Finite deformation analysis of the rotating cylindrical hollow disk composed of functionally-graded incompressible hyper-elastic material

Abstract

The deformations and stresses of a rotating cylindrical hollow disk made of incompressible functionally-graded hyper-elastic material are theoretically analyzed based on the finite elasticity theory. The hyper-elastic material is described by a new micro-macro transition model. Specially, the material shear modulus and density are assumed to be a function with a power law form through the radial direction, while the material inhomogeneity is thus reflected on the power index m. The integral forms of the stretches and stress components are obtained. With the obtained complicated integral forms, the composite trapezoidal rule is utilized to derive the analytical solutions, and the explicit solutions for both the stretches and the stress components are numerically obtained. By comparing the results with two classic models, the superiority of the model in our work is demonstrated. Then, the distributions of the stretches and normalized stress components are discussed in detail under the effects of m. The results indicate that the material inhomogeneity and the rotating angular velocity have significant effects on the distributions of the normalized radial and hoop stress components and the stretches. We believe that by appropriately choosing the material inhomogeneity and configuration parameters, the functionally-graded material (FGM) hyper-elastic hollow cylindrical disk can be designed to meet some unique requirements in the application fields, e.g., soft robotics, medical devices, and conventional aerospace and mechanical industries.