# Research on the Water Entry of the Fuselage Cylindrical Structure Based on the Improved SPH Model
###### Abstract  
During aircraft landing on water, the intense impact load may lead to significant local deformation of the fuselage skin. Ensuring the aircraft's integrity and reliability is of paramount importance. This paper investigates the fuselage skin's dynamic response during water entry. In the simulation of complex water entry problems, the smoothed particle hydrodynamics (SPH) method can fully leverage the advantages of the particle method. However, the traditional SPH method still suffers from the drawbacks of tensile instability, significantly affecting the computational accuracy. Therefore, this paper first introduces the improved SPH model addressing fluid and solid tensile instability issues. Furthermore, the Riemann-based contact algorithm at the fluid-solid interface is also demonstrated. Based on the above improved SPH model, the simulation of water entry of the elastic cylinder is performed to validate the efficacy of the improved SPH model. Then, the dynamic response characteristics of elastic fuselage skin and the skin-stringer-floor-column structure when it enters the water are analyzed, including the deformation features and slamming force. Lastly, based on the presented damage model, a study is conducted on the water entry of the metallic elastic-plastic skin-stringer-floor-column structure, analyzing the locations of failure and providing guidance for the structural safety design of engineering. smoothed particle hydrodynamics; water entry; tensile instability; skin-stringer-floor-column structure; dynamic response +
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analysis [6; 7; 8; 9; 10]. Numerical simulation is not restricted by real conditions and does not overlook actual flow phenomena due to excessive simplification, making it a popular method for simulating the aircraft water entry process [11; 12]. When simulating water surface flipping, splashing, and oscillations, the meshes undergo severe deformation, affecting computational stability [13; 14]. Using dynamic mesh or overall moving mesh methods increases computational complexity or affects the capturing accuracy of the free surface. Meshless methods provide a solution to these problems. As a classical Lagrangian particle method, smoothed particle hydrodynamics (SPH) has been applied in the simulation of the free surface, shock wave, underwater explosion, water ditching, porous media, landslide, debris flow, and so on [15; 16; 17; 18; 19; 20; 21; 22; 23]. However, according to the comparison of SPH simulation and experimental results of water entry applications, it has been determined that traditional SPH can lead to tensile instability [24], thereby affecting the simulation of the motion attitude and impact force of the structure. The fundamental reason for tensile instability is that the stress state and the kernel do not match each other, which depends on the product of the stress and the second derivative of the kernel function, as determined via stability analysis [25]. Similarly, the moving particle semi-implicit (MPS) method, a similar method to SPH, still suffers from numerical instability [26; 27; 28]. Therefore, researchers have made improvements to SPH. For example, the kernel consistency and convergence of the SPH method are enhanced theoretically [29; 30; 31; 32; 33; 34; 35; 36]. [PERSON] and [PERSON] [37; 38] modified the kernel estimation using the Taylor expansion theory and proposed a corrected SPH and regenerated kernel function method. [PERSON] et al. [33] presented an expression for the error in a SPH estimate and revisited the derivation of the SPH equations for fluids, paying particular attention to the conservation principles. [PERSON] et al. [35] indicated that the formal numerical convergence in SPH is possible and derived an optimal compromised form of scaling for N\({}_{\text{nb}}\), where N\({}_{\text{nb}}\) is the number of neighbor particles within the smoothing volume used to compute smoothed estimates. Numerical techniques are also put forward to improve the tensile stability of SPH. [PERSON] et al.