrukturen unter verwendung von lochpositionierungkriterien. Ph.D. Thesis, Universitat Gesamthochschule-Siegen, Siegen - Germany.
- Sokołowski, J. and Żochowski, A. (1999a) On the topological derivative in shape optimization. SIAM Journal on Control and Optimization, 37(4): 1251–1272.
- Sokołowski, J. and Żochowski, A. (1999b) Topological derivatives for elliptic problems. Inverse Problems, 15(1): 123–134.
- Sokołowski, J. and Żochowski, A. (2001) Topological derivatives of shape functionals for elasticity systems. Mechanics of Structures and Machines, 29(3): 333–351.
- Sokołowski, J. and Zolésio, J. P. (1992) Introduction to Shape Optimization - Shape Sensitivity Analysis. Springer-Verlag, Berlin, Germany.
- Xavier, M. and Van Goethem, N. (2022) Brittle fracture on plates governed by topological derivatives. Engineering Computations, 39(1): 421–437.
- Yera, R., Forzani, L., Méndez, C.G. and Huespe, A.E. (2022) A topology optimization algorithm based on topological derivative and levelset function for designing phononic crystals. Engineering Computations, 39(1): 354–379.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-fda3535a-7d62-4a7b-8f7c-5e84c0982f31