## 1 Introduction  
With the continuous exploration and development of oil and gas resources, deep development has become the primary focus of oil and gas exploration. However, the operating environment for perforated string remains harsh, and the stress and deformation of the perforated string are complex. High-density shock loads with significant power generate large shock waves, which exert substantial forces on the perforated string, posing serious threats to the safety and reliability of the perforated string system [1, 2, 3, 4, 5].  
Finite element analysis software was employed to simulate the effect of effective stress on perforated string under shock loading, considering factors such as perforated string length, wall thickness, and distance from the restraining end. Countermeasureswere proposed to mitigate the impact effects [6]. A software model was utilized to predict transient pressure waves and structural loads on oil and gas well components, assessing the sensitivity of shock load effects on the design parameters of the perforated string system [7]. A dynamic load testing system was used to conduct pressure and acceleration tests on a perforated string, identifying the dynamic response characteristics of the perforated string [8]. Finite element analysis software was applied to examine the transient response stress intensity of the perforated string, with the results indicating that the maximum equivalent force in the thick-walled injection perforated string was small, thus suggesting high safety for the perforated string [9]. The finite element transient dynamic response method was employed to analyze the dynamic displacement, velocity, acceleration and equivalent force of the perforated string, exploring the relationships between ammunition density, charge, length and perforated string strength under shock loading [10]. A vibration mechanics model for the shot hole perforated string was established, and the relationship between intrinsic frequency, vibration type and displacement was analyzed. The dynamic response characteristics were obtained by applying a finite element model with measured loads [11]. Numerical simulations were conducted to examine the intrinsic relationships between various factors and the dynamic response of the perforated string, leading to the derivation and verification of a peak stress prediction model based on engineering parameters [12]. A three-dimensional impact dynamics model for the perforated string was developed, analyzing its dynamics based on field data and conducting a safety assessment [13]. A nonlinear dynamics model for horizontal wells was proposed to analyze the effect of high-temperature and high-pressure injection loads on vibration in ultra-deep wells [14]. The 3D finite element model of a perforated pipe string was established to reveal the dynamic mechanical behavior, weak points and key positions of perforated pipe string, and to study the response law of pipe string under different working conditions [15].  
Existing methods often involve high computational costs and limited adaptability to local engineering scenarios and are mainly focused on isolated dynamic factors. In order to solve these limitations, a simplified finite element model is established in this paper. On the basis of theoretical analysis and numerical simulation, the safety of perforated pipe string under impact load is systematically studied, the influence of key factors is quantified, and the change law of peak pressure and axial force of perforated pipe string under impact load is studied. The feasibility and scientific validity of the model are verified by the safety check and calculation of the example well.