Stability behaviors and governing equations of the volleyball game ball via GDQ and analytical methods

This research examines the stability characteristics of lightweight, functionally graded materials (FGMs) that are specifically designed for volleyballs. The focus is on applications that enhance the aerodynamic efficiency, durability, and stability of the ball during play. The focus is on the integration of porous, micro-scale tubular structures into the FGM-based ball material to achieve an optimal balance between flexibility and impact resistance, thereby ensuring stability in the face of the high-speed, dynamic forces that are characteristic of volleyball. Utilizing the Generalized Differential Quadrature Method (GDQM) and analytical techniques, we formulate and resolve the governing stability equations under settings that replicate the pressures experienced during gaming. A framework is provided to customize material characteristics according to game dynamics and ball interaction with external elements, enhancing control, bounce consistency, and player feedback. The results indicate that FGM constructions including optimal porosity and layering provide improved durability and impact performance, hence enhancing ball stability and playability. This study examines sustainable and recyclable alternatives for FGMs, with the objective of improving the environmental advantages of sporting equipment materials. This study's insights aid in the creation of superior volleyballs optimized for performance and durability in competitive environments.