The current research work investigates the static, buckling, and free vibration behavior of carbon nanotube-reinforced composite (CNTRC) beam using the inverse hyperbolic shear deformation theory. This theory is based upon the shear strain shape function yielding a nonlinear distribution of transverse shear stresses and inherently satisfies the traction-free boundary conditions at the upper and lower surfaces of the beam structures omitting the requirement of the shear correction factor. The governing differential equations are developed using Hamilton's principle, and the closed-form solutions are obtained using Navier's approach. The rule of mixture is adopted to estimate the material characteristics of CNTRC beams. The four different ways of CNT’s reinforcement distribution are used such as uniform distribution, O-beam, X-beam, and V-beam for the analysis. The analytical results in terms of deflection, stresses, critical buckling load as well as natural frequencies of the CNT-reinforced composite beam are obtained for various span thickness ratios, CNT volume fractions, and CNT reinforcement distributions. The result shows that the present theory predicts the responses of the CNTRC beam quite accurately as compared to the existing theories. Some new results are also included for the benchmark solutions of the new research.

目前的研究工作利用反双曲剪切变形理论研究碳纳米管增强复合材料（CNTRC）梁的静态、屈曲和自由振动行为。该理论基于剪切应变形函数，产生横向剪切应力的非线性分布，并且本质上满足梁结构上表面和下表面的无牵引边界条件，省略了剪切修正系数的要求。控制微分方程是使用哈密尔顿原理开发的，并且使用纳维方法获得闭式解。采用混合规则来估计CNTRC梁的材料特性。采用均匀分布、O型梁、X型梁、V型梁四种不同的CNT增强体分布方式进行分析。针对不同的跨厚比、CNT 体积分数和 CNT 增强分布，获得了 CNT 增强复合梁的挠度、应力、临界屈曲载荷以及固有频率的分析结果。结果表明，与现有理论相比，本理论对 CNTRC 梁响应的预测相当准确。新研究的基准解决方案还包括一些新结果。