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Erschienen in: Structural and Multidisciplinary Optimization 4/2019

06.11.2018 | Research Paper

An optimality criteria-based method for the simultaneous optimization of the structural design and placement of piezoelectric actuators

verfasst von: Alexandre Molter, Lucas dos Santos Fernandez, Jonathan Brum Lauz

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 4/2019

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Abstract

This work provides an optimality criteria-based method for the simultaneous optimization of the structural design and optimal placement of piezoelectric actuators for statically loaded structures. The goal of the topology optimization is to find the optimal distribution of the structural and piezoelectric materials in the compliance minimization context with a volume constraint for each material. All expressions used in the implementation of the resulting algorithm are developed in detail. Some numerical complications inherent to the type of problem we are dealing with are discussed and a numerical procedure is proposed for each one. Results are shown for two-dimensional beams through four numerical examples.

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Literatur
Zurück zum Zitat Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202CrossRef Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202CrossRef
Zurück zum Zitat Bendsøe MP (1995) Optimization of structural topology, shape and material. Springer, BerlinCrossRefMATH Bendsøe MP (1995) Optimization of structural topology, shape and material. Springer, BerlinCrossRefMATH
Zurück zum Zitat Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69(9–10):635–654MATH Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69(9–10):635–654MATH
Zurück zum Zitat Bendsøe MP, Sigmund O (2003) Topology optimization. Theory methods and applications. Springer, BerlinMATH Bendsøe MP, Sigmund O (2003) Topology optimization. Theory methods and applications. Springer, BerlinMATH
Zurück zum Zitat Buehler MJ, Bettig B, Parker GG (2004) Topology optimization of smart structures using a homogenization approach. J Intell Mater Syst Struct 15:655–667CrossRef Buehler MJ, Bettig B, Parker GG (2004) Topology optimization of smart structures using a homogenization approach. J Intell Mater Syst Struct 15:655–667CrossRef
Zurück zum Zitat Carbonari RC, Silva ECN, Nishiwaki S (2007) Optimum placement of piezoelectric material in piezoactuator design. Smart Mater Struct 16:207–220CrossRef Carbonari RC, Silva ECN, Nishiwaki S (2007) Optimum placement of piezoelectric material in piezoactuator design. Smart Mater Struct 16:207–220CrossRef
Zurück zum Zitat Cardoso EL, Fonseca JSO (2004) An incremental Lagrangian formulation to the analysis of piezoelectric bodies subjected to geometric non-linearities. Int J Numer Meth Eng 59:963–987CrossRefMATH Cardoso EL, Fonseca JSO (2004) An incremental Lagrangian formulation to the analysis of piezoelectric bodies subjected to geometric non-linearities. Int J Numer Meth Eng 59:963–987CrossRefMATH
Zurück zum Zitat De Leon DM, de Souza CE, Fonseca JSO, da Silva RGA (2012) Aeroelastic tailoring using fiber orientation and topology optimization. Struct Multidiscipl Optim 46(5):663–677MathSciNetCrossRefMATH De Leon DM, de Souza CE, Fonseca JSO, da Silva RGA (2012) Aeroelastic tailoring using fiber orientation and topology optimization. Struct Multidiscipl Optim 46(5):663–677MathSciNetCrossRefMATH
Zurück zum Zitat Deaton JD, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscipl Optim 49(1):1–38MathSciNetCrossRef Deaton JD, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscipl Optim 49(1):1–38MathSciNetCrossRef
Zurück zum Zitat Fernandez LS, Molter A, Botelho FS (2017) Simultaneous topology optimization and proportional actuators localization. SeMA J 74(4):385–409MathSciNetCrossRefMATH Fernandez LS, Molter A, Botelho FS (2017) Simultaneous topology optimization and proportional actuators localization. SeMA J 74(4):385–409MathSciNetCrossRefMATH
Zurück zum Zitat Frecker MI (2003) Recent advances in optimization of smart structures and actuators. J Intell Mater Syst Struct 14:207–216CrossRef Frecker MI (2003) Recent advances in optimization of smart structures and actuators. J Intell Mater Syst Struct 14:207–216CrossRef
Zurück zum Zitat Gonçalves JF, De Leon DM, Perondi EA (2017) Topology optimization of embedded piezoelectric actuators considering control spillover effects. J Sound Vib 388:20–41CrossRef Gonçalves JF, De Leon DM, Perondi EA (2017) Topology optimization of embedded piezoelectric actuators considering control spillover effects. J Sound Vib 388:20–41CrossRef
Zurück zum Zitat Gonçalves JF, De Leon DM, Perondi EA (2018) Simultaneous optimization of piezoelectric actuator topology and polarization. Struct Multidiscipl Optim 58(3):1139–1154MathSciNetCrossRef Gonçalves JF, De Leon DM, Perondi EA (2018) Simultaneous optimization of piezoelectric actuator topology and polarization. Struct Multidiscipl Optim 58(3):1139–1154MathSciNetCrossRef
Zurück zum Zitat Gupta V, Sharma M, Thakur N (2010) Optimization criteria for optimal placement of piezoelectric sensors and actuators on a smart structure: a technical review. J Intell Mater Syst Struct 21:1227–1243CrossRef Gupta V, Sharma M, Thakur N (2010) Optimization criteria for optimal placement of piezoelectric sensors and actuators on a smart structure: a technical review. J Intell Mater Syst Struct 21:1227–1243CrossRef
Zurück zum Zitat Kang Z, Tong L (2008) Integrated optimization of material layout and control voltage for piezoelectric laminated plates. J Intell Mater Syst Struct 19:889–904CrossRef Kang Z, Tong L (2008) Integrated optimization of material layout and control voltage for piezoelectric laminated plates. J Intell Mater Syst Struct 19:889–904CrossRef
Zurück zum Zitat Kang Z, Wang R, Tong L (2011) Combined optimization of bi-material structural layout and voltage distribution for in-plane piezoelectric actuation. Comput Methods in Appl Mech Eng 200(13–16):1467–1478MathSciNetCrossRefMATH Kang Z, Wang R, Tong L (2011) Combined optimization of bi-material structural layout and voltage distribution for in-plane piezoelectric actuation. Comput Methods in Appl Mech Eng 200(13–16):1467–1478MathSciNetCrossRefMATH
Zurück zum Zitat Kharmanda G, Olhoff N, Mohamed A, Lemaire M (2004) Reliability-based topology optimization. Struct Multidiscipl Optim 26(5):295–307CrossRef Kharmanda G, Olhoff N, Mohamed A, Lemaire M (2004) Reliability-based topology optimization. Struct Multidiscipl Optim 26(5):295–307CrossRef
Zurück zum Zitat Luo Z, Gao W, Song C (2010) Design of multi-phase piezoelectric actuators. J Intell Mater Syst Struct 21:1851–1865CrossRef Luo Z, Gao W, Song C (2010) Design of multi-phase piezoelectric actuators. J Intell Mater Syst Struct 21:1851–1865CrossRef
Zurück zum Zitat Ma Z. -D., Kikuch N, Hagiwara L (1993) Structural topology and shape optimization for a frequency response problem. Comput Mech 13:157–174MathSciNetCrossRefMATH Ma Z. -D., Kikuch N, Hagiwara L (1993) Structural topology and shape optimization for a frequency response problem. Comput Mech 13:157–174MathSciNetCrossRefMATH
Zurück zum Zitat Matsui K, Terada K (2004) Continuous approximation of material distribution for topology optimization. Int J Numer Meth Eng 59:1925–1944MathSciNetCrossRefMATH Matsui K, Terada K (2004) Continuous approximation of material distribution for topology optimization. Int J Numer Meth Eng 59:1925–1944MathSciNetCrossRefMATH
Zurück zum Zitat Molter A, Fernandez LdS, Fonseca JSO (2016) Simultaneous topology optimization of structure and piezoelectric actuators distribution. Appl Math Model 40(9–10):5576–5588MathSciNetCrossRef Molter A, Fernandez LdS, Fonseca JSO (2016) Simultaneous topology optimization of structure and piezoelectric actuators distribution. Appl Math Model 40(9–10):5576–5588MathSciNetCrossRef
Zurück zum Zitat Molter A, da Silveira OAA, Bottega V, Fonseca JSO (2013) Integrated topology optimization and optimal control for vibration suppression in structural design. Struct Multidiscipl Optim 47:389–397MathSciNetCrossRefMATH Molter A, da Silveira OAA, Bottega V, Fonseca JSO (2013) Integrated topology optimization and optimal control for vibration suppression in structural design. Struct Multidiscipl Optim 47:389–397MathSciNetCrossRefMATH
Zurück zum Zitat Piefort V (2001) Finite element modeling of piezoelectric active structures. Ph.D. Thesis. Université Libre de Bruxelles, Bruxelles, Belgique Piefort V (2001) Finite element modeling of piezoelectric active structures. Ph.D. Thesis. Université Libre de Bruxelles, Bruxelles, Belgique
Zurück zum Zitat Qi H, Fang D, Yao Z (1997) FEM analysis of electro-mechanical coupling effect of piezoelectric materials. Comput Mater Sci 8:283–290CrossRef Qi H, Fang D, Yao Z (1997) FEM analysis of electro-mechanical coupling effect of piezoelectric materials. Comput Mater Sci 8:283–290CrossRef
Zurück zum Zitat Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Struct Mach 25(4):493–524CrossRef Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Struct Mach 25(4):493–524CrossRef
Zurück zum Zitat Sigmund O (2001) A 99 line topology optimization code written in matlab. Struct Multidiscipl Optim 21 (2):120–127CrossRef Sigmund O (2001) A 99 line topology optimization code written in matlab. Struct Multidiscipl Optim 21 (2):120–127CrossRef
Zurück zum Zitat Silva ECN (2003) Topology optimization applied to the design of linear piezoelectric motors. J Intell Mater Syst Struct 14:309– 322CrossRef Silva ECN (2003) Topology optimization applied to the design of linear piezoelectric motors. J Intell Mater Syst Struct 14:309– 322CrossRef
Zurück zum Zitat Silveira OAA, Fonseca JSO, Santos IF (2014) Actuator topology design using the controllability Gramian. Struct Multidiscipl Optim 51(1):145–157MathSciNetCrossRef Silveira OAA, Fonseca JSO, Santos IF (2014) Actuator topology design using the controllability Gramian. Struct Multidiscipl Optim 51(1):145–157MathSciNetCrossRef
Zurück zum Zitat Wang Y, Luo Z, Zhang X, Kang Z (2014) Topological design of compliant smart structures with embedded movable actuators. Smart Mater Struct 23(4):045024CrossRef Wang Y, Luo Z, Zhang X, Kang Z (2014) Topological design of compliant smart structures with embedded movable actuators. Smart Mater Struct 23(4):045024CrossRef
Zurück zum Zitat Yang K, Zhu J, Wu M, Zhang W (2018) Integrated optimization of actuators and structural topology of piezoelectric composite structures for static shape control. Comput Methods Appl Mech Engrg 334(1):440–469MathSciNetCrossRef Yang K, Zhu J, Wu M, Zhang W (2018) Integrated optimization of actuators and structural topology of piezoelectric composite structures for static shape control. Comput Methods Appl Mech Engrg 334(1):440–469MathSciNetCrossRef
Zurück zum Zitat Zhou M, Rozvany GIN (1991) The COC algorithm, Part II: topological, geometrical and generalized shape optimization. Comput Methods in Appl Mech Eng 89:309–336CrossRef Zhou M, Rozvany GIN (1991) The COC algorithm, Part II: topological, geometrical and generalized shape optimization. Comput Methods in Appl Mech Eng 89:309–336CrossRef
Zurück zum Zitat Zuo W, Saitou K (2017) Multi-material topology optimization using ordered SIMP interpolation. Struct Multidisc Optim 55(2):477–491MathSciNetCrossRef Zuo W, Saitou K (2017) Multi-material topology optimization using ordered SIMP interpolation. Struct Multidisc Optim 55(2):477–491MathSciNetCrossRef
Metadaten
Titel
An optimality criteria-based method for the simultaneous optimization of the structural design and placement of piezoelectric actuators
verfasst von
Alexandre Molter
Lucas dos Santos Fernandez
Jonathan Brum Lauz
Publikationsdatum
06.11.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 4/2019
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-018-2116-y

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