In this paper, the size-dependent analysis of geometrically imperfect porous functionally graded (FG) nanoplates is studied by an isogeometric approach based on a new refined plate theory. Simultaneous effects of initial geometric imperfection and porosity on the natural frequency and deflection of the FG nanoplates are investigated. The initial geometric imperfection is considered as an initial curvature and modeled by an analytical function in the governing equations of the nanoplate. Material properties of porous FG nanoplate are defined by a modified power-law function, and two types of distribution for porosity are used. A four-variable refined plate theory with a new polynomial shape function is proposed. Based on Hamilton’s principle, a weak form of static and free vibration problem for nonlocal plate is derived. The discrete system of equations is solved by an isogeometric approach based on NURBS basis functions, and the accuracy of the present study is verified by comparing the results with solutions given in published papers. Present results indicate the importance of porosity parameter, porosity distributions, nonlocal parameter, material index, plate geometrical parameters, and specially imperfection amplitude on the static and free vibration behavior of FG nanoplates.

在本文中，基于等精度几何方法，基于一种新的改进的板理论，研究了几何不完美的多孔功能梯度（FG）纳米板的尺寸依赖性分析。研究了初始几何缺陷和孔隙率对FG纳米板的固有频率和挠度的同时影响。初始几何缺陷被视为初始曲率，并通过纳米板的控制方程中的解析函数进行建模。多孔FG纳米板的材料性能由修正的幂律函数定义，并使用两种类型的孔隙率分布。提出了具有新的多项式形状函数的四变量精制板理论。根据汉密尔顿原理，推导了非局部板的静，自由振动问题的弱形式。离散方程组通过基于NURBS基函数的等几何方法求解，并且通过将结果与已发表论文中给出的解决方案进行比较，验证了本研究的准确性。目前的结果表明，孔隙率参数，孔隙率分布，非局部参数，材料指数，板的几何参数，特别是缺陷振幅对FG纳米板的静态和自由振动行为的重要性。