AI-driven prediction of linear and nonlinear buckling in nonuniform functionally graded micro-tubes for sports equipment in sports training

Yan Li , Mostafa Habibi , Maryam Bagheri

Abstract

This study investigates the buckling behavior of axially functionally graded (AFG) non-uniform cylindrical beams with specific applications in sports equipment, using a combination of artificial intelligence (AI) and advanced numerical methods. Unlike traditional approaches, this work employs non-classical size-dependent theory and high-order tube theory to more accurately capture the mechanical responses of non-uniform geometries, which are crucial for optimizing the performance and safety of sports equipment such as poles, racquets, and composite materials used in various athletic applications. The beam under consideration has a non-uniform external surface while maintaining a uniform internal radius, with material properties varying continuously along the beam's length. The governing equations are derived using the nonlocal strain gradient theory in conjunction with Von-Karman's nonlinear theory and high-order cylindrical beam theory. These partial differential equations are solved using the Generalized Differential Quadrature Method (GDQM), a powerful numerical technique known for its high accuracy and computational efficiency. Furthermore, to enhance the predictive capability of the model, the results are tested and trained using a neural network (NN), which provides reliable predictions of buckling behavior under various boundary conditions and material distributions. By integrating artificial intelligence with advanced analytical methods, this research offers a practical framework for accurately predicting buckling in non-uniform cylindrical beams, proving beneficial for both theoretical studies and real-world applications in sports engineering. This approach demonstrates the potential for more efficient design and optimization of sports equipment, enhancing athletic performance and ensuring safety compared to traditional methods.

Key Words

artificial intelligence; buckling analysis; high-order theory; neural network; nonlinear analysis; numerical method

Address

Yan Li — School of Physical Education, Zhengzhou Vocational and Technical College, Zhengzhou 100043, Henan, China
Mostafa Habibi — Universidad UTE, Facultad de Arquitectura y Urbanismo, Calle Rumipamba S/N y Bourgeois, Quito, 170147, Ecuador/ Department of Biomaterials, Saveetha Dental College and Hospital, Saveetha Institute of Medical and Technical Sciences, Chennai, 600 077, India/ Department of Mechanical Engineering, Faculty of Engineering, Haliç University, 34060, Istanbul, Turkey/ Institute of Research and Development, Duy Tan University, Da Nang, 550000, Viet Nam
Maryam Bagheri — Hoonam Sanat Farnak, Engineering and Technology Company, Ilam, Iran

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