I. Introduction
Injection production string (IPS) serves as an important link for transmitting energy and information between the ground and underground and plays an important role in layered water injection, layered gas injection, CO2 injection, and production [1], [2], [3], [4], [5], [6]. The axial force of IPS changes greatly due to high pressure, high corrosion, and large fluctuation of parameters, such as temperature and pressure difference between the inside and outside of the string along the borehole direction. When the force exceeds the maximum static friction between the rubber barrel and casing or the tensile limit of IPS, accidents during injection production, such as packer sealing failure and tubing string fracture, will occur [7], [8].