Abstract In this paper, a novel nonlocal strain gradient isogeometric model using the nonlocal strain gradient theory (NSGT) and isogeometric analysis (IGA) is developed to analyze free vibration and bending behaviors of functionally graded (FG) plates. Based on the higher-order shear deformation theory (HSDT) and NSGT, the weak form of the governing equation motion of the plates is presented. To homogenize material properties, the Mori-Tanaka scheme is used. The proposed model is capable of capturing both nonlocal effects and strain gradient effects in nanoplate structures due to adding two parameters, i.e. nonlocal and strain gradient parameters, into the elastic constants of FG materials. Thanks to those two parameters, both stiffness reduction and stiffness enhancement mechanism of FG plates are observed. The principle of virtual work is used to derive governing equations, subsequently, the natural frequencies and deflections of the FG plates are determined. Numerical results are presented to evaluate effects of the geometry, boundary condition, length-to-thickness ratio, exponential factor, nonlocal parameter and strain gradient parameter on the natural frequency and deflection of FG plates. In addition, the pure nonlocal and strain gradient models can be restored from the proposed model when taking the zero of the strain gradient and nonlocal parameters, respectively.

中文翻译：

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功能梯度板自由振动和弯曲分析的非局部应变梯度等几何模型

摘要 在本文中，使用非局部应变梯度理论（NSGT）和等几何分析（IGA）开发了一种新的非局部应变梯度等几何模型来分析功能梯度（FG）板的自由振动和弯曲行为。基于高阶剪切变形理论（HSDT）和NSGT，提出了板的控制方程运动的弱形式。为了使材料特性均质化，使用了 Mori-Tanaka 方案。由于将两个参数（即非局部和应变梯度参数）添加到 FG 材料的弹性常数中，所提出的模型能够捕获纳米板结构中的非局部效应和应变梯度效应。由于这两个参数，观察到 FG 板的刚度降低和刚度增强机制。利用虚功原理推导出控制方程，进而确定FG板的固有频率和挠度。数值结果用于评估几何形状、边界条件、长厚比、指数因子、非局部参数和应变梯度参数对 FG 板的固有频率和挠度的影响。此外，当应变梯度和非局部参数分别取零时，可以从所提出的模型中恢复纯非局部和应变梯度模型。FG板的固有频率和挠度的非局部参数和应变梯度参数。此外，当应变梯度和非局部参数分别取零时，可以从所提出的模型中恢复纯非局部和应变梯度模型。FG板的固有频率和挠度的非局部参数和应变梯度参数。此外，当应变梯度和非局部参数分别取零时，可以从所提出的模型中恢复纯非局部和应变梯度模型。