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Fluid-structure interaction (FSI) is a crucial topic in the field of computational mechanics. Shells, as one of the representative structural types, have been widely studied for their interactions with fluids and applied in various fields such as ship and marine equipment design, aerospace engineering, and civil architecture, among others, garnering increasing attention. The SPH-FEM coupling method is a pure Lagrangian-based fluid-structure coupling solution method. It utilizes FEM to simulate the solid domain and SPH to model the fluid domain, solving the problem in a unified Lagrangian frame through the coupling algorithm. It takes advantage of the high precision and ease of handling complex boundaries of FEM in simulating structures, and the benefits of SPH in tracking interfaces when simulating free surface flows, making it highly suitable for computing FSI problems.This paper employs a SPH-FEM coupling method based on the normal flux method to simulate the interaction between fluids and shells, with the aim of providing a reliable and accurate coupling method for SPH and shell finite elements. The SPH-FEM coupling method used in this paper adopts the conventional sequential staggered (CSS) method, where the fluid domain transmits forces to the solid domain, and the solid domain transmits displacements and velocities to the fluid domain, with the two computational domains calculated alternately. To simulate the shell element, the paper employs the reduced-integration R-M shell element (also known as 3D degenerate shell element), which considers transverse shear deformation and is suitable for thin, medium, and thick shells.Based on this theoretical basis, the paper develops an R-M shell linear elasticity dynamics solver using the open-source library called Eigen and verifies the program with a standard model. The SPH module uses the δ-SPH framework and introduces the normal flux method to modify the continuity and momentum equations. This correction can be regarded as additional interaction forces exerted by shell elements on fluid particles at the interface and is easier to implement in the program.To validate this SPH-FEM coupling method for shell elements, numerical simulations were conducted for standard examples, such as the three-dimensional dam break problem with an elastic gate. The results show that this normal flux-based SPH-FEM coupling method has good accuracy in both solid and fluid domains when calculating the coupling of shell structures and fluids.

FSI, SPH-FEM, normal flux method