## 1 Introduction
[35] optimized the segmented slip structure of small-diameter dissolvable bridge plugs by adjusting the slip cone angle and hoop dimensions to accommodate shale gas horizontal well casing deformations. Through mechanical analysis and experimental validation, the modified design demonstrated enhanced anchoring and load-bearing capacity, meeting segmented fracturing operational requirements. [PERSON] et al. [36] investigated slip anchoring mechanics through slip-line theory, finite element analysis, and experimental validation, quantifying casing penetration depth and evaluating parameter and load effects on anchoring performance. [PERSON] [37] evaluated the connection efficiency of pipe fittings in the hydraulic system of transportation machinery based on the finite element analysis method and obtained the influence laws of two 45\({}^{\circ}\) and 90\({}^{\circ}\) angle fitting connection types on pressure drop, turbulence model, energy loss, and flow coefficient. In terms of experimental research, [PERSON] [38] experimentally determined the anchoring load range for a specific packer shackle configuration through controlled laboratory testing. [PERSON] et al. [39] further advanced this understanding by investigating slip formation mechanics, with particular emphasis on how critical geometric parameters--including top angle, inclination angle, and wedge angle--influence slip--casing contact characteristics. In finite element research, recent computational studies have significantly advanced the understanding of slip-casing interaction dynamics. [PERSON] et al. [40] employed finite element analysis (FEA) to characterize stress distribution patterns in slip structures, identifying the central region as the primary casing penetration zone. Building on this foundation, [PERSON] [41] developed a sophisticated FEA model to investigate casing-pressure-induced slip damage mechanisms, subsequently optimizing critical shackle parameters. For specific field applications, [PERSON] et al. [42] designed Y422 retrievable bridge plugs tailored for marginal reservoir development in Daqing oilfield, conducting comprehensive FEA to elucidate structural stress distribution characteristics in slip components. [PERSON] et al. [43] developed a hydraulic pump degradable bridge plug design, employing computational fluid dynamics to systematically evaluate its sealing capacity, anchorage behavior, and erosion resistance under flow conditions. Complementing this work, [PERSON] [44] conducted a finite element analysis of slip-casing interactions, deriving critical stress-displacement relationships that informed subsequent shackle design optimizations. [PERSON] et al. [45; 46] investigated fracture mechanisms in integral slips during bridge plug sealing operations. Through integrated fracture testing and computational modeling, the researchers optimized the stress slot design of dissolvable bridge plug integral slips. This systematic approach resulted in significantly enhanced anchoring performance and pressure-bearing capacity. Existing studies have extensively investigated slip anchorage performance in conventional packer tools, but research gaps remain regarding novel dissolvable ball seat (DBS) systems. The current literature predominantly focuses on traditional metal slips, which serve as critical components for ensuring reliable casing-wall anchorage. However, the tight sticking performance of DBS systems presents unique challenges that directly determine the success of horizontal well fracturing operations. This study addresses these knowledge gaps through three key contributions: (1) the establishment of a mechanical model for DBS cavity structure, (2) the comprehensive finite element analysis of anchor age performance, and (3) the systematic optimization of tooth geometry (top angle and inclination angle). The resulting structural improvements enhance the metal anchorage capability of DBS systems, ultimately meeting the stringent requirements of horizontal well fracturing applications.