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

doi:10.1007/s10483-023-3014-6

Applied Mathematics and Mechanics (English Edition) ›› 2023, Vol. 44 ›› Issue (8): 1367-1384.doi: https://doi.org/10.1007/s10483-023-3014-6

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

Libiao XIN¹, Yang WANG¹, Zhiqiang LI², Y. B. LI³

1. College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, China;
2. College of Aeronautics and Astronautics, Taiyuan University of Technology, Taiyuan 030024, China;
3. Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27606, U.S.A.

收稿日期:2023-01-12 修回日期:2023-05-11 发布日期:2023-07-27
通讯作者: Libiao XIN, E-mail: xinlibiao@tyut.edu.cn
基金资助:
the National Natural Science Foundation of China (No. 11972144), the Shanxi Province Specialized Research and Development Breakthrough in Key Core and Generic Technologies (Key Research and Development Program) (No. 2020XXX017), and the Fundamental Research Program of Shanxi Province of China (No. 202203021211134)

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

Libiao XIN¹, Yang WANG¹, Zhiqiang LI², Y. B. LI³

1. College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, China;
2. College of Aeronautics and Astronautics, Taiyuan University of Technology, Taiyuan 030024, China;
3. Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27606, U.S.A.

Received:2023-01-12 Revised:2023-05-11 Published:2023-07-27
Contact: Libiao XIN, E-mail: xinlibiao@tyut.edu.cn
Supported by:
the National Natural Science Foundation of China (No. 11972144), the Shanxi Province Specialized Research and Development Breakthrough in Key Core and Generic Technologies (Key Research and Development Program) (No. 2020XXX017), and the Fundamental Research Program of Shanxi Province of China (No. 202203021211134)

摘要/Abstract

摘要： 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.

关键词: functionally-graded material(FGM), incompressible, hyper-elastic model, rotating hollow cylindrical disk

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.

Key words: functionally-graded material(FGM), incompressible, hyper-elastic model, rotating hollow cylindrical disk

中图分类号:

Libiao XIN, Yang WANG, Zhiqiang LI, Y. B. LI. Finite deformation analysis of the rotating cylindrical hollow disk composed of functionally-graded incompressible hyper-elastic material[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(8): 1367-1384.

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

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

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