力学与实践 ›› 2018, Vol. 40 ›› Issue (2): 167-172.DOI: 10.6052/1000-0879-17-361

• 应用研究 • 上一篇    下一篇

非局部应变梯度理论下纳米梁的力学特性研究1)

张英蓉, 沈火明2), 张波   

  1. 西南交通大学力学与工程学院,成都610031;
    应用力学与结构安全四川省重点实验室,成都610031;
  • 收稿日期:2017-10-25 修回日期:2017-11-13 出版日期:2018-04-15 发布日期:2018-05-18
  • 通讯作者: 2) 沈火明,教授. E-mail: hmshen123@126.com
  • 基金资助:
    1) 国家自然科学基金资助项目(11672252,11602204).

INVESTIGATIONS ON THE MECHANICAL CHARACTERISTICS OF NANOBEAMS BASED ON THE NONLOCAL STRAIN GRADIENT THEORY1)

ZHANG Yingrong, SHEN Huoming2), ZHANG Bo   

  1. School of Mechanics & Engineering, Southwest Jiaotong University, Chengdu 610031, China;
    Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, Chengdu 610031, China;
  • Received:2017-10-25 Revised:2017-11-13 Online:2018-04-15 Published:2018-05-18

摘要: 基于非局部应变梯度理论,建立了一种具有尺度效应的高阶剪切变形纳米梁的力学模型. 其中,考虑了应变场和一阶应变梯度场下的非局部效应. 采用哈密顿原理推导了纳米梁的控制方程和边界条件,并给出了简支边界条件下静弯曲、自由振动和线性屈曲问题的纳维级数解. 数值结果表明,非局部效应对梁的刚度产生软化作用,应变梯度效应对纳米梁的刚度产生硬化作用,梁的刚度整体呈现软化还是硬化效应依赖于非局部参数与材料特征尺度的比值. 梁的厚度与材料特征尺度越接近,非局部应变梯度理论与经典弹性理论所预测结果之间的差异越显著.

关键词: 非局部应变梯度理论|尺度效应|高阶剪切变形|纳米梁

Abstract: A size-dependent mechanical model of nanobeam is built within the framework of the nonlocal strain gradient theory. The present model considers the nonlocal effects of the strain field and first gradient strain field, as well as the high-order shear deformation effect. Governing equations and boundary conditions are derived simultaneously by using Hamilton’s principle. The Navier-type solutions are developed for nanobeams with simply-supported boundary conditions. Parametric studies are performed to exhibit the static bending, free vibration and linear buckling behaviors of nanobeams with different groups of geometrical and material parameters. It is found that the non-local effect produces a softening effect on the stiffness of the beam while the strain gradient effect produces a hardening effect, the stiffness of nanobeams is significantly dependent on the ratio between the nonlocal parameter and strain gradient parameter. In addition, the stiffness-hardening or stiffness-softing effects become increasingly significant as the thickness is close to the material characteristic and can be negligible when the thickness is sufficient large.

Key words: nonlocal strain gradient theory|size effect|high-order shear deformation|nanobeam

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