The structural complexity of high-tech industries is often compromised by a combination of thermal, mechanical, and geometric weaknesses. New generation materials and engineering the structure of materials are among the techniques that engineers employ to eliminate these effects. In this study, a comprehensive analysis solution is derived using Lekhnitskii’s complex variable approach with the use of general mapping functions, the concept of functionally graded materials (FGMs), and holomorphic functions in the form of Laurent series. This general solution is used for the thermoelastic analysis of perforated functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates with polygonal hole. A refined-calibrated rule of mixtures is used to approximate the material property of FG-CNTRC plates according to gradational changes in direction of thickness and available molecular dynamics simulations results. After validation of present analytical solution results with finite element analysis results and available mechanical analysis of composite plates results, stress and moment resultants due to remoting heat flux-mechanical loading is studied. The effect of FG-CNTRC material properties, heat flux condition, and four parameters affecting the shape of the polygonal holes has been investigated. During the present parametric analysis, the results clearly show that the parameters related to the FG-CNTRC material properties, flux conditions, and hole geometry each provide a reliable tool for designers to influence the stress and moment resultants to minimize undesirable stresses. This general formulation is able to calculate thermoelastic parameters (thermal and mechanical parameters, separately) for the generalized problems of the FGM plate or composite laminates with a polygonal hole.

高科技产业的结构复杂性常常受到热、机械和几何弱点的综合影响。新一代材料和材料结构工程是工程师用来消除这些影响的技术之一。在本研究中，利用 Lekhnitskii 的复变量方法，结合一般映射函数、功能梯度材料 (FGM) 的概念以及洛朗级数形式的全纯函数，得出了综合分析解决方案。该通用解决方案用于具有多边形孔的穿孔功能梯度碳纳米管增强复合材料（FG-CNTRC）板的热弹性分析。根据厚度方向的梯度变化和可用的分子动力学模拟结果，使用混合物的精细校准规则来近似 FG-CNTRC 板的材料性能。在用有限元分析结果和可用的复合板力学分析结果验证当前的解析解结果后，研究了由于远程热通量-机械载荷而产生的应力和力矩合力。研究了 FG-CNTRC 材料特性、热通量条件以及影响多边形孔形状的四个参数的影响。在目前的参数分析过程中，结果清楚地表明，与 FG-CNTRC 材料特性、通量条件和孔几何形状相关的参数均为设计人员提供了可靠的工具，以影响应力和力矩合成，以最大限度地减少不需要的应力。 该通用公式能够针对 FGM 板或具有多边形孔的复合材料层压板的一般问题计算热弹性参数（分别是热参数和机械参数）。