Static analysis of 2D-FG nonlocal porous tube using gradient strain theory and based on the first and higher-order beam theory

Xiaozhong Zhang , Jianfeng Li , Yan Cui , Mostafa Habibi , H. Elhosiny Ali , Ibrahim Albaijan , Tayebeh Mahmoudi

Abstract

This article focuses on the study of the buckling behavior of two-dimensional functionally graded (2D-FG) nanosize tubes, including porosity, based on the first shear deformation and higher-order theory of the tube. The nano-scale tube is simulated using the nonlocal gradient strain theory, and the general equations and boundary conditions are derived using Hamilton's principle for the Zhang-Fu's tube model (as a higher-order theory) and Timoshenko beam theory. Finally, the derived equations are solved using a numerical method for both simply-supported and clamped boundary conditions. A parametric study is performed to investigate the effects of different parameters, such as axial and radial FG power indices, porosity parameter, and nonlocal gradient strain parameters, on the buckling behavior of the bi-dimensional functionally graded porous tube. Keywords: Nonlocal strain gradient theory; buckling; Zhang-Fu's tube model; Timoshenko theory; Two-dimensional functionally graded materials; Nanotubes; Higher-order theory.

Key Words

buckling; higher-order theory; nanotubes; nonlocal strain gradient theory; Timoshenko theory; twodimensional functionally graded materials; Zhang-Fu's tube model

Address

Xiaozhong Zhang — Department of International Applied Technology, Yibin University, Yibin 644000, Sichuan, China
Jianfeng Li — 1)Faculty of Engineering, China University of Geosciences (Wuhan), Wuhan 430000, Hubei, China 2)Zhongjiao Yuanzhou Transportation Technology Group Co., Ltd. Fujian Branch, Fuzhou 350109, Fujian, China 3)Hainan Cloud Spacetime Information Technology Co., Ltd, Danzhou 571700, Hainan, China 4)XING YUN CHEN (Hongkong) Technology Co., Ltd, Hongkong 999077, China
Yan Cui — School of Civil Engineering, Hebei Polytechnic Institute, Shijiazhuang 050091, Hebei, China
Mostafa Habibi — 1)Faculty of Architecture and Urbanism, UTE University, Calle Rumipamba S/N and Bourgeois, Quito, Ecuador 2)Department of Biomaterials, Saveetha Dental College and Hospital, Saveetha Institute of Medical and Technical Sciences, Chennai 600 077, India 3)Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam 4)Center of Excellence in Design, Robotics, and Automation, Department of Mechanical Engineering, India
H. Elhosiny Ali — Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
Ibrahim Albaijan — Mechanical Engineering Department, College of Engineering at Al Kharj, Prince Sattam Bin Abdulaziz University, Al Kharj 11942, Saudi Arabia
Tayebeh Mahmoudi — Hoonam Sanat Farnak Engineering and Technology Company, Postal code: 6931876647, Ilam, Iran

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