The manuscript aims to investigate the static behavior of laminated nanoplates in hygro-thermal environment. The theoretical framework is based on the Kirchhoff hypothesis for thin structures including the effect of material length scales, which is described by a nonlocal model. For this purpose, the plane stress constitutive laws for laminates are enriched by a size-dependent parameter according to the principles of strain gradient theory. The variational form of such a peculiar theoretical formulation is developed to obtain the corresponding finite element (FE) model, due to the lack of similar numerical approaches in the literature. The difficulties arisen by the presence of higher-order derivatives of the displacements are overcome by using Hermite interpolating polynomials. Conforming and nonconforming FE formulations are presented to this aim. A broad validation procedure is carried out in terms of displacement and stress analysis to verify the accuracy of the approach. The comparison is accomplished taking into account the analytical solution given by the Navier methodology for cross-ply and angle-ply simply supported plates in hygro-thermal environment. The general model allows to extend the analysis to various boundary conditions and lamination schemes.

该手稿旨在研究湿热环境下层压纳米板的静态行为。该理论框架基于基尔霍夫（Kirchhoff）假说，该假说是针对薄结构的，其中包括材料长度尺度的影响，这由非局部模型来描述。为此，根据应变梯度理论的原理，通过尺寸相关的参数来丰富层压板的平面应力本构律。由于文献中缺乏相似的数值方法，因此开发了这种特殊的理论公式的变体形式以获得相应的有限元（FE）模型。通过使用Hermite插值多项式克服了位移的高阶导数的存在所带来的困难。为此，提出了合格和不合格的FE配方。在位移和应力分析方面进行了广泛的验证程序，以验证该方法的准确性。考虑到湿热环境中交叉层和角层简单支撑板的Navier方法给出的分析解决方案，完成了比较。通用模型允许将分析扩展到各种边界条件和层压方案。