留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于偶应力理论的压电材料轴对称接触问题

吕鑫 柯燎亮 苏洁

吕鑫, 柯燎亮, 苏洁. 基于偶应力理论的压电材料轴对称接触问题[J]. 应用数学和力学, 2024, 45(10): 1268-1278. doi: 10.21656/1000-0887.450190
引用本文: 吕鑫, 柯燎亮, 苏洁. 基于偶应力理论的压电材料轴对称接触问题[J]. 应用数学和力学, 2024, 45(10): 1268-1278. doi: 10.21656/1000-0887.450190
Lü Xin, KE Liaoliang, SU Jie. An Axisymmetric Contact Problem of Piezoelectric Materials Based on the Couple Stress Theory[J]. Applied Mathematics and Mechanics, 2024, 45(10): 1268-1278. doi: 10.21656/1000-0887.450190
Citation: Lü Xin, KE Liaoliang, SU Jie. An Axisymmetric Contact Problem of Piezoelectric Materials Based on the Couple Stress Theory[J]. Applied Mathematics and Mechanics, 2024, 45(10): 1268-1278. doi: 10.21656/1000-0887.450190

基于偶应力理论的压电材料轴对称接触问题

doi: 10.21656/1000-0887.450190
基金项目: 

12021002)

国家自然科学基金(12332006

详细信息
    作者简介:

    吕鑫(1993—),女,博士生(E-mail: lvxin@tju.edu.cn);柯燎亮(1979—),男,教授,博士(通讯作者. E-mail: llke@tju.edu.cn);苏洁(1988—),女,副教授,博士(E-mail: jiesu@tju.edu.cn).

    通讯作者:

    柯燎亮(1979—),男,教授,博士(通讯作者. E-mail: llke@tju.edu.cn).

  • 中图分类号: O34

An Axisymmetric Contact Problem of Piezoelectric Materials Based on the Couple Stress Theory

Funds: 

12021002)

The National Science Foundation of China(12332006

  • 摘要: 基于偶应力理论,研究了刚性绝缘球压头与横观各向同性压电半空间尺度依赖的轴对称接触问题.利用Hankel积分变换和积分最小二乘法,获得了接触压力.讨论了特征材料长度对接触压力分布、接触半径和压痕深度的影响.结果表明,基于偶应力理论获得的接触压力结果明显大于经典结果.
  • [2]NIX W D, GAO H. Indentation size effects in crystalline materials: a law for strain gradient plasticity[J].Journal of the Mechanics and Physics of Solids,1998,46(3): 411-425.
    STELMASHENKO N A, WALLS M G, BROWN L M, et al. Microindentations on W and Mo oriented single crystals: an STM study[J].Acta Metallurgica et Materialia,1993,41(10): 2855-2865.
    [3]MILLER R E, SHENOY V B. Size-dependent elastic properties of nanosized structural elements[J].Nanotechnology,2000,11(3): 139-147.
    [4]ZISIS T, GOURGIOTIS P A, BAXEVANAKIS K P, et al. Some basic contact problems in couple stress elasticity[J].International Journal of Solids and Structures,2014,51(11/12): 2084-2095.
    [5]GOURGIOTIS P, ZISIS T. Two-dimensional indentation of microstructured solids characterized by couple-stress elasticity[J].The Journal of Strain Analysis for Engineering Design,2016,51(4): 318-331.
    [6]ZISIS T. Anti-plane loading of microstructured materials in the context of couple stress theory of elasticity: half-planes and layers[J].Archive of Applied Mechanics,2018,88(1): 97-110.
    [7]ZISIS T. Burmister’s problem extended to a microstructuredlayer[J].Journal of Mechanics of Materials and Structures,2018,13(2): 203-223.
    [8]GOURGIOTIS P A, ZISIS T, GIANNAKOPOULOS A E, et al. The Hertz contact problem in couple-stress elasticity[J].International Journal of Solids and Structures,2019,168: 228-237.
    [9]KARURIYA A N, BHANDAKKAR T K. Plane strain indentation on finite thickness bonded layer in couple stress elasticity[J].International Journal of Solids and Structures,2017,108: 275-288.br> [10]SONG H X, KE L L, WANG Y S. Sliding frictional contact analysis of an elastic solid with couple stresses[J].International Journal of Mechanical Sciences,2017,133: 804-816.
    [11]SONG H X, KE L, WANG Y, et al. Two-dimensional frictionless contact of a coated half-plane based on couple stress theory[J].International Journal of Applied Mechanics,2018,10(5): 1850049.
    [12]WANG Y, SHEN H, ZHANG X, et al. Semi-analytical study of microscopic two-dimensional partial slip contact problem within the framework of couple stress elasticity: cylindrical indenter[J].International Journal of Solids and Structures,2018,138: 76-86.
    [13]MEZ I, EL-BORGI S. Sliding frictional contact problem of a layer indented by a rigid punch in couple stress elasticity[J].Mathematics and Mechanics of Solids,2023,28(3): 730-747.
    [14]NABHANI M, EL KHLIFI M, GBEHE O S T, et al. Coupled couple stress and surface roughness effects on elasto-hydrodynamic contact[J].Lubrication Science,2014,26(4): 251-271.
    [15]WANG Y X, ZHANG X, SHEN H, et al. Three-dimensional contact analysis with couple stress elasticity[J].International Journal of Mechanical Sciences,2019,153: 369-379.
    [16]WANG Y X, ZHANG X, SHEN H, et al. Couple stress-based 3D contact of elastic films[J].International Journal of Solids and Structures,2020,191: 449-463.
    [17]LI P X, LIU T J. Axisymmetric adhesive contact of multi-layer couple-stress elastic structures involving graded nanostructured materials[J].Applied Mathematical Modelling,2022,111: 501-520.
    [18]ZHOU Y T, TIAN X J, DING S H. Microstructure size-dependent contact behavior of a thermoelectric film bonded to an elastic substrate with couple stress theory[J].International Journal of Solids and Structures,2022,256: 111982.
    [19]LU R, LI M H, YANG Y, et al. Accurate extraction of large electromechanical coupling in piezoelectric MEMS resonators[J].Journal of Microelectromechanical Systems,2019,28(2): 209-218.
    [20]WANG Z L, SONG J. Piezoelectric nanogenerators based on zinc oxide nanowire arrays[J].Science,2006,312(5771): 242-246.
    [21]MIRZAEI A, LEE J H, MAJHI S M, et al. Resistive gas sensors based on metal-oxide nanowires[J].Journal of Applied Physics,2019,126(24): 241102.
    [22]SAHU S A, SINGHAL A, CHAUDHARY S. Surface wave propagation in functionally graded piezoelectric material: an analytical solution[J].Journal of Intelligent Material Systems and Structures,2018,29(3): 423-437.
    [23]LI Y S, PAN E. Static bending and free vibration of a functionally graded piezoelectric microplate based on the modified couple-stress theory[J].International Journal of Engineering Science,2015,97: 40-59.
    [24]RAZAVI H, BABADI A F, BENI Y T. Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory[J].Composite Structures,2017,160: 1299-1309.
    [25]WANG X, PAN E, FENG W J. Anti-plane Green’s functions and cracks for piezoelectric material with couple stress and electric field gradient effects[J].European Journal of Mechanics A: Solids,2008,27(3): 478-486.
    [26]SUN Y Y, SU J, SONG H X, et al. The size-dependent frictionless contact of piezoelectric materials[J].International Journal of Mechanical Sciences,2024,261: 108685.
    [27]KE L L, YANG J, KITIPORNCHAI S, et al. Electro-mechanical frictionless contact behavior of a functionally graded piezoelectric layered half-plane under a rigid punch[J].International Journal of Solids and Structures,2008,45(11/12): 3313-3333.
    [28]SU J, KE L L, WANG Y S. Axisymmetric frictionless contact of a functionally graded piezoelectric layered half-space under a conducting punch[J].International Journal of Solids and Structures,2016,90: 45-59.
    [29]CHEN W T, ENGEL P A. Impact and contact stress analysis in multilayer media[J].International Journal of Solids and Structures,1972,8(11): 1257-1281.
    [30]O’SULLIVAN T C, KING R B. Sliding contact stress field due to a spherical indenter on a layered elastic half-space[J].Journal of Tribology,1988,110(2): 235-240.
    [31]LV X, KE L L, SU J, et al. Axisymmetric contact vibration analysis of a rigid spherical punch on a piezoelectric half-space[J].International Journal of Solids and Structures,2021,210: 224-236.
    [32]WANG G F, YU S W, FENG X Q. A piezoelectric constitutive theory with rotation gradient effects[J].European Journal of Mechanics A: Solids,2004,23(3): 455-466.
    [33]MINDLIN R D. Influence of couple-stresses on stress concentrations[J].Experimental Mechanics,1963,3(1): 1-7.
    [34]LIU C, YU J, ZHANG B, et al. Reflection and transmission of elastic waves in the multilayered orthotropic couple-stressed plates sandwiched between two elastic half-spaces[J].Applied Mathematical Modelling,2019,75: 52-72.
  • 加载中
计量
  • 文章访问数:  81
  • HTML全文浏览量:  17
  • PDF下载量:  27
  • 被引次数: 0
出版历程
  • 收稿日期:  2024-07-01
  • 修回日期:  2024-08-13
  • 网络出版日期:  2024-10-31
  • 刊出日期:  2024-10-01

目录

    /

    返回文章
    返回