Theoretical modeling of nonlinear rotational stiffness for missile radial countersunk screw lap joints

Radial countersunk screw lap joints are widely employed to connect adjacent cabin sections in small- and medium-diameter missiles. However, the analysis and design of joint stiffness pose challenges because of geometric discontinuities, clearance, and friction nonlinearities. In this paper, a theoretical model for rapid and reliable prediction of nonlinear joint stiffness is developed. The joint is first discretized into multiple subjoints, each of which is defined to carry only a tensile or compressive load under external loading. The evolution of contact states is incorporated to simulate nonlinear tension and compression stiffness. By combining Bernoulli’s hypothesis with the ellipsoidal deformation theory, the joint rotational stiffness is derived. Finally, the effectiveness of the proposed stiffness prediction method is validated via experiments and detailed simulations. Furthermore, an orthogonal experimental design is used to analyze the importance of critical design parameters. The results indicate that the proposed theoretical model provides satisfactory accuracy. The specification and number of screws are the primary factors influencing the joint rotational stiffness, whereas the lap length and cabin thickness exert a secondary effect. This study presents an explicit theoretical mapping between the structural design parameters and joint nonlinear stiffness, thus facilitating improved design and optimization of jointed structures.