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功能梯度压电板柱面弯曲的弹性力学解

沈璐璐 蔡方圆 杨博

沈璐璐,蔡方圆,杨博. 功能梯度压电板柱面弯曲的弹性力学解 [J]. 应用数学和力学,2022,43(X):1-10 doi: 10.21656/1000-0887.430224
引用本文: 沈璐璐,蔡方圆,杨博. 功能梯度压电板柱面弯曲的弹性力学解 [J]. 应用数学和力学,2022,43(X):1-10 doi: 10.21656/1000-0887.430224
SHEN Lulu, CAI Fangyuan, YANG Bo. Elasticity Solutions for Cylindrical Bending of Functionally Graded Piezoelectric Plates[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.430224
Citation: SHEN Lulu, CAI Fangyuan, YANG Bo. Elasticity Solutions for Cylindrical Bending of Functionally Graded Piezoelectric Plates[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.430224

功能梯度压电板柱面弯曲的弹性力学解

doi: 10.21656/1000-0887.430224
基金项目: 国家自然科学基金(11872336);机械结构强度与振动国家重点实验室开放课题项目(SV2020-KF-13)
详细信息
    作者简介:

    沈璐璐(1990—),女,讲师,博士 (E-mail:lulushen@zstu.edu.cn

    蔡方圆(1998—),女,硕士研究生 (E-mail:13588750105@163.com

    杨博(1979—),男,教授,博士(通讯作者. E-mail:youngbo@zstu.edu.cn

  • 中图分类号: O343.1

Elasticity Solutions for Cylindrical Bending of Functionally Graded Piezoelectric Plates

  • 摘要: 功能梯度压电材料(FGPM)同时兼具功能梯度材料和压电材料特性,可为多功能或智能化轻质结构设计提供支撑,在诸多领域有着广泛的应用前景。将Mian和Spencer功能梯度板理论由功能梯度弹性材料推广到功能梯度压电材料,解析研究了FGPM板的柱面弯曲问题,其中,材料弹性常数、压电和介电参数沿板厚方向可以任意连续变化。最终,给出了FGPM板受横向均布荷载作用下柱面弯曲问题的弹性力学解。通过算例分析,重点讨论了压电效应对FGPM板静力响应的影响。
  • 图  1  均布荷载作用下 FGPM 板示意图

    Figure  1.  Schematic diagram of FGPM plate under uniform load

    图  2  无量纲位移$\overline U $对比图

    Figure  2.  Dimensionless displacement $\overline U $comparison

    图  3  无量纲挠度$ \overline W $对比图

    Figure  3.  Dimensionless deflection $ \overline W $ comparison

    图  4  无量纲应力对比图

    Figure  4.  Dimensionless stress comparison

    图  5  7种边界条件下的无量纲挠度分布图

    Figure  5.  Dimensionless displacement under seven boundary condition

    表  1  $ z = 0 $处无量纲位移$ \bar W $对比

    Table  1.   Comparison dimensionless displacement $\bar W $ at $ z = 0 $

    x00.10.20.30.40.50.60.70.80.91.0
    this paper061.162115.183157.221183.821192.924183.819157.223115.18461.1590
    FEM061.16411.669156.379182.810191.863182.822156.384114.67061.1640
    errors(δ/%)0.0030.4460.5360.5500.5500.5420.5340.4460.008
    下载: 导出CSV

    表  2  n=0,z=0处无量纲位移w/h对比

    Table  2.   Dimensionless displacement comparison at n=0,z=0

    x00.10.20.30.40.50.60.70.80.91.0
    ref. [22]w/h00.1950.3770.5200.6120.6520.6010.5120.3850.2050
    this paperw/h00.2080.3920.5330.6270.6580.6280.5370.3910.2060
    下载: 导出CSV

    表  3  n=10,z=0处无量纲位移w/h对比

    Table  3.   Dimensionless displacement comparison at n=10,z=0

    x00.10.20.30.40.50.60.70.80.91.0
    ref. [22] w/h00.5821.0861.4881.7471.8261.7501.4801.0940.6050
    this paperw/h00.6331.1921.6181.9051.9971.9071.6321.1870.6270
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-07-06
  • 录用日期:  2022-09-29
  • 修回日期:  2022-09-29
  • 网络出版日期:  2022-10-21

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