功能梯度空心及实心圆柱体旋转时的弹性及粘弹性解

Elastic and Viscoelastic Solutions for Rotating Functionally Graded Hollow and Solid Cylinders

逐步分析了旋转的功能梯度空心及实心长圆柱体问题的解.假设圆柱体的弹性模量和材料密度沿径向呈指数变化,Poisson比为常数.由平衡方程、相容方程、弹性变形理论及应力-应变关系,导出了统一的控制方程.根据超几何函数,求解该二阶微分控制方程,得到旋转功能梯度圆柱体的弹性变形.检验并讨论了圆柱体中的应力与非均质参数、几何、边界条件之间的相互关系.将旋转功能梯度空心及实心圆柱体的分析结果,与旋转均质各向同性圆柱体的结果进行了对比分析.同时,提出了旋转粘弹性圆柱体的粘弹性解,并验证了空心及实心圆柱体中应力与时间参数间的依赖关系.

Analytical solutions for rotating functionally graded hollow and solid long cylinders are developed. Young＇ s modulus and material density of the cylinder are assumed to vary exponentially through the radial direction and Poisson＇ s ratio was assumed to be constant. A unified governing equation was derived from the equilibrium equations, compatibility equation, deformation theory of elasticity and the stress-strain relationships. The governing second-order differential equation was solved in terms of a hypergeometric function for the elastic deformation of rotating functionally graded cylinders. Dependence of stresses in the cylinder on the inhomogeneous parameters, geometry and boundary conditions was examined and discussed. Proposed solution was validated by comparing the results for rotating functionally graded hollow and solid cylinders to the results for rotating homogeneous isotropic cylinders. In addition, a viscoelastic solution for the rotating viscoelastic cylinder was presented. Moreover, the dependence of stresses in hollow and solid cylinders on the time parameter was examined.