# Design and Simulation Analysis of a New Type of Assembled UHPC Collision Avoidance
## 2 Device Construction Design and Finite Element Modeling
### Finite Element Modeling
#### 2.2.3 Ship Finite Element Modeling  
In this paper, a 5000 DWT river-sea direct cargo ship is selected as the representative ship for the calculations. The ship is divided into two parts, namely the bow and the hull. Since the deformation and failure of the hull are mainly concentrated in the bow of the ship during the impact process, and the hull will not undergo a large plastic deformation or experience a high stress phenomenon [37]. The hull head shell adopts 163 elements to model and accurately simulate the bow, inner keel, deck and bulkhead components according to the actual drawings, totaling 9630 elements. According to the rigid material model, there are 12,647 units. The ship structure and finite element model are shown in Figure 12.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Material Property** & **LS-DYNA Parameter** & **Values** \\ \hline Mass density & RO & 2500 kg\(\cdot\)m\({}^{-3}\) \\ Initial shear modulus & G & 11 GPa \\ Initial bulk modulus, K. & BULK & 14 GPa \\ Failure envelope parameter, \(\alpha\) & ALPHA & \(2.7\times 10^{7}\) \\ Failure envelope linear coefficient, \(\theta\). & THETA & 0.11 \\ Failure envelope exponential coefficient, \(\gamma\) & GAMMA & \(8\times 10^{6}\) \\ Failure envelope exponent, \(\beta\) & BETA & \(1.4\times 10^{-7}\) \\ Cap, surface axis ratio. & R & 4.43 \\ Hardening law exponent. & D & \(4.6\times 10^{-10}\) \\ Hardening law coefficient & W & 0.42 \\ Hardening law exponent & X\({}_{0}\) & \(1.1\times 10^{8}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Concrete material parameters of the pier impact zone.  
Figure 11: Finite element model of the pier with the meshed impact zone.  
Figure 10: Span layout of the Honghe Bridge in Zhuhai.  
To ensure a more realistic impact effect, the mesh of the bow impact area is refined, and the minimum element characteristic length is 500 mm. When the equivalent plastic strain of the element exceeds the defined limit plastic strain, a fracture failure of the element will occur. Considering that a collision between a ship and a bridge is a very complex dynamic response process, the following strengthening bilinear plastic model (MAT_PLASTIC_KINEMATIC) is adopted for the bow material and reinforcement of the UHPC box wall. The strain rate [38,39] is considered by the Cowper-Symonds model, and the yield stress is as follows:  
\[\frac{\sigma_{0}{{}^{\prime}}}{\sigma_{0}}=1+\left(\frac{\varepsilon}{D} \right)^{\frac{1}{q}} \tag{1}\]  
where \(\sigma_{0}{{}^{\prime}}\) is the dynamic yield stress at the uniaxial plastic strain rate, \(\varepsilon\), \(\sigma_{0}\) is the corresponding static yield stress, and the bow material is ordinary low carbon steel with material constants D = 40.4 and q = 5. The equivalent stiffness of the ship model in this study is 12.89 MN/m, which is between of the equivalent stiffness of an inland waterway ship that is equal to 5 MN/m and the equivalent stiffness of ocean-going ship that is equal to 15 MN/m in the European Code, reflecting the accuracy of the ship modeling.