Abstract

This paper investigates the bending, buckling and free vibration behaviors of porous functionally graded curved nanobeams with different boundary conditions via a nonlocal strain gradient theory. The stresses are dependent on the strain gradients according to the nonlocal strain gradient theory. This theory contains both nonlocal and material length-scale parameters. The three-variable sinusoidal shear deformation beam theory is used to describe the displacement field and do not need any shear correction factor. The nonlocal strain gradient theory is employed to capture both hardening and softening stiffness influences on the present nanobeams. The material properties for the present porous functionally graded curved nanobeams are varying through-the-thickness due to the power law model. Hamilton’s principle is applied to obtain the governing equations of porous functionally graded curved nanobeams. Numerical results are validated by comparison with the corresponding ones of perfect functionally graded curved nanobeams in the literature. The effects of the strain gradient parameter, opening angle, nonlocal parameter, boundary conditions, power-law index, porosity factor on the bending, buckling and free vibration frequencies of perfect and porous functionally graded curved nanobeams are all investigated.

中文翻译：

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不同边界条件下多孔功能梯度弯曲纳米束的非局部应变梯度理论

摘要

本文通过非局部应变梯度理论研究了具有不同边界条件的多孔功能梯度弯曲纳米束的弯曲，屈曲和自由振动行为。根据非局部应变梯度理论，应力取决于应变梯度。该理论包含非局部和材料长度尺度参数。三变量正弦剪切变形梁理论用于描述位移场，不需要任何剪切​​校正因子。非局部应变梯度理论用于捕获对当前纳米束的硬化和软化刚度影响。由于幂律模型，本发明的多孔功能梯度弯曲纳米束的材料性能在整个厚度范围内变化。利用汉密尔顿原理获得多孔的功能梯度梯度纳米束的控制方程。通过与文献中功能完善的梯度弯曲纳米束的相应结果进行比较，验证了数值结果。研究了应变梯度参数，开度角，非局部参数，边界条件，幂律指数，孔隙率对完善和多孔的功能梯度弯曲纳米束的弯曲，屈曲和自由振动频率的影响。