Abstract
Structures exhibiting band gap properties, i.e., having frequency ranges for which the structure attenuates propagating waves, have applications in damping of acoustic and elastic wave propagation and in optical communication. A topology optimization method for synthesis of such structures, employing a time domain formulation, is developed. The method is extended to synthesis of pulse converting structures with possible applications in optical communication.
Similar content being viewed by others
References
Allaire G, Francfort GA (1993) A numerical algorithm for topology and shape optimization. In: Bendsøe MP, Soares CAM (eds) Topology optimization of structures. Klüwer, pp 239–248
Bendsøe MP, Sigmund O (2003) Topology Optimization: theory, methods and applications. Springer, Berlin
Burger M, Osher S, Yablonovitch E (2004) Inverse problem techniques for the design of photonic crystals. IEICE Trans Electron E87-C(3):258–265
Chung YS, Cheon C, Hahn SY (2000) Reconstruction of dielectric cylinders using FDTD and topology optimization technique. IEEE Trans Magn 36(4):956–959
Cox SJ, Dobson DC (1999) Maximizing band gaps in two-dimensional photonic crystals. SIAM J Appl Math 59(6): 2108–2120
Frey WR, Tortorelli DA, Johnson HT (2005) Topology optimization of a photonic crystal waveguide termination to maximize directional emission. Appl Phys Lett 86(11):111–114
Halkjær S, Sigmund O, Jensen JS (2005) Inverse design of phononic crystals by topology optimization. Z Kristallogr 220(9–10):895–905
Halkjær S, Sigmund O, Jensen JS (2006) Maximizing band gaps in plate structures. Struct Multidisc Optim 32(4):263–275
Haug E, Arora J (1978) Design sensitivity analysis of elastic mechanical systems. Comput Methods Appl Mech Eng 15(1):35–62
Hussein MI, Hamza K, Hulbert GM, Scott RA, Saitou K (2006) Multiobjective evolutionary optimization of periodic layered materials for desired wave dispersion characteristics. Struct Multidisc Optim 31(1):60–75
Jensen JS (2007) Topology optimization of dynamics problems with Padé approximants. Int J Numer Methods Eng doi:10.1002/nme.2065
Jensen JS, Sigmund O (2004) Systematic design of photonic crystal structures using topology optimization: low-loss waveguide bends. Appl Phys Lett 84(12):2022–2024
Jensen JS, Sigmund O (2005) Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide. J Opt Soc Am B Opt Phys 22(6):1191–1198
Li Y, Saitou K, Kikuchi N (2004) Topology optimization of thermally actuated compliant mechanisms considering time-transient effect. Finite Elem Anal Des 40(11):1317–1331
Michaleris P, Tortorelli DA, Vidal C (1994) Tangent operators and design sensitivity formulations for transient non-linear coupled problems with applications in elastoplasticity. Int J Numer Methods Eng 37(14):2471–2499
Nomura T, Sato K, Taguchi K, Kashiwa T, Nishiwaki S (2007) Structural topology optimization for the design of broadband dielectric resonator antennas using the finite difference time domain technique. Int J Numer Methods Eng 71(11):1261–1296
Pedersen C (2004) Crashworthiness design of transient frame structures using topology optimization. Comput Methods Appl Mech Eng 193(6–8):653–678
Sigmund O, Jensen JS (2003) Systematic design of phononic band gap materials and structures by topology optimization. Philos Trans Royal Soc Math Phys Eng Sci 361:1001–1019
Smith FG, King TA (2000) Optics and photonics—an introduction. Wiley
Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Model 24:359–373
Tsuji Y, Hirayama K, Nomura T, Sato K, Nishiwaki S (2006) Design of optical circuit devices based on topology optimization. IEEE photonics Technol Lett 18(5–8):850–852
Turteltaub S (2001) Optimal material properties for transient problems. Struct Multidisc Optim 22(2):157–166
Turteltaub S (2005) Optimal non-homogeneous composites for dynamic loading. Struct Multidisc Optim 30(2):101–112
Zwyssig C, Kolar J (2006) Design considerations and experimental results of a 100 W, 500 000 rpm electrical generator. J Micromechanics Microengineering 16:297–302
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dahl, J., Jensen, J.S. & Sigmund, O. Topology optimization for transient wave propagation problems in one dimension. Struct Multidisc Optim 36, 585–595 (2008). https://doi.org/10.1007/s00158-007-0192-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-007-0192-5