变厚度各向异性功能梯度转动圆盘的弹性分析

Elastic Analysis of Anisotropic Functionally Graded Rotating Disks With Non-Uniform Thicknesses

研究了任意梯度变化的变厚度各向异性转动圆盘的弹性问题.假设圆盘绕刚性轴匀速转动,其材料性能和厚度沿径向任意梯度变化.考虑圆盘在中心转轴处受位移约束,外侧自由,根据各向异性转动圆盘的平衡微分方程,得到关于径向应力的Fredholm积分方程,继而通过对Fredholm积分方程进行数值求解,得到结构的位移场和应力场.对具体梯度变化情况仅需代入相应梯度变化进行求解即可.数值算例部分,通过假设厚度、弹性模量等参数为特殊的幂函数形式,将由Fredholm积分方程求出的数值解与对应的精确解进行对比,以及针对常见的Voigt模型,将由该方法算得的数值解和ANSYS有限元计算结果进行对比,验证了该方法的准确性和精度.其次,针对Voigt模型,重点分析了厚度变化、材料性能梯度参数、各向异性度等对应力场和位移场的影响.提出了针对材料性能和厚度沿径向呈任意梯度变化的圆盘结构弹性分析方法,将为优化功能梯度圆盘的结构和材料参数、有效调整构件应力分布、提高结构安全性,提供强有力的工具;算例分析结果对功能梯度圆盘在复杂条件下的结构安全设计有重要的理论指导意义.

The elastic problem of anisotropic functionally graded rotating disks with non-uniform thicknesses was studied.The material properties and thicknesses of the disk change with an arbitrary gradient along the radial direction, and the disk displacement is constrained at the central axis of rotation and the edge is free. According to the equilibrium differential equations for the anisotropic rotating disk, the Fredholm integral equation of radial stresses was obtained, and then numerically solved to calculate the displacement and stress fields. For any specific situation of gradient change, it is only needed to substitute the corresponding gradient parameters into the equation for solution. In the numerical examples, firstly,the parameters such as the thickness and the elastic modulus were assumed to be of special power functions. The numerical solutions obtained from the Fredholm integral equation were compared with the corresponding exact solutions and the FEM solutions by the ANSYS software for the common Voigt model, to validate the method. Then, the effects of the thickness change, the gradient parameters and different degrees of anisotropy on the stress and displacement fields, were numerically analyzed with the common Voigt model. The proposed elastic analysis method for disk structures with arbitrary gradient changes along the radial direction, is promising in the application of structural optimization. The analysis results can guide the engineers to design safer and more economical functionally graded structures.