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Static response of functionally graded piezoelectric-piezomagnetic hollow cylinder/spherical shells with axial/spherical symmetry

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Abstract

The magneto-electro-elastic coupling static problem for a functionally graded piezoelectric-piezomagnetic (FGPEPM) cylinder/spherical shell is studied for various axial/spherical symmetric loads. On the basis of unified basic equations with geometric parameters and the material assumption of exponential inhomogeneous properties, the analytical solutions for the physical quantities of displacement, stress, electric potential, and magnetic potential of the FGPEPM hollow cylinder/spherical shell are obtained. In the numerical discussions, the static response of the FGPEPM cylinder/spherical shell is numerically solved under mechanical load on the inner surface or given an electric/magnetic potential difference between the inner and outer surfaces when the material on the inner surface is assumed to be BaTiO3-CoFeO4. The distribution of radial and circumferential stress and the electric and magnetic potentials under different functionally graded (FG) parameters are presented. The influence of FG parameters on the positive (converse) piezoelectric, positive (converse) piezomagnetic, and positive (converse) magnetoelectric potentials is discussed in detail.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China [Grant No. 11802225] and the Natural Science Basic Research Plan in the Shaanxi Province of China [Program No. 2019JQ-261].

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Authors and Affiliations

  1. School of Civil Engineering and Institute of Mechanics and Technology, Xi’an University of Architecture and Technology, Xi’an, Shaanxi, 710055, China

    Shi Pengpeng & Hao Shuai

  2. School of Mathematics and Statistics, Ningxia University, Yinchuan, Ningxia, 750021, China

    Shi Pengpeng & Xie Jun

Authors
  1. Shi Pengpeng
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  2. Xie Jun
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  3. Hao Shuai
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Corresponding author

Correspondence to Shi Pengpeng.

Additional information

Recommended by Editor Seungjae Min

Pengpeng Shi is a Professor in the School of Civil Engineering, Xi’an University of Architecture and Technology. He obtained his Ph.D. degree in Mechano-Electronic Engineering at Xidian University, Shaanxi, China, 2017. His research interests include elasticity and fracture mechanics of multifield coupling materials, magnetic nondestructive testing technique for ferromagnetic materials, and mathematical physics methods involved in mechanic analysis.

Jun Xie received his B.S. degree from the School of Mathematics and Statistics at the Ningxia University, Ningxia, China, in 2018. He is currently working toward his Ph.D. in the School of Mathematics and Statistics, Ningxia University, Ningxia, China. His research interests include the application of complex analysis in mechanics and the mechanics of multifield coupling materials.

Shuai Hao received her M.S. degree in Structural Engineering from the University of Manchester, UK, in 2017. She is currently working toward her Ph.D. in Disaster Prevention and Mitigation Engineering at Xi’an University of Architecture and Technology, Shaanxi, China. Her research interests include magnetic nondestructive testing technique for ferromagnetic materials and fracture/fatigue mechanics.

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Pengpeng, S., Jun, X. & Shuai, H. Static response of functionally graded piezoelectric-piezomagnetic hollow cylinder/spherical shells with axial/spherical symmetry. J Mech Sci Technol 35, 1583–1596 (2021). https://doi.org/10.1007/s12206-021-0322-9

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  • DOI: https://doi.org/10.1007/s12206-021-0322-9

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