## 1 Introduction  
In rough seas, severe impacts usually occur between waves and the bottom of a high-speed vessel, causing impulsive loads on the hull of the vessel. These hydrodynamic impact loads are characterized by pressures with high peaks and short durations, which may dominate in the design of the hull structure. The impact problem between the vessel and the waves is often simplified as the impact between a two dimensional (2D) section and static water. As the V-shaped cross-section is a typical section form of the bottoms of high-speed vessels [1], the water entry problem of 2D wedge sections has attracted a great deal of research. Pioneering work can be traced back to [PERSON] [2] and [PERSON] [3]. Based on momentum conservation and the concept of added mass, [PERSON] [2] performed a theoretical investigation of the hydrodynamic loads acting on a wedge. By taking into consideration the local rise of water surface during the water impact, [PERSON] [3] improved the model proposed by [PERSON] [2]. [PERSON] and [PERSON] [4], presenting a nonlinear boundary element method (BEM) for simulating the water entry of 2D sections. [PERSON] et al. [5] assessed the accuracy of several analytical models for the prediction of hydrodynamic forces and pressure distributions. During the water entry of finite width wedges, the jet root may be separated from the surface of the wedge. [PERSON] et al. [6] investigated the flow separation with analytical separation models. [PERSON] et al. [7] proposed a semi-analytical model considering flow separation and negative pressure correction. This semi-analytical model is verified by comparing with numerical results computed using the commercial finite element code LS-DYNA. [PERSON] et al. [8] presented a two-fluid BEM for the water entry of a free-fall wedge, and the role of the air flow on the closure of the 2D cavity was investigated. [PERSON] et al. [9] developed a BEM model to simulate the free-fall water entry of a wedge with the flow separation. Both vertical and oblique water entries of the wedge were discussed using this method. [PERSON] et al. [10] investigated the water impact problem of a symmetrical wedge using computational fluid dynamics (CFD) simulations. Their numerical results were in good agreement with the experimental data reported by [PERSON] et al. [11]. [PERSON] et al. [12] experimentally characterized the 3D hydrodynamic loading on a rigid wedge by measuring the velocity field on several different planes. Their experimental findings on edge effects were applied to the water entry of 2D elastic wedges in the follow-up study [13]. Since the Wagner theory is convenient to predict the hydrodynamic impact loads, it has been widely used in the water entry of 2D elastic wedges, such as the work of [PERSON] et al. [14], [PERSON] and [PERSON] [15], [PERSON] and [PERSON] [16] and [PERSON] and [PERSON] [17]. [PERSON] et al. [18] established a semi-analytical model for the water entry of 2D elastic wedges by combining the Euler-Bernoulli beam theory with the potential flow theory. Their method was further extended to water exit problems [19]. With the improvement of numerical methods for the fluid domain, many CFD methods have been applied to solve fluid-structure interaction problems during the water entry of 2D elastic wedges, such as the BEM method [20], the finite volume method (FVM) [21; 22], the smoothed particle hydrodynamics (SPH) method [23; 24] and the arbitrary Lagrangian-Eulerian (ALE) method [25; 26]. Three-dimensional (3D) stiffened plates with several longitudinal stiffeners and transverse frames are typical forms of the ship structure. The bottom segment of a high speed ship can be seen as a 3D wedge composed of stiffened plates. However, studies on the dynamic response of a 3D wedge under the hydrodynamic impact are scarce. [PERSON] [27] performed a coupled analysis between the cross-fluid domain and the 3D wedge. The cross-fluid domain was solved using 2D Wagner theory, and the structure model had to satisfy the orthogonal plate theory.