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Interference connection is an effective method for improving the fatigue life of bolt connections. In this paper, a new method of interference connection was designed based on the shape memory effect of shape memory alloy. Using the method of numerical simulation, a finite element model was established to analyze the stress–strain rule of the bolt and the hole wall under different interference fit sizes. The results show that the stress concentration is formed at the orifice of the connecting plate. When the interference fit size is less than 1%, the connection hole has elastic deformation. When the interference fit size is 1.5%, the hole wall has plastic deformation. When the interference fit size is 2.5%, the maximum stress on the connecting plate is close to the tensile limit of the material. If the interference fit size continues to increase, the strength of the connection structure will be damaged. The connection experiments with different interference fit size were designed, and the interference force was calculated by the pull-out force. The experimental results were compared with the numerical simulation results. The change trend of the interference force with the interference fit size is consistent, which verifies the rationality of the finite element simulation.