A Parametric Study on the Centrifugal Force-Induced Stress and Displacements in Power-Law Graded Hyperbolic Discs

Abstract An extensive parametric study on the variation of the centrifugal-force-induced stress and displacements with the inhomogeneity indexes, profile parameters and boundary conditions is conducted based on the author’s recently published analytical formulas for radially functionally power-law graded rotating hyperbolic discs under axisymmetric conditions. The radial variation of the thickness of the disc is chosen to obey a hyperbolic function defined either convergent or divergent. In the present work, contrary to the published one, it is assumed that both Young’s modulus and density radially vary with the same inhomogeneity index to enable to conduct a parametric study. Under this additional assumption, for the values of the chosen power-law indexes β = − 5, 0, 5 for the material grading rule, and the chosen profile parameters m = − 1, − 0.75, − 0.5, − 0.25, 0, 0.25, 0.5, 0.75, 1 for a hyperbolic disc; the variations of the radial stress, the hoop stress and the radial displacement are all illustrated graphically for a rotating disc whose both surfaces are stress-free, for a rotating disc mounted a rigid shaft at its center and its outer surface is stress-free, and finally for a rotating disc attached a rigid shaft at its center and guided at its outer surface (a rigid casing exists at the outer surface).

摘要 本文基于作者近期发表的轴对称条件（axisymmetric conditions）下径向幂律功能梯度（radially functionally power-law graded）旋转双曲圆盘解析公式（analytical formulas），开展了全面参数化研究，系统探讨了离心力诱发应力（centrifugal-force-induced stress）与位移随非均匀性指数（inhomogeneity indexes）、轮廓参数（profile parameters）及边界条件（boundary conditions）的变化规律。圆盘厚度的径向变化遵循收敛型或发散型双曲函数（hyperbolic function）分布。与已有研究不同，本文假设杨氏模量（Young’s modulus）与密度（density）均以相同的非均匀性指数沿径向变化，以开展参数化分析。在此附加假设下，针对材料梯度规则（material grading rule）取幂律指数β=-5、0、5，且双曲圆盘轮廓参数取m=-1、-0.75、-0.5、-0.25、0、0.25、0.5、0.75、1的工况，分别对三种边界条件下的旋转圆盘进行了分析并以图形形式展示其径向应力（radial stress）、环向应力（hoop stress）与径向位移（radial displacement）的变化规律：其一为内外表面均无应力（stress-free）的旋转圆盘；其二为中心安装刚性轴（rigid shaft）、外表面无应力的旋转圆盘；其三为中心安装刚性轴、外表面受刚性壳体（rigid casing）约束的旋转圆盘。