Functionally graded material shafts are the main part of many modern rotary machines such as turbines and electric motors. The purpose of this study is to present an analytical solution of the elastic-plastic deformation of functionally graded material hollow rotor under a high centrifugal effect and finally determine the maximum allowed angular velocity of a hollow functionally graded material rotating shaft. Introducing non-dimensional parameters, the equilibrium equation has been analytically solved. The results for variable material properties are compared with the homogeneous rotor and the case in which Young’s modulus is the only variable while density and yield stress are considered to be constant. It is shown that material variation has a considerable effect on the stress and strain components and radial displacement. Considering variable density and yield stress causes yielding onset from inner, outer, or simultaneously from both inner and outer rotor shaft radius in contrast to earlier researches that modulus of elasticity was the only variable. The effects of the density on the failure of a functionally graded material elastic fully plastic in a hollow rotating shaft are investigated for the first time in this study with regard to Tresca’s yield criterial. Numerical simulations are used to verify the derived formulations which are in satisfying agreement.

中文翻译：

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高离心力作用下FGM空心转子的弹塑性变形分析研究

功能分级的材料轴是许多现代旋转机械（例如涡轮机和电动机）的主要部分。这项研究的目的是提供功能梯度材料空心转子在高离心力作用下的弹塑性变形的解析解，并最终确定功能梯度材料空心转子的最大允许角速度。引入无量纲参数后，已经对平衡方程进行了解析求解。将材料性能可变的结果与均质转子进行了比较，其中杨氏模量是唯一变量，而密度和屈服应力被认为是恒定的情况。结果表明，材料变化对应力和应变分量以及径向位移有很大影响。与早期的研究（弹性模量是唯一的变量）相反，考虑到可变的密度和屈服应力会导致内，外或同时从内和外转子轴半径开始屈服。在本研究中，首次根据Tresca的屈服准则研究了密度对功能梯度材料在空心旋转轴中弹性完全塑性的破坏的影响。数值模拟被用来验证所得出的满足令人满意的公式。在本研究中，首次根据Tresca的屈服准则研究了密度对功能梯度材料在空心旋转轴中完全塑性的材料的破坏的影响。数值模拟被用来验证所得出的满足令人满意的公式。在本研究中，首次根据Tresca的屈服准则研究了密度对功能梯度材料在空心旋转轴中弹性完全塑性的破坏的影响。数值模拟被用来验证所得出的满足令人满意的公式。