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A novel size-dependent nonlocal strain gradient isogeometric model for functionally graded carbon nanotube-reinforced composite nanoplates
Engineering with Computers ( IF 8.7 ) Pub Date : 2021-03-12 , DOI: 10.1007/s00366-021-01353-3
P. Phung-Van , Chien H. Thai

The paper presents a novel nonlocal strain gradient isogeometric model for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates. To observe the length scale and size-dependency effects of nanostructures, the nonlocal strain gradient theory (NSGT) is considered. The present model is efficient to capture both nonlocal effects and strain gradient effects in nanoplate structures. In addition, the material properties of the FG-CNTRC are assumed to be graded in the plate thickness direction. Based on the higher order shear deformation theory (HSDT), the weak form of the governing equations of motion of the nanoplates is presented using the principle of virtual work. Afterward, the natural frequency and deflection of the nanoplates are made out of isogeometric analysis (IGA). Thanks to higher order derivatives and continuity of NURBS basic function, IGA is suitable for the weak form of NSGT which requires at least the third-order derivatives in approximate formulations. Effects of nonlocal parameter, strain gradient parameter, carbon nanotube (CNT) volume fraction, distributions of CNTs and length-to-thickness ratios on deflection and natural frequency of the nanoplates are examined and discussed in detail. Numerical results are developed to show the phenomenon of stiffness-softening and stiffness-hardening mechanisms of the present model.



中文翻译:

功能梯度碳纳米管增强复合纳米板的新型尺寸依赖的非局部应变梯度等几何模型

本文提出了一种功能梯度碳纳米管增强复合材料(FG-CNTRC)纳米板的新型非局部应变梯度等几何模型。为了观察纳米结构的长度尺度和尺寸依赖性效应,考虑了非局部应变梯度理论(NSGT)。本模型有效地捕获了纳米板结构中的非局部效应和应变梯度效应。另外,假定FG-CNTRC的材料性能在板厚度方向上是渐变的。基于高阶剪切变形理论(HSDT),利用虚功原理给出了纳米板运动控制方程的弱形式。然后,通过等几何分析(IGA)确定纳米板的固有频率和挠度。由于高阶导数和NURBS基本功能的连续性,IGA适合于NSGT的弱形式,该形式至少需要近似公式中的三阶导数。研究并讨论了非局部参数,应变梯度参数,碳纳米管(CNT)的体积分数,碳纳米管的分布以及长厚比对纳米板的挠度和固有频率的影响。数值结果表明了本模型的刚度软化和刚度硬化机理。研究并详细讨论了碳纳米管的分布以及长厚比对纳米板的挠度和固有频率的影响。数值结果表明了本模型的刚度软化和刚度硬化机理。研究并详细讨论了碳纳米管的分布以及长厚比对纳米板的挠度和固有频率的影响。数值结果表明了本模型的刚度软化和刚度硬化机理。

更新日期:2021-03-12
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