The paper presents a finite element method to investigate the critical buckling loads and the natural frequencies of laminated Kirchhoff plates including the nonlocal strain gradient effect, which could have considerably consequences at the nanoscale. With respect to the existing literature, the proposed numerical methodology is developed to deal with general stacking sequences of orthotropic layers with arbitrary orientations and various boundary conditions. The resulting membrane-bending coupling is emphasized in the formulation, which requires to study the whole set of partial differential equations. The membrane and bending degrees of freedom are all approximated by means of Hermite interpolating functions with higher-order continuity requirements. To this aim, regular rectangular finite elements based on conforming (C) and nonconforming (NC) approaches are used. A wide validation procedure is carried out to prove the effectiveness of the proposed formulation. A set of new results is presented for general mechanical configurations with arbitrary restraints.

本文提出了一种有限元方法来研究层压基尔霍夫板的临界屈曲载荷和自然频率，包括非局部应变梯度效应，这可能在纳米尺度上产生相当大的影响。相对于现有文献，提出的数值方法被开发用于处理具有任意方向和各种边界条件的正交各向异性层的一般堆叠序列。公式中强调了由此产生的膜弯曲耦合，这需要研究整套偏微分方程。膜自由度和弯曲自由度均通过具有高阶连续性要求的 Hermite 插值函数近似。为了这个目标，使用基于符合 (C) 和非符合 (NC) 方法的规则矩形有限元。进行了广泛的验证程序以证明所提出的配方的有效性。为具有任意约束的一般机械配置提供了一组新结果。