Physics-informed deep neural networks for sports applications: Enhancing tennis handle performance with nanocomposites

In this paper, we propose a new framework that merges physics-informed deep neural networks (PINNs) with novel material modeling to assess the performance of tennis handles reinforced with graphene oxide powder nanocomposites. The tennis handle is modeled as a thin shell structure within the cylindrical coordinate framework to accurately capture the complex curved geometry of the handle as well as its vibration response under dynamic loading conditions. The effective mechanical properties of the nanocomposite reinforced structure use the Halpin–Tsai micromechanical model to represent the ability of the graphene oxide powders to reinforce the polymeric matrix. The structural response is captured in terms of a higher-order shear deformation theory (HSDT) based on Taylor's series expansion, which is an improvement compared to classical and conventional first-order shear models typically used due to its ability to account for variation in shear strain through thickness. The governing motion equations are developed through Hamilton's principle, accounting for both inertial and elastic energy contributors. To tackle the resulting high-dimensional system, a PINN architecture with Legendre polynomial expansions provides a physics-constrained and computationally efficient surrogate representation for detailed vibration and stability analyses. Legendre polynomials allow the neural network to have a larger representation capacity while grasping smoothness and orthogonality within the solution space. Results show that the stiffness, damping, and energy absorption capacity of tennis handles improved significantly with graphene oxide nanocomposites. Also, the proposed PINN framework achieved better accuracy than traditional numerical methods, such as finite differences, computer finite element analysis, calculations made using Matlab simulation toolboxes, and higher-order polynomial interpolation. This hybrid physics–AI methodology improves sports by assisting with the optimization of tennis handle designs and also provides a generalized method for the use of physics-informed machine learning in sports equipment design.