Analytical solution for displacement and stress distributions of double-layer interference-fit functionally graded cylinder/sphere structures under coupled effects of magnetic field and internal pressure
Abstract：With the advancement of composite manufacturing techniques, functionally graded (FG) materials have emerged as an effective solution to the interface issues inherent in traditional composite materials due to their spatially continuous gradient properties. The application of the interference fit technique in FG cylinder/sphere structures further enhances the load-bearing capacity and fatigue life. Therefore, investigating the mechanical behavior of such structures under multi-field coupling is essential for ensuring structural reliability. However, the exact analytical models are still lacking for the mechanical response of double-layer interference-fit FG structures subjected to combined internal pressure and magnetic field, particularly when material properties follow a power-law gradient. This gap continues to constrain their optimal design and safety assessment. This study aims to develop an analytical model for predicting the mechanical response of double-layer interference-fit FG cylinder/sphere structures subjected to coupled internal pressure and magnetic field. Under the assumption of axial/spherical symmetry, considering the power-law variation of elastic modulus and Lorentz force along the thickness direction, this study first derives the governing equations and fundamental solutions for the displacement and stresses based on the fundamental equations of elasticity theory and boundary conditions. Subsequently, by investigating the relationship between the interference value and the displacement at the contact interface, an expression for the contact pressure as a function of the interference value is obtained. Consequently, a comprehensive analytical model is developed for the displacement and stresses in a double-layer interference-fit FG structures under the coupled effects of internal pressure and magnetic field. The model can accurately describe the mechanical response of the interference fit under multi-physics coupling, and reveal the effects of the interference value, material gradient parameter, geometric dimension and external magnetic field on the displacement and stress distributions of the structures. It provides a theoretical and computational foundation for the mechanical design of the FG interference fit. The results indicate that by adjusting these parameters, the interfacial stress distribution can be optimized and stress concentration mitigated, thereby enhancing the load-bearing capacity and reliability. The analytical model in this work provides a theoretical and numerical basis for the design and assessment of interference-fit FG structures under multi-physical field coupling.
2026, Vol. 47 
