In this study, for the first time, an approximate solution procedure based on the Chebyshev tau method (CTM) is developed for bending analysis of functionally graded nano/micro-scaled sandwich beams. The proposed approach has the advantage of decreasing the problem to the solution of a system of algebraic equations, which may then be solved by any numerical method. In the CTM, the solution is approximated via a truncated Chebyshev series expansion and the Chebyshev polynomials are used as the test function. Based on the proposed technique, sandwich beams with elastically restrained edges under arbitrary non-uniform distributed normal and shear loads can be analyzed. The effectiveness of the CTM is illustrated by comparison of the obtained results for various end supports with those extracted from the ABAQUS software. In each considered cases, the numerical results indicate that the proposed scheme is of high accuracy and is efficient for solving the ordinary differential equations and systems of them.

中文翻译：

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Chebyshev tau法在非均匀法向和剪力作用下弹性约束的功能梯度纳米/微米级夹层梁弯曲分析中的应用

在这项研究中，首次开发了一种基于Chebyshev tau方法（CTM）的近似求解程序，用于功能梯度的纳米/微米级夹层梁的弯曲分析。所提出的方法具有将问题减少到代数方程组的解的优点，然后可以通过任何数值方法来求解。在CTM中，通过截断的Chebyshev级数展开来近似解，并且将Chebyshev多项式用作测试函数。基于所提出的技术，可以分析在任意不均匀分布的法向荷载和剪切荷载作用下具有弹性约束边缘的夹层梁。通过比较各种终端支架的获得结果与从ABAQUS软件提取的结果，可以说明CTM的有效性。在每种考虑的情况下，