Top

Structural and Multidisciplinary Optimization

Published in:

11-01-2019 | Research Paper

Topology optimization of conductors in electrical circuit

Authors: Katsuya Nomura, Shintaro Yamasaki, Kentaro Yaji, Hiroki Bo, Atsuhiro Takahashi, Takashi Kojima, Kikuo Fujita

Published in: Structural and Multidisciplinary Optimization | Issue 6/2019

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This study proposes a topology optimization method for realizing a free-form design of conductors in electrical circuits. Conductors in a circuit must connect components, such as voltage sources, resistors, capacitors, and inductors, according to the given circuit diagram. The shape of conductors has a strong effect on the high-frequency performance of a circuit due to parasitic circuit elements such as parasitic inductance and capacitance. In this study, we apply topology optimization to the design of such conductors to minimize parasitic effects with maximum flexibility of shape manipulation. However, when the distribution of conductors is repeatedly updated in topology optimization, disconnections and connections of conductors that cause open and short circuits, respectively, may occur. To prevent this, a method that uses fictitious electric current and electric field calculations is proposed. Disallowed disconnections are prevented by limiting the maximum value of the fictitious current density in conductors where a current is induced. This concept is based on the fact that an electric current becomes concentrated in a thin conductor before disconnection occurs. Disallowed connections are prevented by limiting the maximum value of the fictitious electric field strength around conductors where a voltage is applied. This is based on the fact that the electric field in a parallel plate capacitor is inversely proportional to the distance between the plates. These limitations are aggregated as a single constraint using the Kreisselmeier-Steinhauser function in the formulation of optimization problems. This constraint prevents only disallowed disconnections and connections, but does not prevent allowed topology changes. The effectiveness of the constraint is confirmed using simple examples, and an actual design problem involving conductors in electromagnetic interference filters is used to verify that the proposed constraint can be utilized for conductor optimization.

previous article An efficient multi-objective optimization method for uncertain structures based on ellipsoidal convex model

next article Tension/compression anisotropy enhanced topology design

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

Aage N, Egede Johansen V (2017) Topology optimization of microwave waveguide filters. Int J Numer Methods Eng 112(3):283–300MathSciNetCrossRef

Aage N, Mortensen N, Sigmund O (2010) Topology optimization of metallic devices for microwave applications. Int J Numer Methods Eng 83(2):228–248MathSciNetMATH

Alexandrov O, Santosa F (2005) A topology-preserving level set method for shape optimization. J Comput Phys 204(1):121–130MathSciNetCrossRefMATH

Allaire G, Dapogny C, Frey P (2011) Topology and geometry optimization of elastic structures by exact deformation of simplicial mesh. Comptes Rendus Mathematique 349(17-18):999–1003MathSciNetCrossRefMATH

Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224MathSciNetCrossRefMATH

Bendsøe MP, Sigmund O (2004) Topology optimization: theory, methods, and applications. Springer, BerlinCrossRefMATH

Chen S, Wang MY, Liu AQ (2008) Shape feature control in structural topology optimization. Comput Aided Des 40(9):951–962CrossRef

Choi JS, Izui K, Nishiwaki S, Kawamoto A, Nomura T (2012) Rotor pole design of ipm motors for a sinusoidal air-gap flux density distribution. Struct Multidiscip Optim 46(3):445–455CrossRef

Christiansen AN, Nobel-jørgensen M, Aage N, Sigmund O, Bærentzen JA (2014) Topology optimization using an explicit interface representation. Struct Multidiscip Optim 49(3):387–399MathSciNetCrossRef

Erentok A, Sigmund O (2008) Three-dimensional topology optimized electrically-small conformal antenna. In: 2008 IEEE antennas and propagation society international symposium. IEEE

Erentok A, Sigmund O (2011) Topology optimization of sub-wavelength antennas. IEEE Trans Antennas Propag 59(1):58–69CrossRef

Frickey DA (1994) Conversions between s, z, y, h, abcd, and t parameters which are valid for complex source and load impedances. IEEE Trans Microwave Theory Tech 42(2):205–211CrossRef

Guo X, Zhang W, Zhong W (2014) Explicit feature control in structural topology optimization via level set method. Comput Methods Appl Mech Eng 272:354–378MathSciNetCrossRefMATH

Ha SH, Cho S (2008) Level set based topological shape optimization of geometrically nonlinear structures using unstructured mesh. Comput Struct 86(13-14):1447–1455CrossRef

Haber RB, Jog CS, Bendsøe MP (1996) A new approach to variable-topology shape design using a constraint on perimeter. Structural Optimization 11(1–2):1–12CrossRef

Han X, Xu C, Prince JL (2003) A topology preserving level set method for geometric deformable models. IEEE Trans Pattern Anal Mach Intell 25(6):755–768CrossRef

Hassan E, Wadbro E, Berggren M (2014) Topology optimization of metallic antennas. IEEE Trans Antennas Propag 62(5):2488–2500MathSciNetCrossRefMATH

Hayt WH, Kemmerly JE, Durbin SM (1986) Engineering circuit analysis. McGraw-Hill, New York

Jensen JS, Sigmund O (2004) Systematic design of photonic crystal structures using topology optimization: low-loss waveguide bends. Appl Phys Lett 84(12):2022–2024CrossRef

Kawamoto A, Matsumori T, Yamasaki S, Nomura T, Kondoh T, Nishiwaki S (2011) Heaviside projection based topology optimization by a PDE-filtered scalar function. Struct Multidiscip Optim 44(1):19–24CrossRefMATH

Kreisselmeier G, Steinhauser R (1979) Systematic control design by optimizing a vector performance index. IFAC Proceedings Volumes 12(7):113–117CrossRefMATH

Kreissl S, Maute K (2012) Levelset based fluid topology optimization using the extended finite element method. Struct Multidiscip Optim 46(3):311–326MathSciNetCrossRefMATH

Kurokawa K (1965) Power waves and the scattering matrix. IEEE Trans Microwave Theory Tech 13(2):194–202CrossRef

Liu S, Wang Q, Gao R (2014) A topology optimization method for design of small GPR antennas. Struct Multidiscip Optim 50(6):1165–1174CrossRef

Luo J, Luo Z, Chen S, Tong L, Wang MY (2008) A new level set method for systematic design of hinge-free compliant mechanisms. Comput Methods Appl Mech Eng 198(2):318–331CrossRefMATH

McRae DS (2000) r-refinement grid adaptation algorithms and issues. Comput Methods Appl Mech Eng 189 (4):1161–1182CrossRefMATH

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):1261–1296CrossRefMATH

Paul CR (2006) Introduction to electromagnetic compatibility. Wiley, New York

Sato Y, Yamada T, Izui K, Nishiwaki S (2017) Manufacturability evaluation for molded parts using fictitious physical models, and its application in topology optimization. Int J Adv Manuf Technol 92(1–4):1391–1409CrossRef

Tsuji Y, Hirayama K, Nomura T, Sato K, Nishiwaki S (2006) Design of optical circuit devices based on topology optimization. IEEE Photon Technol Lett 18(7):850–852CrossRef

Van Miegroet L, Duysinx P (2007) Stress concentration minimization of 2d filets using X-FEM and level set description. Struct Multidiscip Optim 33(4-5):425–438CrossRef

Wang F, Lazarov BS, Sigmund O (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidiscip Optim 43(6):767–784CrossRefMATH

Wang S, Wang MY (2006) A moving superimposed finite element method for structural topology optimization. Int J Numer Methods Eng 65(11):1892–1922MathSciNetCrossRefMATH

Wang S, Lee FC, Chen DY, Odendaal WG (2004) Effects of parasitic parameters on EMI filter performance. IEEE Trans on Power Electron 19(3):869–877CrossRef

Wei P, Wang MY, Xing X (2010) A study on X-FEM in continuum structural optimization using a level set model. Comput Aided Des 42(8):708–719CrossRef

Wrenn GA (1989) An indirect method for numerical optimization using the Kreisselmeir-Steinhauser function. NASA Contractor Report (4220)

Xia Q, Shi T, Liu S, Wang MY (2012) A level set solution to the stress-based structural shape and topology optimization. Comput Struct 90:55–64CrossRef

Yamada T, Watanabe H, Fujii G, Matsumoto T (2013) Topology optimization for a dielectric optical cloak based on an exact level set approach. IEEE Trans Magn 49(5):2073–2076CrossRef

Yamasaki S, Nomura T, Kawamoto A, Sato K, Nishiwaki S (2011) A level set-based topology optimization method targeting metallic waveguide design problems. Int J Numer Methods Eng 87(9):844–868MathSciNetCrossRefMATH

Yamasaki S, Yamada T, Matsumoto T (2013) An immersed boundary element method for level-set based topology optimization. Int J Numer Methods Eng 93(9):960–988MathSciNetCrossRefMATH

Yamasaki S, Kawamoto A, Nomura T, Fujita K (2015) A consistent grayscale-free topology optimization method using the level-set method and zero-level boundary tracking mesh. Int J Numer Methods Eng 101(10):744–773MathSciNetCrossRefMATH

Yamasaki S, Kawamoto A, Saito A, Kuroishi M, Fujita K (2017a) Grayscale-free topology optimization for electromagnetic design problem of in-vehicle reactor. Struct Multidiscip Optim 55(3):1079–1090MathSciNetCrossRef

Yamasaki S, Yamanaka S, Fujita K (2017b) Three-dimensional grayscale-free topology optimization using a level-set based r-refinement method. Int J Numer Methods Eng 112(10):1402–1438MathSciNetCrossRef

Yoo J, Kikuchi N, Volakis JL (2000) Structural optimization in magnetic devices by the homogenization design method. IEEE Trans Magn 36(3):574–580CrossRef

Zhang W, Zhong W, Guo X (2014) An explicit length scale control approach in SIMP-based topology optimization. Comput Methods Appl Mech Eng 282:71–86MathSciNetCrossRefMATH

Zhou S, Li W, Li Q (2010) Level-set based topology optimization for electromagnetic dipole antenna design. J Comput Phys 229(19):6915–6930MathSciNetCrossRefMATH

Title: Topology optimization of conductors in electrical circuit
Authors: Katsuya Nomura
Shintaro Yamasaki
Kentaro Yaji
Hiroki Bo
Atsuhiro Takahashi
Takashi Kojima
Kikuo Fujita
Publication date: 11-01-2019
Publisher: Springer Berlin Heidelberg
Published in: Structural and Multidisciplinary Optimization / Issue 6/2019
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI: https://doi.org/10.1007/s00158-018-02187-2

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 6/2019

Combined length scale and overhang angle control in minimum compliance topology optimization for additive manufacturing

An efficient multi-objective optimization method for uncertain structures based on ellipsoidal convex model

Distortion energy-based topology optimization design of hyperelastic materials

Performance assessment of a cross-validation sampling strategy with active surrogate model selection

Innovative designs of an in-tank hydrogen valve towards direct metal laser sintering compatibility and fatigue life enhancement

Evaluation and assessment of non-normal output during robust optimization

Premium Partners