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Published in: Structural and Multidisciplinary Optimization 5/2019

18-10-2019 | Research Paper

Discrete material optimization of vibrating composite plate and attached piezoelectric fiber composite patch

Authors: Bin Niu, Yao Shan, Erik Lund

Published in: Structural and Multidisciplinary Optimization | Issue 5/2019

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Abstract

This work deals with the layout optimization of piezoelectric fiber composite patches on a vibrating laminated composite plate and the discrete material design of the composite plate. The vibration of the composite plate is excited by an external mechanical loading, and a sinusoidal voltage with given amplitude and frequency is applied on the piezoelectric fiber composite patches. The analysis of the composite structure with piezoelectric fiber composite patches is performed via a finite element method in condensed form, where the piezoelectric effects are considered as induced force. As a view to minimize the dynamic response of the vibrating laminated composite structure, the Discrete Material Optimization method is employed to perform the design optimization of piezoelectric fiber composite patches and the stacking sequence, fiber angles, and selection of material for the composite structure. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

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Literature
go back to reference Allaire G, Jouveb O (2001) Eigenfrequency optimization in optimal design. Comput Meth Appl Mech Eng 190(28):3565–3579MathSciNetMATH Allaire G, Jouveb O (2001) Eigenfrequency optimization in optimal design. Comput Meth Appl Mech Eng 190(28):3565–3579MathSciNetMATH
go back to reference Anton SR, Sodano HA (2007) A review of power harvesting using piezoelectric materials (2003–2006). Smart Mater Struct 16(3):R1–R21 Anton SR, Sodano HA (2007) A review of power harvesting using piezoelectric materials (2003–2006). Smart Mater Struct 16(3):R1–R21
go back to reference Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202 Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202
go back to reference 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
go back to reference Bruyneel M (2011) SFP—a new parameterization based on shape functions for optimal material selection: application to conventional composite plies. Struct Multidiscip Optim 43(1):17–27 Bruyneel M (2011) SFP—a new parameterization based on shape functions for optimal material selection: application to conventional composite plies. Struct Multidiscip Optim 43(1):17–27
go back to reference Bruyneel M, Fleury C (2002) Composite structures optimization using sequential convex programming. Adv Eng Softw 33(7):697–711MATH Bruyneel M, Fleury C (2002) Composite structures optimization using sequential convex programming. Adv Eng Softw 33(7):697–711MATH
go back to reference Diaz AR, Kikuchi N (1992) Solutions to shape and topology eigenvalue optimization problems using a homogenization method. Int J Numer Methods Eng 35(7):1487–1502MathSciNetMATH Diaz AR, Kikuchi N (1992) Solutions to shape and topology eigenvalue optimization problems using a homogenization method. Int J Numer Methods Eng 35(7):1487–1502MathSciNetMATH
go back to reference Donoso A, Sigmund O (2009) Optimization of piezoelectric bimorph actuators with active damping for static and dynamic loads. Struct Multidiscip Optim 38(2):171–183 Donoso A, Sigmund O (2009) Optimization of piezoelectric bimorph actuators with active damping for static and dynamic loads. Struct Multidiscip Optim 38(2):171–183
go back to reference Du J, Olhoff N (2007) Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Struct Multidiscip Optim 34(2):91–110MathSciNetMATH Du J, Olhoff N (2007) Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Struct Multidiscip Optim 34(2):91–110MathSciNetMATH
go back to reference Duan Z, Yan J, Zhao G (2015) Integrated optimization of the material and structure of composites based on the Heaviside penalization of discrete material model. Struct Multidiscip Optim 51(3):721–732 Duan Z, Yan J, Zhao G (2015) Integrated optimization of the material and structure of composites based on the Heaviside penalization of discrete material model. Struct Multidiscip Optim 51(3):721–732
go back to reference Frecker MI (2003) Recent advances in optimization of smart structures and actuators. J Intell Mater Syst Struct 14(4):207–216 Frecker MI (2003) Recent advances in optimization of smart structures and actuators. J Intell Mater Syst Struct 14(4):207–216
go back to reference Gao F, Shen Y, Li L (2000) The optimal design of piezoelectric actuators for plate vibroacoustic control using genetic algorithms with immune diversity. Smart Mater Struct 9(4):485–491 Gao F, Shen Y, Li L (2000) The optimal design of piezoelectric actuators for plate vibroacoustic control using genetic algorithms with immune diversity. Smart Mater Struct 9(4):485–491
go back to reference Gao T, Zhang WH, Duysinx P (2013) Simultaneous design of structural layout and discrete fiber orientation using bi-value coding parameterization and volume constraint. Struct Multidiscip Optim 48(6):1075–1088MathSciNet Gao T, Zhang WH, Duysinx P (2013) Simultaneous design of structural layout and discrete fiber orientation using bi-value coding parameterization and volume constraint. Struct Multidiscip Optim 48(6):1075–1088MathSciNet
go back to reference Gaul DIHL, Kögl DIM, Wagner DIM (2003) Boundary element methods for engineers and scientists. Springer, Berlin HeidelbergMATH Gaul DIHL, Kögl DIM, Wagner DIM (2003) Boundary element methods for engineers and scientists. Springer, Berlin HeidelbergMATH
go back to reference Jaewook L, Dongjin K, Tsuyoshi N, Dede EM, Jeonghoon Y (2018) Topology optimization for continuous and discrete orientation design of functionally graded fiber-reinforced composite structures. Compos Struct 201:217–233 Jaewook L, Dongjin K, Tsuyoshi N, Dede EM, Jeonghoon Y (2018) Topology optimization for continuous and discrete orientation design of functionally graded fiber-reinforced composite structures. Compos Struct 201:217–233
go back to reference Jog CS (2002) Topology design of structures subjected to periodic loading. J Sound Vib 253(3):687–709 Jog CS (2002) Topology design of structures subjected to periodic loading. J Sound Vib 253(3):687–709
go back to reference Kang Z, Tong L (2008a) Topology optimization-based distribution design of actuation voltage in static shape control of plates. Comput Struct 86(19–20):1885–1893 Kang Z, Tong L (2008a) Topology optimization-based distribution design of actuation voltage in static shape control of plates. Comput Struct 86(19–20):1885–1893
go back to reference Kang Z, Tong L (2008b) Integrated optimization of material layout and control voltage for piezoelectric laminated plates. J Intell Mater Syst Struct 19(8):889–904 Kang Z, Tong L (2008b) Integrated optimization of material layout and control voltage for piezoelectric laminated plates. J Intell Mater Syst Struct 19(8):889–904
go back to reference Kiyono CY, Silva ECN, Reddy JN (2012) Design of laminated piezocomposite shell transducers with arbitrary fiber orientation using topology optimization approach. Int J Numer Methods Eng 90(12):1452–1484MATH Kiyono CY, Silva ECN, Reddy JN (2012) Design of laminated piezocomposite shell transducers with arbitrary fiber orientation using topology optimization approach. Int J Numer Methods Eng 90(12):1452–1484MATH
go back to reference Kiyono CY, Silva ECN, Reddy JN (2016a) A novel fiber optimization method based on normal distribution function with continuously varying fiber path. Compos Struct 160:503–515 Kiyono CY, Silva ECN, Reddy JN (2016a) A novel fiber optimization method based on normal distribution function with continuously varying fiber path. Compos Struct 160:503–515
go back to reference Kiyono CY, Silva ECN, Reddy JN (2016b) Optimal design of laminated piezocomposite energy harvesting devices considering stress constraints. Int J Numer Methods Eng 105(12):883–914MathSciNet Kiyono CY, Silva ECN, Reddy JN (2016b) Optimal design of laminated piezocomposite energy harvesting devices considering stress constraints. Int J Numer Methods Eng 105(12):883–914MathSciNet
go back to reference Kögl M, Bucalem ML (2005) A family of piezoelectric MITC plate elements. Comput Struct 83(15–16):1277–1297 Kögl M, Bucalem ML (2005) A family of piezoelectric MITC plate elements. Comput Struct 83(15–16):1277–1297
go back to reference Kögl M, Silva ECN (2005) Topology optimization of smart structures: design of piezoelectric plate and shell actuators. Smart Mater Struct 14(2):387–399 Kögl M, Silva ECN (2005) Topology optimization of smart structures: design of piezoelectric plate and shell actuators. Smart Mater Struct 14(2):387–399
go back to reference Lund E (2009) Buckling topology optimization of laminated multi-material composite shell structures. Compos Struct 91(2):158–167MathSciNet Lund E (2009) Buckling topology optimization of laminated multi-material composite shell structures. Compos Struct 91(2):158–167MathSciNet
go back to reference Lund E, Stegmann J (2006) Eigenfrequency and buckling optimization of laminated composite shell structures using discrete material optimization. Bendsøe MP, Olhoff N, Sigmund O (eds) IUTAM symposium on topological design optimization of structures, machines and materials, Springer, Dordrecht, Netherlands Lund E, Stegmann J (2006) Eigenfrequency and buckling optimization of laminated composite shell structures using discrete material optimization. Bendsøe MP, Olhoff N, Sigmund O (eds) IUTAM symposium on topological design optimization of structures, machines and materials, Springer, Dordrecht, Netherlands
go back to reference Nelli Silva EC, Nishiwaki S, Kikuchi N (1999) Design of piezocomposite materials and piezoelectric transducers using topology optimization. Part III. Arch Comput Meth Eng 6(4):305–329MathSciNet Nelli Silva EC, Nishiwaki S, Kikuchi N (1999) Design of piezocomposite materials and piezoelectric transducers using topology optimization. Part III. Arch Comput Meth Eng 6(4):305–329MathSciNet
go back to reference Niu B, Olhoff N, Lund E, Cheng G (2010) Discrete material optimization of vibrating laminated composite plates for minimum sound radiation. Int J Solids Struct 47(16):2097–2114MATH Niu B, Olhoff N, Lund E, Cheng G (2010) Discrete material optimization of vibrating laminated composite plates for minimum sound radiation. Int J Solids Struct 47(16):2097–2114MATH
go back to reference Niu B, He X, Shan Y, Yang R (2018) On objective functions of minimizing the vibration response of continuum structures subjected to external harmonic excitation. Struct Multidiscip Optim 57(6):2291–2307MathSciNet Niu B, He X, Shan Y, Yang R (2018) On objective functions of minimizing the vibration response of continuum structures subjected to external harmonic excitation. Struct Multidiscip Optim 57(6):2291–2307MathSciNet
go back to reference Olhoff N (1976) Optimization of vibrating beams with respect to higher order natural frequencies. J Struct Mech 4(1):87–122 Olhoff N (1976) Optimization of vibrating beams with respect to higher order natural frequencies. J Struct Mech 4(1):87–122
go back to reference Olhoff N (1977) Maximizing higher order Eigenfrequencies of beams with constraints on the design geometry. Mech Base Des Struct Mach 5(2):107–134 Olhoff N (1977) Maximizing higher order Eigenfrequencies of beams with constraints on the design geometry. Mech Base Des Struct Mach 5(2):107–134
go back to reference Olhoff N, Du J (2014) In: Rozvany G, Lewiński T (eds) Topological design for minimum dynamic compliance of structures under forced vibration. Topology optimization in structural and continuum mechanics. Springer, Heidelberg Olhoff N, Du J (2014) In: Rozvany G, Lewiński T (eds) Topological design for minimum dynamic compliance of structures under forced vibration. Topology optimization in structural and continuum mechanics. Springer, Heidelberg
go back to reference Olhoff N, Niu B, Cheng G (2012) Optimum design of band-gap beam structures. Int J Solid Struct 49(22):3158–3169 Olhoff N, Niu B, Cheng G (2012) Optimum design of band-gap beam structures. Int J Solid Struct 49(22):3158–3169
go back to reference Padoin E, Santos IF, Perondi EA, Menuzzi O, Gonçalves JF (2018) Topology optimization of piezoelectric macro-fiber composite patches on laminated plates for vibration suppression. Struct Multidiscip Optim Padoin E, Santos IF, Perondi EA, Menuzzi O, Gonçalves JF (2018) Topology optimization of piezoelectric macro-fiber composite patches on laminated plates for vibration suppression. Struct Multidiscip Optim
go back to reference Qing HQ (2012) Advanced mechanics of piezoelectricity. Higher Education Press, BeijingMATH Qing HQ (2012) Advanced mechanics of piezoelectricity. Higher Education Press, BeijingMATH
go back to reference Quek ST, Wang SY, Ang KK (2003) Vibration control of composite plates via optimal placement of piezoelectric patches. J Intell Mater Syst Struct 14(4):229–245 Quek ST, Wang SY, Ang KK (2003) Vibration control of composite plates via optimal placement of piezoelectric patches. J Intell Mater Syst Struct 14(4):229–245
go back to reference Qureshi EM, Shen X, Chen JJ (2014) Vibration control laws via shunted piezoelectric transducers: a review. Int J Aeronaut Space Sci 15(1):1–19 Qureshi EM, Shen X, Chen JJ (2014) Vibration control laws via shunted piezoelectric transducers: a review. Int J Aeronaut Space Sci 15(1):1–19
go back to reference Ray MC, Reddy JN (2013) Active damping of laminated cylindrical shells conveying fluid using 1–3 piezoelectric composites. Compos Struct 98:261–271 Ray MC, Reddy JN (2013) Active damping of laminated cylindrical shells conveying fluid using 1–3 piezoelectric composites. Compos Struct 98:261–271
go back to reference Rozvany GIN, Zhou M, Birker T (1992) Generalized shape optimization without homogenization. Struct Optim 4(3–4):250–252 Rozvany GIN, Zhou M, Birker T (1992) Generalized shape optimization without homogenization. Struct Optim 4(3–4):250–252
go back to reference Ruiz D, Díaz-Molina A, Sigmund O, Donoso A, Bellido JC, Sánchez-Rojas JL (2018) Optimal design of robust piezoelectric unimorph microgrippers. Appl Math Model 55:1–12MathSciNet Ruiz D, Díaz-Molina A, Sigmund O, Donoso A, Bellido JC, Sánchez-Rojas JL (2018) Optimal design of robust piezoelectric unimorph microgrippers. Appl Math Model 55:1–12MathSciNet
go back to reference Salas RA, Ramírez-Gil Fran FJ, Montealegre-Rubio W, Silva ECN, Reddy JN (2018) Optimized dynamic design of laminated piezocomposite multi-entry actuators considering fiber orientation. Comput Methods Appl Mech Eng 335:223–254MathSciNet Salas RA, Ramírez-Gil Fran FJ, Montealegre-Rubio W, Silva ECN, Reddy JN (2018) Optimized dynamic design of laminated piezocomposite multi-entry actuators considering fiber orientation. Comput Methods Appl Mech Eng 335:223–254MathSciNet
go back to reference Sigmund O, Jensen JS (2003) Systematic design of phononic band-gap materials and structures by topology optimization. Philos Trans 361(1806):1001–1019MathSciNetMATH Sigmund O, Jensen JS (2003) Systematic design of phononic band-gap materials and structures by topology optimization. Philos Trans 361(1806):1001–1019MathSciNetMATH
go back to reference Silva ECN, Kikuchi N (1999) Design of piezocomposite materials and piezoelectric transducers using topology optimization—part III. Arch Comput Meth Eng 6(4):305–329 Silva ECN, Kikuchi N (1999) Design of piezocomposite materials and piezoelectric transducers using topology optimization—part III. Arch Comput Meth Eng 6(4):305–329
go back to reference Sørensen SN, Lund E (2013) Topology and thickness optimization of laminated composites including manufacturing constraints. Struct Multidiscip Optim 48(2):249–265MathSciNet Sørensen SN, Lund E (2013) Topology and thickness optimization of laminated composites including manufacturing constraints. Struct Multidiscip Optim 48(2):249–265MathSciNet
go back to reference Sørensen R, Lund E (2015a) Thickness filters for gradient based multi-material and thickness optimization of laminated composite structures. Struct Multidiscip Optim 52(2):227–250 Sørensen R, Lund E (2015a) Thickness filters for gradient based multi-material and thickness optimization of laminated composite structures. Struct Multidiscip Optim 52(2):227–250
go back to reference Sørensen R, Lund E (2015b) In-plane material filters for the discrete material optimization method. Struct Multidiscip Optim 52(4):645–661MathSciNet Sørensen R, Lund E (2015b) In-plane material filters for the discrete material optimization method. Struct Multidiscip Optim 52(4):645–661MathSciNet
go back to reference Stegmann J, Lund E (2005) Discrete material optimization of general composite shell structures. Int J Numer Methods Eng 62(14):2009–2027MATH Stegmann J, Lund E (2005) Discrete material optimization of general composite shell structures. Int J Numer Methods Eng 62(14):2009–2027MATH
go back to reference Sun HL, Chen HB, Zhang K, Zhang PQ (2008) Research on performance indices of vibration isolation system. Appl Acoust 69(9):789–795 Sun HL, Chen HB, Zhang K, Zhang PQ (2008) Research on performance indices of vibration isolation system. Appl Acoust 69(9):789–795
go back to reference Sun H, Yang ZC, Li KX, Li B, Xie J, Wu D, Zhang LL (2009) Vibration suppression of a hard disk driver actuator arm using piezoelectric shunt damping with a topology-optimized PZT transducer. Smart Mater Struct 18(6):065010 Sun H, Yang ZC, Li KX, Li B, Xie J, Wu D, Zhang LL (2009) Vibration suppression of a hard disk driver actuator arm using piezoelectric shunt damping with a topology-optimized PZT transducer. Smart Mater Struct 18(6):065010
go back to reference Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MathSciNetMATH Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MathSciNetMATH
go back to reference Tzou HS, Tseng CI (1990) Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: a piezoelectric finite element approach. J Sound Vib 138(1):17–34 Tzou HS, Tseng CI (1990) Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: a piezoelectric finite element approach. J Sound Vib 138(1):17–34
go back to reference Vatanabe SL, Paulino GH, Silva ECN (2013) Design of functionally graded piezocomposites using topology optimization and homogenization—toward effective energy harvesting materials. Comput Methods Appl Mech Eng 266:205–218MathSciNetMATH Vatanabe SL, Paulino GH, Silva ECN (2013) Design of functionally graded piezocomposites using topology optimization and homogenization—toward effective energy harvesting materials. Comput Methods Appl Mech Eng 266:205–218MathSciNetMATH
go back to reference Wang J, Mak CM (2013) An indicator for the assessment of isolation performance of transient vibration. J Vib Control 19(16):2459–2468 Wang J, Mak CM (2013) An indicator for the assessment of isolation performance of transient vibration. J Vib Control 19(16):2459–2468
go back to reference Wang SY, Tai K, Quek ST (2006) Topology optimization of piezoelectric sensors/actuators for torsional vibration control of composite plates. Smart Mater Struct 15(15):253 Wang SY, Tai K, Quek ST (2006) Topology optimization of piezoelectric sensors/actuators for torsional vibration control of composite plates. Smart Mater Struct 15(15):253
go back to reference Xia Q, Shi T (2018) A cascadic multilevel optimization algorithm for the design of composite structures with curvilinear fiber based on Shepard interpolation. Compos Struct 188:209–219 Xia Q, Shi T (2018) A cascadic multilevel optimization algorithm for the design of composite structures with curvilinear fiber based on Shepard interpolation. Compos Struct 188:209–219
go back to reference Zhang X, Kang Z (2014) Topology optimization of piezoelectric layers in plates with active vibration control. J Intell Mater Syst Struct 25(6):697–712 Zhang X, Kang Z (2014) Topology optimization of piezoelectric layers in plates with active vibration control. J Intell Mater Syst Struct 25(6):697–712
go back to reference Zhang X, Kang Z, Li M (2014) Topology optimization of electrode coverage of piezoelectric thin-walled structures with CGVF control for minimizing sound radiation. Struct Multidiscip Optim 50(5):799–814MathSciNet Zhang X, Kang Z, Li M (2014) Topology optimization of electrode coverage of piezoelectric thin-walled structures with CGVF control for minimizing sound radiation. Struct Multidiscip Optim 50(5):799–814MathSciNet
go back to reference Zheng B, Chang CJ, Gea HC (2009) Topology optimization of energy harvesting devices using piezoelectric materials. Struct Multidiscip Optim 38(1):17–23 Zheng B, Chang CJ, Gea HC (2009) Topology optimization of energy harvesting devices using piezoelectric materials. Struct Multidiscip Optim 38(1):17–23
Metadata
Title
Discrete material optimization of vibrating composite plate and attached piezoelectric fiber composite patch
Authors
Bin Niu
Yao Shan
Erik Lund
Publication date
18-10-2019
Publisher
Springer Berlin Heidelberg
Published in
Structural and Multidisciplinary Optimization / Issue 5/2019
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-019-02359-8

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