Effects of Thermal and Elastic Terms on the Stress-Strain Behaviour of the Dynamics of a Rigid Body

Rigid body dynamics traditional assumes no deformation under external forces, yet materials exhibit elastic and thermal effects that significantly influence stress and strain distributions. This study develops a couple thermoelastic framework to investigate how thermal and elastic terms affect the dynamic response of rigid bodies. The governing partial differential equations were derived by integrating principles from continuum mechanics, thermodynamics, and rigid body motion. Analytical example of a heated plate subjected to thermal gradients and external forces, was solved to demonstrate the model’s predictive capability. The result shows that constrained thermal expansion generates significant stresses, while elasticity governs deformation recovery and structural stability. The interaction of these effects shapes displacement fields,alters stress distributions, and impact vibration behaviour under dynamic loading. These findings provide insights into the performance of materials and structures exposed to fluctuating mechanical and thermal conditions, particularly in aerospace, mechanical, and structural engineering applications. The proposed model offers a unified theoretical framework for predicting thermoelastic effects in rigid bodies and supports the design of safer and more durable components. Future research may extend the approach to nonlinear and transient conditions for enhanced predictive accuracy.