Nonlinear Aero-Thermo-Elastic Analysis of MD-FGM Golf Club Blades with Variable Thickness as Key Components of Sports Equipment

This paper presents a nonlinear aero-thermo-elastic analysis for multi-directional functionally graded material (MD-FGM) with the effect of variable thickness in different directions, in addition to utilizing temperature dependence. The purpose of this exercise is to evaluate the structural stability and dynamic behavior of the blades, while also including a higher-order deformation theory, by means of hyperbolic function and Von-Karman nonlinearity. The MD-FGM sector plate model is based upon temperature-dependent materials and variable thickness distribution effects, which directly affect mechanical performance and reliability during dynamic conditions. The modeling is based on Hamilton’s principle, with Krumhaar’s adaptation of supersonic piston theory incorporated to adequately model the aerodynamic loads. Using the governing equations, including both structure and thermal growth, with the two-dimensional generalized differential quadrature (GDQ) method, and implementing the Gauss–Chebyshev–Lobatto function to improve numerical integration accuracy in the solution process. This process is relevant to sports equipment for the manufacture of golf clubs, additionally highlighting control over the material properties and the geometry of the blades. The results highlighted the significant effect of material grading and geometry of blades in determining dynamic stability and offered valuable observations into the design of high-performance sporting equipment when temperature and aerodynamic effects can compromise long-term reliability and efficiency.