In this study, the thermal buckling and postbuckling of functionally graded (FG) nanocomposite annular sector plates reinforced by carbon nanotubes (CNTs) are numerically analyzed. The effective material properties of FG nanocomposite are temperature-dependent (TD) and evaluated via the modified micromechanical method and rule of mixture. Based on the higher-order shear deformation theory (HSDT) and using the principle of virtual work and variational differential quadrature (VDQ) approach, the unified weak form of discretized nonlinear governing equilibrium equations is derived. Then, by using the linear part of equations and solving the derived eigenvalue problem, the critical temperature rise and associated mode shapes are obtained, which are used as the initial guess in solving the nonlinear thermal postbuckling problem. The pseudo-arc-length method and an iterative solver are employed to obtain the nonlinear thermal postbuckling equilibrium path of the FG nanocomposite annular sector plates. The influences of geometrical parameters, boundary conditions (BCs), CNT volume fraction, and CNT distribution pattern on the critical temperature rise and thermal postbuckling behavior of the FG nanocomposite annular sector plates are evaluated and discussed. Also, comparisons are made between the results considering the TD and temperature-independent (TID) properties. It is demonstrated that for higher values of sector angle, the effect of sector angle on the critical temperature rise and thermal postbuckling path is negligible. Moreover, by increasing the sector angle, the effect of BCs of straight edges vanishes, and the critical temperature rise and thermal postbuckling curves of for BCs of CSCS and SCSC approach those for CCCC and SSSS ones.

中文翻译：

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碳纳米管增强的温度相关功能梯度纳米复合环形扇形板的热后屈曲

在这项研究中，数值分析了由碳纳米管 (CNT) 增强的功能梯度 (FG) 纳米复合环形扇形板的热屈曲和后屈曲。FG 纳米复合材料的有效材料性能与温度相关 (TD)，并通过改进的微机械方法和混合规则进行评估。基于高阶剪切变形理论(HSDT)，利用虚功原理和变分求积(VDQ)方法，推导了离散非线性控制平衡方程的统一弱形式。然后，利用方程的线性部分，求解导出的特征值问题，得到临界温升和相关的振型，作为求解非线性热后屈曲问题的初始猜测值。采用拟弧长法和迭代求解器获得了FG纳米复合环形扇形板的非线性热后屈曲平衡路径。评估和讨论了几何参数、边界条件 (BCs)、CNT 体积分数和 CNT 分布模式对 FG 纳米复合环形扇形板的临界温升和热后屈曲行为的影响。此外，还对考虑到 TD 和温度无关 (TID) 特性的结果进行了比较。结果表明，对于较高的扇形角值，扇形角对临界温升和热后屈曲路径的影响可以忽略不计。此外，通过增加扇形角，直边的 BC 的影响消失了，