High-efficiency theoretical model for predicting contact forces and deformations in threaded connections under complex loading

Threaded connection is a common structural form in mechanical engineering, with their complex nonlinear behavior under combined loading critically affecting structural performance. While existing simplified models and finite element analysis (FEA) methods describe force distribution under single loading conditions, accurately modeling threaded connections under complex loading remains challenging. This paper proposes a simplified theoretical model to efficiently predict contact forces and deformation distributions under tension, torsion, bending, and shear. The model treats bolt and nut bodies as Euler-Bernoulli beams and represents thread stiffness using equivalent trapezoidal cantilever beams, reducing computational complexity while retaining essential mechanical characteristics. The paper introduces reference helical curves and derives a deformation coordination relationship based on contact constraints. The model’s calculations are validated against FEA results, demonstrating both high precision and significant computational efficiency under complex loading conditions. This work provides an efficient and reliable tool for analyzing threaded connections, offering promising engineering applications.