A Fast Analytical Method for Elastic–Plastic Analysis of Threaded Connections

Threaded connections are fundamental in engineering structures, yet their elastic–plastic behavior under load remains challenging to model analytically. The yield limit can be reached under relatively small external loads, and elastic–plastic behavior has predominantly been studied using finite element models. While these models are highly valuable, they are often restricted to specific cases. This paper presents a novel extension of Maduschka’s classical method, offering a fast and efficient analytical approach to evaluate the behavior of screw–nut–washer assemblies. The method tracks plastic strain progression from initial yielding to full yield conditions and is validated against high-fidelity axisymmetric and 3D finite element analyses (FEAs) across a range of thread dimensions (M16–M36). Results demonstrate strong agreement with FEA benchmarks while achieving significant computational speedups, making the method suitable for iterative and large-scale analyses. In addition, the comparison with results available in the literature further supports the reliability of the proposed method. Its robustness to variations in geometry, friction, and thread count positions it as a foundation for reduced-order models, ready for integration into complex finite element frameworks commonly used in structural health monitoring and digital twin technologies.