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

准三维功能梯度微梁的尺度效应模型及微分求积有限元

刘松正 张波 沈火明 张旭

刘松正, 张波, 沈火明, 张旭. 准三维功能梯度微梁的尺度效应模型及微分求积有限元[J]. 应用数学和力学, 2021, 42(6): 623-636. doi: 10.21656/1000-0887.410260
引用本文: 刘松正, 张波, 沈火明, 张旭. 准三维功能梯度微梁的尺度效应模型及微分求积有限元[J]. 应用数学和力学, 2021, 42(6): 623-636. doi: 10.21656/1000-0887.410260
LIU Songzheng, ZHANG Bo, SHEN Huoming, ZHANG Xu. Microbeam Model and Related Differential Quadrature Finite Elements[J]. Applied Mathematics and Mechanics, 2021, 42(6): 623-636. doi: 10.21656/1000-0887.410260
Citation: LIU Songzheng, ZHANG Bo, SHEN Huoming, ZHANG Xu. Microbeam Model and Related Differential Quadrature Finite Elements[J]. Applied Mathematics and Mechanics, 2021, 42(6): 623-636. doi: 10.21656/1000-0887.410260

准三维功能梯度微梁的尺度效应模型及微分求积有限元

doi: 10.21656/1000-0887.410260
基金项目: 

国家自然科学基金青年科学基金(11602204)

2020年度中央高校基本科研业务费基础研究培育项目(2682020ZT106)

详细信息
    作者简介:

    刘松正(1995—),男,硕士生(E-mail: 635823637@qq.com);张波(1984—),男,讲师,博士(通讯作者. E-mail: zhangbo2008@home.swjtu.edu.cn).

    通讯作者:

    张波(1984—),男,讲师,博士(通讯作者. E-mail: zhangbo2008@home.swjtu.edu.cn).

  • 中图分类号: TB383|TB34

Microbeam Model and Related Differential Quadrature Finite Elements

Funds: 

The National Natural Science Foundation of China(11602204)

  • 摘要: 基于修正的偶应力理论与四参数高阶剪切-法向伸缩变形理论,提出了一种具有尺度依赖性的准三维功能梯度微梁模型,并应用于小尺度功能梯度梁的静力弯曲和自由振动分析中.采用第二类Lagrange方程,推导了微梁的运动微分方程及边界条件.针对一般边值问题,构造了一种融合Gauss-Lobatto求积准则与微分求积准则的2节点16自由度微分求积有限元.通过对比性研究,验证了理论模型以及求解方法的有效性.最后,探究了梯度指数、内禀特征长度、几何参数及边界条件对微梁静态响应与振动特性的影响.结果表明,该文所发展的梁模型及微分求积有限元适用于研究各种长细比的功能梯度微梁的静/动力学问题,引入尺度效应会显著地改变微梁的力学特性.
  • [2]LI Z, HE Y, LEI J, et al. A standard experimental method for determining the material length scale based on modified couple stress theory[J]. International Journal of Mechanical Sciences,2018,141: 198-205.
    LAM D C C, YANG F, CHONG A C M, et al. Experiments and theory in strain gradient elasticity[J]. Journal of the Mechanics and Physics of Solids,2003, 51(8): 1477-1508.
    [3]LIU D, HE Y, TANG X, et al. Size effects in the torsion of microscale copper wires: experiment and analysis[J]. Scripta Materialia,2012,66(6): 406-409.
    [4]YANG F, CHONG A C M, LAM D C C, et al. Couple stress based strain gradient theory for elasticity[J]. International Journal of Solids and Structures,2002,39(10): 2731-2743.
    [5]ZHANG B, HE Y, LIU D, et al. An efficient size-dependent plate theory for bending, buckling and free vibration analyses of functionally graded microplates resting on elastic foundation[J]. Applied Mathematical Modelling,2015,39(13): 3814-3845.
    [6]ZHANG B, HE Y, LIU D, et al. A size-dependent third-order shear deformable plate model incorporating strain gradient effects for mechanical analysis of functionally graded circular/annular microplates[J]. Composites(Part B): Engineering,2015,79: 553-580.
    [7]LEI J, HE Y, ZHANG B, et al. A size-dependent FG micro-plate model incorporating higher-order shear and normal deformation effects based on a modified couple stress theory[J]. International Journal of Mechanical Sciences,2015,104: 8-23.
    [8]NGUYEN H X, NGUYEN T N, ABDEL-WAHAB M, et al. A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory[J]. Computer Methods in Applied Mechanics and Engineering,2017,313: 904-940.
    [9]杨子豪, 贺丹. 基于精化锯齿理论的功能梯度夹心微板静弯曲模型[J]. 计算力学学报, 2018,35(6): 757-762. (YANG Zihao, HE Dan. Static bending model of functionally graded sandwich micro-plates based on the refined zigzag theory[J]. Chinese Journal of Computational Mechanics,2018, 35(6): 757-762. (in Chinese))
    [10]KARAMANLI A, VO T P. Size dependent bending analysis of two directional functionally graded microbeams via a quasi-3D theory and finite element method[J]. Composites(Part B): Engineering,2018,144: 171-183.
    [11]周博, 郑雪瑶, 康泽天, 等. 基于修正偶应力理论的Timoshenko微梁模型和尺寸效应研究[J]. 应用数学和力学, 2019,40(12): 1321-1334. (ZHOU Bo, ZHENG Xueyao, KANG Zetian, et al. A Timoshenko micro-beam model and its size effects based on the modified couple stress theory[J]. Applied Mathematics and Mechanics,2019,40(12): 1321-1334. (in Chinese))
    [12]曹源, 雷剑. 基于正弦剪切变形理论的功能梯度材料三明治微梁的静动态特性[J]. 复合材料学报, 2020,37(1): 223-235. (CAO Yuan, LEI Jian. Static and dynamic properties of functionally graded materials sandwich microbeams based sinusoidal shear deformation theory[J]. Acta Materiae Compositae Sinica,2020,37(1): 223-235. (in Chinese))
    [13]THAI C H, FERREIRA A J M, TRAN T D, et al. A size-dependent quasi-3D isogeometric model for functionally graded graphene platelet-reinforced composite microplates based on the modified couple stress theory[J]. Composite Structures,2020,234: 111695.
    [14]CARRERA E, BRISCHETTO S, CINEFRA M, et al. Effects of thickness stretching in functionally graded plates and shells[J]. Composites Part B: Engineering,2011,42(2): 123-133.
    [15]NEVES A M A, FERREIRA A J M, CARRERA E, et al. A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates[J]. Composite Structures,2012,94(5): 1814-1825.
    [16]LEE W H, HAN S C, PARK W T. A refined higher order shear and normal deformation theory for E-, P-, and S-FGM plates on Pasternak elastic foundation[J]. Composite Structures,2015,122: 330-342.
    [17]ZHANG B, LI H, KONG L, et al. Size-dependent vibration and stability of moderately thick functionally graded micro-plates using a differential quadrature-based geometric mapping scheme[J]. Engineering Analysis With Boundary Elements,2019,108: 339-365.
    [18]ZHANG B, LI H, KONG L, et al. Coupling effects of surface energy, strain gradient, and inertia gradient on the vibration behavior of small-scale beams[J]. International Journal of Mechanical Sciences,2020,184: 105834.
    [19]ZHANG B, LI H, KONG L, et al. Size-dependent static and dynamic analysis of Reddy-type micro-beams by strain gradient differential quadrature finite element method[J]. Thin-Walled Structures,2020,148: 106496.
    [20]ZHANG B, LI H, LIU J, et al. Surface energy-enriched gradient elastic Kirchhoff plate model and a novel weak-form solution scheme[J].European Journal of Mechanics A: Solids,2020,85: 104118.
    [21]VO T P, THAI H T, NGUYEN T K, et al. A quasi-3D theory for vibration and buckling of functionally graded sandwich beams[J]. Composite Structures,2015, 119: 1-12.
  • 加载中
计量
  • 文章访问数:  642
  • HTML全文浏览量:  121
  • PDF下载量:  33
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-09-07
  • 修回日期:  2021-05-06

目录

    /

    返回文章
    返回