In this work we investigate the buckling response of sandwich plates with a polymeric core and two face sheets reinforced by carbon nanotubes (CNTs). The problem is tackled analytically by means of a higher-order sandwich plate theory, where the face sheets are modeled according to a classical plate theory and modified strain gradient theory with temperature-dependent and moisture-dependent material properties. A Mori–Tanaka method is applied to determine the mechanical properties associated with the face sheets, while considering the agglomeration effect of CNTs. The governing equations of the problem are derived from the Hamilton’s principle, whose solutions are recovered by means of a Navier–Stokes method. A thorough sensitivity study of the structural response to different parameters includes the agglomeration and volume fraction of CNTs, the material length scale parameter, the side and aspect ratios, together with the temperature variation and humidity conditions. The sandwich plates are assumed to be immersed within an orthotropic Pasternak foundation, whose normal and shear moduli can affect the overall buckling response of the structure. Numerical experiments show that sandwich plates with nanocomposite face sheets, resting on orthotropic elastic foundations, feature an increased stiffness, where the proposed formulation yields accurate results, due to the possibility of considering the variation in temperature, humidity and agglomeration of the reinforcing CNTs within the solution.

在这项工作中，我们研究了具有聚合物芯和两块由碳纳米管（CNT）增强的面板的夹心板的屈曲响应。该问题是通过高阶夹心板理论来解决的，该面板根据经典的板理论和修正的应变梯度理论对面板进行建模，并具有与温度和湿度有关的材料特性。在考虑CNT的团聚作用的同时，采用了Mori–Tanaka方法来确定与面板相关的机械性能。该问题的控制方程式是从汉密尔顿原理导出的，该方法的求解可通过Navier–Stokes方法进行恢复。对结构对不同参数的响应的彻底敏感性研究包括CNT的团聚和体积分数，材料长度比例参数，侧面和长宽比以及温度变化和湿度条件。假定夹层板浸入正交各向异性的Pasternak基础内，其法向和剪切模量会影响结构的整体屈曲响应。数值实验表明，具有纳米复合材料面板的三明治板位于正交各向异性弹性基础上，具有增加的刚度，由于考虑到温度，湿度和增强碳纳米管内附聚的变化，建议的配方可产生准确的结果。解。假定夹层板浸入正交各向异性的Pasternak基础内，其法向和剪切模量会影响结构的整体屈曲响应。数值实验表明，具有纳米复合材料面板的三明治板位于正交各向异性弹性基础上，具有增加的刚度，由于考虑到温度，湿度和增强碳纳米管内附聚的变化，建议的配方可产生准确的结果。解。假定夹层板浸入正交各向异性的Pasternak基础内，其法向和剪切模量会影响结构的整体屈曲响应。数值实验表明，具有纳米复合材料面板的三明治板位于正交各向异性弹性基础上，具有增加的刚度，由于考虑到温度，湿度和增强碳纳米管内附聚的变化，建议的配方可产生准确的结果。解。