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Structural and Multidisciplinary Optimization

, Volume 60, Issue 5, pp 1759–1782 | Cite as

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

  • Bin NiuEmail author
  • Yao Shan
  • Erik Lund
Research Paper
  • 242 Downloads

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.

Keywords

Piezoelectric effect Layout optimization Laminated composite structure Dynamic response Harmonic excitation 

Notes

Funding information

This work is partially supported by the National Natural Science Foundation of China (NSFC Nos. 51975087, 51790172, 51505064, 51675082), Natural Science Foundation of Liaoning Province (no. 2015020154), and Fundamental Research Funds for the Central Universities (DUT17ZD207). These supports are gratefully appreciated.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Allaire G, Jouveb O (2001) Eigenfrequency optimization in optimal design. Comput Meth Appl Mech Eng 190(28):3565–3579MathSciNetzbMATHGoogle Scholar
  2. Anton SR, Sodano HA (2007) A review of power harvesting using piezoelectric materials (2003–2006). Smart Mater Struct 16(3):R1–R21Google Scholar
  3. Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202Google Scholar
  4. Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69(9–10):635–654zbMATHGoogle Scholar
  5. 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):17–27Google Scholar
  6. Bruyneel M, Fleury C (2002) Composite structures optimization using sequential convex programming. Adv Eng Softw 33(7):697–711zbMATHGoogle Scholar
  7. Diaz AR, Kikuchi N (1992) Solutions to shape and topology eigenvalue optimization problems using a homogenization method. Int J Numer Methods Eng 35(7):1487–1502MathSciNetzbMATHGoogle Scholar
  8. Donoso A, Sigmund O (2009) Optimization of piezoelectric bimorph actuators with active damping for static and dynamic loads. Struct Multidiscip Optim 38(2):171–183Google Scholar
  9. 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):91–110MathSciNetzbMATHGoogle Scholar
  10. 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):721–732Google Scholar
  11. Frecker MI (2003) Recent advances in optimization of smart structures and actuators. J Intell Mater Syst Struct 14(4):207–216Google Scholar
  12. 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):485–491Google Scholar
  13. 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):1075–1088MathSciNetGoogle Scholar
  14. Gaul DIHL, Kögl DIM, Wagner DIM (2003) Boundary element methods for engineers and scientists. Springer, Berlin HeidelbergzbMATHGoogle Scholar
  15. 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 201:217–233Google Scholar
  16. Jog CS (2002) Topology design of structures subjected to periodic loading. J Sound Vib 253(3):687–709Google Scholar
  17. Kang Z, Tong L (2008a) Topology optimization-based distribution design of actuation voltage in static shape control of plates. Comput Struct 86(19–20):1885–1893Google Scholar
  18. Kang Z, Tong L (2008b) Integrated optimization of material layout and control voltage for piezoelectric laminated plates. J Intell Mater Syst Struct 19(8):889–904Google Scholar
  19. 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):1452–1484zbMATHGoogle Scholar
  20. Kiyono CY, Silva ECN, Reddy JN (2016a) A novel fiber optimization method based on normal distribution function with continuously varying fiber path. Compos Struct 160:503–515Google Scholar
  21. 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):883–914MathSciNetGoogle Scholar
  22. Kögl M, Bucalem ML (2005) A family of piezoelectric MITC plate elements. Comput Struct 83(15–16):1277–1297Google Scholar
  23. Kögl M, Silva ECN (2005) Topology optimization of smart structures: design of piezoelectric plate and shell actuators. Smart Mater Struct 14(2):387–399Google Scholar
  24. Lund E (2009) Buckling topology optimization of laminated multi-material composite shell structures. Compos Struct 91(2):158–167MathSciNetGoogle Scholar
  25. 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, NetherlandsGoogle Scholar
  26. 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):305–329MathSciNetGoogle Scholar
  27. 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):2097–2114zbMATHGoogle Scholar
  28. 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):2291–2307MathSciNetGoogle Scholar
  29. Olhoff N (1976) Optimization of vibrating beams with respect to higher order natural frequencies. J Struct Mech 4(1):87–122Google Scholar
  30. Olhoff N (1977) Maximizing higher order Eigenfrequencies of beams with constraints on the design geometry. Mech Base Des Struct Mach 5(2):107–134Google Scholar
  31. 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, HeidelbergGoogle Scholar
  32. Olhoff N, Niu B, Cheng G (2012) Optimum design of band-gap beam structures. Int J Solid Struct 49(22):3158–3169Google Scholar
  33. 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 OptimGoogle Scholar
  34. Qing HQ (2012) Advanced mechanics of piezoelectricity. Higher Education Press, BeijingzbMATHGoogle Scholar
  35. 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):229–245Google Scholar
  36. Qureshi EM, Shen X, Chen JJ (2014) Vibration control laws via shunted piezoelectric transducers: a review. Int J Aeronaut Space Sci 15(1):1–19Google Scholar
  37. Ray MC, Reddy JN (2013) Active damping of laminated cylindrical shells conveying fluid using 1–3 piezoelectric composites. Compos Struct 98:261–271Google Scholar
  38. Rozvany GIN, Zhou M, Birker T (1992) Generalized shape optimization without homogenization. Struct Optim 4(3–4):250–252Google Scholar
  39. 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 55:1–12MathSciNetGoogle Scholar
  40. 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 335:223–254MathSciNetGoogle Scholar
  41. Sigmund O, Jensen JS (2003) Systematic design of phononic band-gap materials and structures by topology optimization. Philos Trans 361(1806):1001–1019MathSciNetzbMATHGoogle Scholar
  42. Silva ECN, Kikuchi N (1999) Design of piezocomposite materials and piezoelectric transducers using topology optimization—part III. Arch Comput Meth Eng 6(4):305–329Google Scholar
  43. Sørensen SN, Lund E (2013) Topology and thickness optimization of laminated composites including manufacturing constraints. Struct Multidiscip Optim 48(2):249–265MathSciNetGoogle Scholar
  44. Sørensen R, Lund E (2015a) Thickness filters for gradient based multi-material and thickness optimization of laminated composite structures. Struct Multidiscip Optim 52(2):227–250Google Scholar
  45. Sørensen R, Lund E (2015b) In-plane material filters for the discrete material optimization method. Struct Multidiscip Optim 52(4):645–661MathSciNetGoogle Scholar
  46. Stegmann J, Lund E (2005) Discrete material optimization of general composite shell structures. Int J Numer Methods Eng 62(14):2009–2027zbMATHGoogle Scholar
  47. Sun HL, Chen HB, Zhang K, Zhang PQ (2008) Research on performance indices of vibration isolation system. Appl Acoust 69(9):789–795Google Scholar
  48. 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):065010Google Scholar
  49. Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MathSciNetzbMATHGoogle Scholar
  50. 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):17–34Google Scholar
  51. 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 266:205–218MathSciNetzbMATHGoogle Scholar
  52. Wang J, Mak CM (2013) An indicator for the assessment of isolation performance of transient vibration. J Vib Control 19(16):2459–2468Google Scholar
  53. 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):253Google Scholar
  54. 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 188:209–219Google Scholar
  55. Zhang X, Kang Z (2014) Topology optimization of piezoelectric layers in plates with active vibration control. J Intell Mater Syst Struct 25(6):697–712Google Scholar
  56. 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):799–814MathSciNetGoogle Scholar
  57. Zheng B, Chang CJ, Gea HC (2009) Topology optimization of energy harvesting devices using piezoelectric materials. Struct Multidiscip Optim 38(1):17–23Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringDalian University of TechnologyDalianPeople’s Republic of China
  2. 2.Department of Materials and ProductionAalborg UniversityAalborgDenmark

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