## 1 Introduction
However, in the study of the structural response problem, the available structural dynamics software cannot deal with nonlinear factors, and ignoring the threaded connection will have a significant impact on the results. In the literature, the contact interface parameterization method has commonly been used to deal with this type of problem, e.g., through spring elements, general elements [11], the virtual material method [12], zero-thickness elements [13], and thin-layer elements (TLEs) [14]. Because of its easy of modeling and the convenience of its parameter determination, the TLE method has been widely used. [PERSON] [15] first proposed the concept of TLE modeling in 1984. The interface between the rock and soil was characterized by a TLE with normal contact stiffness and shear stiffness. [PERSON] et al. [16] used a TLE to represent the contact stiffness of a bolt joint. The variation in the contact stiffness at the bolt interface with the bolt preload was obtained. [PERSON] et al. [14] applied TLEs to represent the shrunken joints of a two-disk rotor in a generator. The damping and contact stiffness parameters obtained experimentally were coupled to the TLE model. An FE model was then used to predict the response characteristics of the generator. [PERSON] et al. [17] introduced TLEs into the FE analysis of threaded pipes coupled to each other by a nut interface. The material parameters of the TLE were adjusted to minimize the residual between the numerical and experimental nonlinear frequency responses. This method significantly reduced the uncertainty of the connection modeling. [PERSON] et al. [18] determined the material parameters of a TLE through general experiments. The parameters were coupled to the FE model to study the vibration and damping characteristics of steel composite structures. The numerical modal analysis results were in good agreement with the experimental results. In the above studies, the TLE method was mainly applied to bolt connections or other joint styles, and established at the contact interface to represent the contact stiffness and friction damping. To date, the TLE method has rarely been used to simulate threaded connections. Considering that the nonlinear factors of threaded connections also comprise the contact stiffness and frictional damping, the TLE method can be extended to threaded connections for further exploration. In the application of the TLE method described above, the TLE material parameters were determined by general experiments [14; 18] or identified using experimentally measured data [12; 16; 17; 19]. Both of these two methods relied on experiments, which complicated the application of the TLE method. In this study, the TLE method was used to characterize the threaded connection of a projectile-fuse system. The material parameters of the TLE were determined theoretically by combining the elastic model of the threaded connection with the basic principles of the TLE. The projectile penetration into a semi-infinite concrete target was tested. Frequency response analysis of the projectile-fuse system was performed using the TLE method. The accuracy and reliability of the TLE method were verified based on a concrete penetration test.