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

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

浙江理工大学建筑工程学院，杭州 310018

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(SV2020-KF-13)

详细信息

作者简介:
沈璐璐（1990—），女，副教授，博士（E-mail：lulushen@zstu.edu.cn）

蔡方圆（1998—），女，硕士生（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
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- 被引次数: 0
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
- 刊出日期: 2023-03-15

Elasticity Solutions for Cylindrical Bending of Functionally Graded Piezoelectric Material Plates

School of Civil Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, P.R.China

摘要

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。
- 压电效应 /
- Mian和Spencer板理论 /
- 柱面弯曲 /
- 弹性力学解
Abstract:
Functionally graded piezoelectric materials (FGPMs), combining the properties of functionally graded materials and piezoelectric materials, provides a new idea for multi-functional and intelligent lightweight components, and has broad application prospects in electronic devices. Based on the elastic and electric equilibrium equations, the Mian and Spencer functionally graded plate theory was extended from elastic materials to piezoelectric materials to study the cylindrical bending of FGPM plates, where the material elastic constants, piezoelectric and dielectric parameters were assumed to vary continuously and arbitrarily along the thickness direction. Accordingly, the elasticity solutions for cylindrical bending of FGPMs plates under the uniform transverse loading were obtained. Numerical examples were given to demonstrate the piezoelectric effects on the static responses of the presented FGPMs plates.
- piezoelectric effect /
- Mian and Spencer plate theory /
- cylindrical bending /
- elasticity solution

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图 1 均布荷载作用下 FGPM 板示意图

Figure 1. Schematic diagram of the FGPM plate under uniform load

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图 2 无量纲位移$\bar U $对比图

Figure 2. Comparison of dimensionless displacement $\bar U $

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图 3 无量纲挠度$ \bar W $对比图

Figure 3. Comparison of dimensionless deflection $ \bar W $

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图 4 无量纲应力对比图

Figure 4. Comparison of dimensionless stress

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图 5 7种边界条件下的无量纲挠度分布图

Figure 5. Comparison of dimensionless displacement under 7 boundary conditions

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表 1 $ z = 0 $处的无量纲位移$ \bar W $对比

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

x	0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
this paper	0	61.162	115.183	157.221	183.821	192.924	183.819	157.223	115.184	61.159	0
FEM	0	61.164	114.669	156.379	182.810	191.863	182.822	156.384	114.670	61.164	0
errors δ/%	−	0.003	0.446	0.536	0.550	0.550	0.542	0.534	0.446	0.008	−

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表 2 n=0，z=0处的无量纲位移w/h对比

Table 2. Comparison of dimensionless displacement at n=0，z=0

	x	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
ref. [22]	w/h	0.195	0.377	0.520	0.612	0.652	0.601	0.512	0.385	0.205	0
this paper	w/h	0.208	0.392	0.533	0.627	0.658	0.628	0.537	0.391	0.206	0

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表 3 n=10，z=0处的无量纲位移w/h对比

Table 3. Comparison of dimensionless displacement at n=10，z=0

	x	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
ref. [22]	w/h	0.582	1.086	1.488	1.747	1.826	1.750	1.480	1.094	0.605	0
this paper	w/h	0.633	1.192	1.618	1.905	1.997	1.907	1.632	1.187	0.627	0

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参考文献(23)

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功能梯度压电板柱面弯曲的弹性力学解

doi: 10.21656/1000-0887.430224

作者简介:
沈璐璐（1990—），女，副教授，博士（E-mail：lulushen@zstu.edu.cn）

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

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

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Elasticity Solutions for Cylindrical Bending of Functionally Graded Piezoelectric Material Plates

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目录

留言板

功能梯度压电板柱面弯曲的弹性力学解

doi: 10.21656/1000-0887.430224

作者简介: 沈璐璐（1990—），女，副教授，博士 （E-mail：lulushen@zstu.edu.cn） 蔡方圆（1998—），女，硕士生 （E-mail：13588750105@163.com） 杨博（1979—），男，教授，博士（通讯作者. E-mail：youngbo@zstu.edu.cn）

计量

出版历程

Elasticity Solutions for Cylindrical Bending of Functionally Graded Piezoelectric Material Plates

计量

出版历程

目录

作者简介:
沈璐璐（1990—），女，副教授，博士（E-mail：lulushen@zstu.edu.cn）

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

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