Neural networks and numerical methods for prediction of imperfect functionally graded beams with porosity consideration for enhanced sports equipment design
This work investigates the buckling and vibrational behavior of functionally graded concrete beams featuring geometric non-uniformities and controlled porosity. The beams incorporate steel-reinforced, eco-efficient, functionally graded concrete, offering a sustainable alternative to conventional monolithic components. Each beam’s external radius varies along its longitudinal axis following linear, convex, or concave profiles, creating intentional geometric non-uniformities that significantly influence structural stability. A theoretical framework combining Hamilton’s principle with nonlocal strain gradient theory and first-order shear deformation theory is developed to capture size-dependent phenomena while accounting for simultaneous material hardening and softening. Governing equations are solved via the finite element method, and a physics-informed neural network is trained on these solutions to enable rapid predictions across diverse design parameters. Systematic parametric studies examine the effects of boundary conditions, material grading profiles, geometric configurations, and nonlocal coefficients on critical buckling loads and fundamental natural frequencies. Results demonstrate that deliberate selection of geometry and functional grading can tailor the mechanical response of porous functionally graded concrete elements. This integrated numerical and machine learning framework supports the design of permanent sports infrastructure, including modular climbing wall bases and outdoor fitness equipment supports. In these applications, controlled porosity and variable geometry reduce self-weight while preserving structural integrity under cyclic loading, addressing traditional limitations of concrete in non-portable sports installations.
Lei Huang — College of Humanities and Social Development, Minxi Vocational and Technical College, Longyan 364000, Fujian, China
Mostafa Habibi — Department of Mechanical Engineering, Faculty of Engineering, Haliç University, Istanbul, Turkey; Department of Biomaterials, Saveetha Dental College and Hospital, Saveetha Institute of Medical and Technical Sciences, Chennai, India
Tayebeh Mahmoudi — Hoonam Sanat Farnak, Engineering and Technology Knowledge-based Enterprise Company, Ilam, Iran
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