In this paper, a high-order cylindrical beam model, where the shear deformation is taken into account, will be used to analyze the buckling behaviors of the functionally graded cylindrical beams with radially and axially varying material inhomogeneities. The coupled governing equations for buckling of a cylindrical beam under axial compression are derived, which can be translated into a single differential equation by introducing an auxiliary function. The shifted Chebyshev polynomials are used to compute the critical buckling loads for kinds of boundary conditions. By comparing with the three-dimensional solutions for buckling of homogeneous circular beams, the validity of the introduced model is confirmed. Two typical material property distributions defined by the exponential- and power-law are considered. A parametric study is carried out to investigate the effects of material gradient indexes on the critical buckling loads.

中文翻译：

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基于高阶圆柱梁模型的双向功能梯度圆柱梁屈曲

在本文中，将使用考虑剪切变形的高阶圆柱梁模型来分析具有径向和轴向变化的材料不均匀性的功能梯度圆柱梁的屈曲行为。导出了圆柱梁轴压屈曲的耦合控制方程，通过引入辅助函数可以将其转化为单微分方程。移位切比雪夫多项式用于计算各种边界条件的临界屈曲载荷。通过与均质圆梁屈曲三维解的比较，验证了所引入模型的有效性。考虑了由指数和幂律定义的两种典型材料特性分布。