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Original Articles

Three-dimensional thermoelectroelastic analysis of structures with distributed piezoelectric sensors and actuators with temperature-dependent material properties

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Pages 3979-3996 | Received 28 May 2022, Accepted 31 May 2022, Published online: 14 Jun 2022

References

  • H. Allik, and T. J. R. Hughes, Finite element method for piezoelectric vibration, Int. J. Numer. Methods Eng., vol. 2, no. 2, pp. 151–157, 1970. DOI: 10.1002/nme.1620020202.
  • K. Y. Sze, L. Q. Yao, and S. Yi, A hybrid stress ANS solid-shell element and its generalization for smart structure modelling. Part II: Smart structure modelling, Int. J. Numer. Methods Eng., vol. 48, no. 4, pp. 565–582, 2000. DOI: 10.1002/(SICI)1097-0207(20000610)48:4<565::AID-NME890>3.0.CO;2-U.
  • S. Lee, N. S. Goo, H. C. Park, K. J. Yoon, and C. Cho, A nine-node assumed strain shell element for analysis of a coupled electro-mechanical system, Smart Mater. Struct., vol. 12, no. 3, pp. 355–362, 2003. DOI: 10.1088/0964-1726/12/3/306.
  • K. Y. Sze, X. M. Yang, and H. Fan, Electric assumption for piezoelectric laminate analysis, Int. J. Solids Struct., vol. 41, no. 9-10, pp. 2363–2382, 2004. DOI: 10.1016/j.ijsolstr.2003.11.018.
  • S. Zheng, X. Wang, and W. Chen, The formulation of a refined hybrid enhanced assumed strain solid shell element and its application to model smart structures containing distributed piezoelectric sensors/actuators, Smart Mater. Struct., vol. 13, no. 4, pp. N43–N50, 2004. DOI: 10.1088/0964-1726/13/4/N02.
  • X. G. Tan, and L. Vu-Quoc, Optimal solid shell element for large deformable composite structures with piezoelectric layers and active vibration control, Int. J. Numer. Methods Eng., vol. 64, no. 15, pp. 1981–2013, 2005. DOI: 10.1002/nme.1433.
  • S. Klinkel, and W. Wagner, A geometrically non-linear piezoelectric solid shell element based on a mixed multi-field variational formulation, Int. J. Numer. Methods Eng., vol. 65, no. 3, pp. 349–382, 2006. DOI: 10.1002/nme.1447.
  • G. M. Kulikov, and S. V. Plotnikova, Geometrically exact four-node piezoelectric solid-shell element, Mech. Adv. Mater. Struct., vol. 15, no. 3–4, pp. 199–207, 2008. DOI: 10.1080/15376490801907673.
  • S. Lentzen, “Nonlinearly Coupled Thermopiezoelectric Modelling and FE-Simulation of Smart Structures,” Fortschritt-Berichte VDI, Reihe 20, Nr. 419, VDI Verlag, Düsseldorf, 2009.
  • K. Schulz, S. Klinkel, and W. Wagner, A finite element formulation for piezoelectric shell structures considering geometrical and material non-linearities, Int. J. Numer. Methods Eng., vol. 87, no. 6, pp. 491–520, 2011. DOI: 10.1002/nme.3113.
  • G. M. Kulikov, and S. V. Plotnikova, Solution of a coupled problem of thermo-piezoelectricity based on a geometrically exact shell element, Mech Compos Mater., vol. 46, no. 4, pp. 349–364, 2010. DOI: 10.1007/s11029-010-9152-z.
  • G. M. Kulikov, and S. V. Plotnikova, Exact geometry piezoelectric solid-shell element based on the 7-parameter model, Mech. Adv. Mater. Struct., vol. 18, no. 2, pp. 133–146, 2011. DOI: 10.1080/15376494.2010.496067.
  • G. M. Kulikov, and S. V. Plotnikova, The use of 9-parameter shell theory for development of exact geometry 12-node quadrilateral piezoelectric laminated solid-shell elements, Mech. Adv. Mater. Struct., vol. 22, no. 6, pp. 490–502, 2015. DOI: 10.1080/15376494.2013.813096.
  • G. M. Kulikov, and S. V. Plotnikova, Exact geometry SaS solid-shell element for 3D stress analysis of FGM piezoelectric structures, Curved Layered Struct., vol. 5, no. 1, pp. 116–135, 2018. DOI: 10.1515/cls-2018-0009.
  • G. M. Kulikov, S. V. Plotnikova, and E. Carrera, Modeling and analysis of spiral actuators by exact geometry piezoelectric solid-shell elements, J. Intell. Mater. Syst. Struct., vol. 31, no. 1, pp. 53–70, 2020. DOI: 10.1177/1045389X19880014.
  • G. M. Kulikov, and S. V. Plotnikova, Solution of three-dimensional problems for thick elastic shells by the method of reference surfaces, Mech. Solids., vol. 49, no. 4, pp. 403–412, 2014. DOI: 10.3103/S0025654414040050.
  • E. Carrera, S. Brischetto, and P. Nali, Plates and Shells for Smart Structures: Classical and Advanced Theories for Modeling and Analysis. Oxford: John Wiley & Sons, 2011.
  • E. Zappino, and E. Carrera, Refined one-dimensional models for the multi-field analysis of layered smart structures, Adv. Struct. Mater., vol. 81, pp. 343–366, 2018.
  • E. Zappino, and E. Carrera, Thermo-piezo-elastic analysis of amplified piezoceramic actuators using a refined one-dimensional model, J. Intell. Mater. Syst. Struct., vol. 29, no. 17, pp. 3482–3494, 2018. DOI: 10.1177/1045389X17721026.
  • G. M. Kulikov, S. V. Plotnikova, and E. Carrera, Hybrid-mixed solid-shell element for stress analysis of laminated piezoelectric shells through higher-order theories, Adv. Struct. Mater., vol. 81, pp. 45–68, 2018.
  • G. M. Kulikov, S. V. Plotnikova, and A. O. Glebov, Assessment of nonlinear exact geometry sampling surfaces solid-shell elements and ANSYS solid elements for 3D stress analysis of piezoelectric shell structures, Int J Numer Methods Eng., vol. 121, no. 17, pp. 3795–3823, 2020. DOI: 10.1002/nme.6382.
  • G. M. Kulikov, and S. V. Plotnikova, Coupled thermoelectroelastic analysis of thick and thin laminated piezoelectric structures by exact geometry solid-shell elements based on the sampling surfaces method, Int J Numer Methods Eng., vol. 122, no. 10, pp. 2446–2477, 2021. DOI: 10.1002/nme.6627.
  • H. J. Lee, and D. A. Saravanos, The effect of temperature dependent material properties on the response of piezoelectric composite materials, J. Intel. Mater. Syst. Struct., vol. 9, no. 7, pp. 503–508, 1998. DOI: 10.1177/1045389X9800900702.
  • H. J. Lee, “Finite Element Analysis of Active and Sensory Thermopiezoelectric Composite Materials,” NASA/TM, 210892, Glenn Research Center, Cleveland, 2001.
  • M. Shariyat, Vibration and dynamic buckling control of imperfect hybrid FGM plates with temperature-dependent material properties subjected to thermo-electro-mechanical loading conditions, Compos. Struct., vol. 88, no. 2, pp. 240–252, 2009. DOI: 10.1016/j.compstruct.2008.04.003.
  • H. W. Joo, C. H. Lee, J. S. Rho, and H. K. Jung, Analysis of temperature rise for piezoelectric transformer using finite-element method, IEEE Trans. Ultrason. Ferroelect. Freq. Contr., vol. 53, pp. 1449–1457, 2006.
  • Y. J. Yang, C. C. Chen, C. W. Kuo, and C. K. Lee, Thermo-piezoelectric finite element modeling for piezoelectric transformers, Jpn. J. Appl. Phys., vol. 47, no. 4, pp. 2182–2188, 2008. DOI: 10.1143/JJAP.47.2182.
  • M. H. Babaei, and G. Akhras, Temperature-dependent response of radially polarized piezoceramic cylinders to harmonic loadings, J. Intel. Mater. Syst. Struct., vol. 22, no. 7, pp. 645–654, 2011. DOI: 10.1177/1045389X11404454.
  • G. M. Kulikov, and S. V. Plotnikova, Exact geometry SaS-based solid-shell element for coupled thermoelectroelastic analysis of smart structures with temperature-dependent material properties, Acta Mech., vol. 233, 2022. DOI: 10.1007/s00707-021-03086-2.
  • T. H. H. Pian, State-of-the-art development of hybrid/mixed finite element method, Finite Elem. Anal. Des., vol. 21, no. 1–2, pp. 5–20, 1995. DOI: 10.1016/0168-874X(95)00024-2.
  • T. H. H. Pian, and K. Sumihara, Rational approach for assumed stress finite elements, Int. J. Numer. Methods Eng., vol. 20, no. 9, pp. 1685–1695, 1984. DOI: 10.1002/nme.1620200911.
  • S. W. Lee, and T. H. H. Pian, Improvement of plate and shell finite elements by mixed formulations, Aiaa J., vol. 16, no. 1, pp. 29–34, 1978. DOI: 10.2514/3.60853.
  • G. Wempner, D. Talaslidis, and C. M. Hwang, A simple and efficient approximation of shells via finite quadrilateral elements, J. Appl. Mech., vol. 49, no. 1, pp. 115–120, 1982. DOI: 10.1115/1.3161951.
  • G. M. Kulikov, and S. V. Plotnikova, Heat conduction analysis of laminated shells by a sampling surfaces method, Mech. Res. Commun., vol. 55, pp. 59–65, 2014. DOI: 10.1016/j.mechrescom.2013.10.018.
  • G. M. Kulikov, and S. V. Plotnikova, A hybrid-mixed four-node quadrilateral plate element based on sampling surfaces method for 3D stress analysis, Int. J. Numer. Methods Eng., vol. 108, no. 1, pp. 26–54, 2016. DOI: 10.1002/nme.5201.
  • G. M. Kulikov, and S. V. Plotnikova, Hybrid-mixed ANS finite elements for stress analysis of laminated composite structures: Sampling surfaces plate formulation, Comp. Methods Appl. Mech. Eng., vol. 303, pp. 374–399, 2016. DOI: 10.1016/j.cma.2016.01.015.
  • G. M. Kulikov, A. A. Mamontov, and S. V. Plotnikova, Coupled thermoelectroelastic stress analysis of piezoelectric shells, Compos. Struct., vol. 124, pp. 65–76, 2015. DOI: 10.1016/j.compstruct.2014.12.045.
  • J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed. Boca Raton, FL: CRC Press, 2004.
  • S. S. Vel, and R. C. Batra, Generalized plane strain thermopiezoelectric analysis of multilayered plates, J. Therm. Stresses vol. 26, no. 4, pp. 353–377, 2003. DOI: 10.1080/713855902.
  • S. N. Kallaev, G. G. Gadjiev, I. K. Kamilov, S. A. Sadykov, Z. M. Omarov, and R. M. Ferzilaev, Thermal conductivity and thermal expansion of ceramics PZT in the region of phase transition, Integr. Ferroelectr., vol. 72, no. 1, pp. 23–26, 2005. DOI: 10.1080/10584580500311646.
  • L. Tang, and W. Cao, Characterization of full set material constants and their temperature dependence for piezoelectric materials using resonant ultrasound spectroscopy, J. Vis. Exp., vol. 110, pp. 53461, 2016.
  • S. S. Vel, and R. C. Batra, Cylindrical bending of laminated plates with distributed and segmented piezoelectric actuators/sensors, Aiaa J., vol. 38, no. 5, pp. 857–867, 2000. DOI: 10.2514/3.14489.
  • S. Kapuria, S. Sengupta, and P. C. Dumir, Three-dimensional solution for a hybrid cylindrical shell under axisymmetric thermoelectric load, Arc. Appl. Mech., vol. 67, no. 5, pp. 320–330, 1997. DOI: 10.1007/s004190050120.
  • I. M. Daniel, and O. Ishai, Engineering Mechanics of Composite Materials, 2nd ed. New York: Oxford University Press, 2006.
  • R. Joven, R. Das, A. Ahmed, P. Roozbehjavan, and B. Minaie, Thermal properties of carbon fiber-epoxy composites with different fabric weaves, in SAMPE Conference, 44th ISTC, Charleston, SC, 2012.
  • G. M. Kulikov, and S. V. Plotnikova, Controlling the shape of laminated composite plates with piezoelectric patches under thermal loading based on the reference surface method, Mech. Solids., vol. 56, no. 5, pp. 646–660, 2021. DOI: 10.3103/S0025654421050137.
  • ANSYS 2019 R2 release, ANSYS Inc, Canonsburg, PA, 2019.

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