Research on an Equivalent Stiffness Calculation Model for Spring Plates Based on Large Deformation Beam Theory

In pressurized water reactor fuel assemblies, fuel rods are secured by grid supports, with grid springs providing crucial preload clamping force. Clamping relaxation can reduce the overall structural stiffness of the assembly, intensify fretting wear between fuel rod cladding and grids, and compromise nuclear reactor safety. Therefore, accurately characterizing the mechanical properties of spring strips is essential for assembly design. This paper presents a pre-deformed insertable spring strip design and establishes an equivalent stiffness calculation model based on post-buckling beam theory. First, the nonlinear governing equations for large deformations were derived under large-deflection assumptions. Then, a double nested Newton shooting method yielded semi-analytical solutions for the system's governing equations, with experimental validation confirming theoretical reliability. Finally, the influence of design parameters on spring preload was investigated, revealing the dependence between spring design parameters and stiffness. This research elucidates the relationship between grid spring dimensions and preload, providing theoretical support for spring design and optimization.