## 1 Introduction  
With rapid economic growth, China's energy demand continues to rise, posing significant challenges to achieving carbon neutrality due to the nation's heavy reliance on coal-based electricity generation [1, 2]. To address this issue, accelerating the exploration and development of oil and gas resources while enhancing production efficiency has become imperative [3; 4; 5; 6]. However, conventional hydrocarbon reserves are insufficient to meet escalating demand, necessitating a strategic shift toward unconventional resources. Notably, shale gas, tight oil, and tight gas--along with other emerging alternatives such as coalbed methane (CBM) [7; 8] and gas hydrates [9; 10]--are increasingly critical in sustaining domestic energy supply [11; 12; 13; 14; 15; 16]. The exploitation of unconventional reservoirs is hindered by their inherently poor rock properties [17; 18; 19] and pronounced formation heterogeneity [20; 21; 22], rendering conventional hydraulic fracturing methods ineffective for optimal resource recovery [23; 24; 25; 26]. To address these challenges, staged volume fracturing technology has emerged as a critical solution for the efficient development of tight oil and gas reservoirs, demonstrating substantial improvements in hydrocarbon production rates [27; 28]. Among recent innovations, dissolvable ball seat (DBS) systems have gained rapid adoption in volume fracturing operations due to their rapid dissolution kinetics, full-bore production capability, and streamlined operational process. This technology has driven transformative advancements in horizontal well segmentation and multi-cluster fracturing techniques, significantly enhancing reservoir stimulation efficiency [29; 30]. However, during volumetric fracturing operations, the DBS system is subjected to significant shock loads and vibrational stresses, which can compromise the anchoring integrity between the DBS and casing. These dynamic conditions may lead to the axial displacement of the DBS, seal slippage, or even leakage failures. Furthermore, under extreme loading conditions, the casing teeth may shear, resulting in complete anchoring failure [31]. Figure 1 illustrates typical failure modes, including slip tooth fracture, casing damage, and the slip breaking off entirely. To address these critical issues, this study conducts a comprehensive anchoring performance analysis of the DBS slip structure. Through advanced simulation techniques, we systematically evaluate the mechanical behavior and reliability of the DBS anchoring system under operational conditions. Current investigations into the seating performance of downhole seal tool slips primarily employ three methodological approaches: experimental laboratory testing, finite element analysis (FEA), and theoretical modeling. Within the theoretical domain, [PERSON] et al. [32] conducted seminal work addressing suspension failure mechanisms in completion packers for offshore thermal recovery wells. Their study introduced innovative structural optimization through the development of non-concentric full-contact molded slips. The research team systematically validated the enhanced suspension capacity of this redesigned  
Figure 1: Failure mode of DBS slip and casing. slip configuration through comprehensive theoretical calculations coupled with finite element simulations, demonstrating significant improvements in operational reliability. [PERSON] et al. [33] conducted a comprehensive investigation into the pressure-bearing capacity and pipe wall interaction characteristics of robotic sealing slips. Through this rigorous methodology, the researchers successfully optimized the slip configuration, achieving significant enhancements in both sealing efficiency and operational durability. [PERSON] et al. [34] optimized toothed dissolvable bridge plug parameters through finite element analysis and orthogonal experiments, significantly enhancing anchoring performance. [PERSON] et al.