# Dynamic Structural Response of a Corrugated Blast Wall Under Hydrogen Blast Loads
## 3 Methods  
### Numerical Model for Dynamic Structural Response Analysis  
A blast wall is a structure designed to prevent propagation of blast load and flame caused by an explosion to the surroundings. In this study, a corrugated blast wall, commonly installed in offshore structures with high explosion risks, was selected as a target structure and applied to numerical simulations. A blast wall is generally a site-specifically designed structure. However, since installation conditions for design did not exist, the intermediate section of design guidance for a corrugated blast wall provided by [PERSON] and [PERSON] [59] was adopted as dimensions of the target structure. The target structure consisted of corrugated panels and angle-type supports and was assumed to be made of duplex stainless steel 2205. A bilinear elasto-plastic model was applied as a material model, and nominal values of material properties were used in the material model to carry out simulations conservatively. The material properties used in the model are provided in Table 3.  
The strain rate effect was considered by the Cowper-Symonds equation [60] as presented in Equation (1), and C of 100 and \(q\) of 4 were used as constants in the equation [61]. In this equation, \(\sigma_{\rm Yd}\) and \(\sigma_{\rm Y}\) are dynamic and static yield strengths, respectively, and \(\hat{\epsilon}\) is the strain rate. \[\frac{\sigma_{\rm Yd}}{\sigma_{\rm Y}}=1.0+(\frac{\hat{\epsilon}}{\mathcal{C} })^{1/q} \tag{1}\]  
To account for damping effects in a numerical simulation, a damping constant of 0.4\(\pi\)/\(T_{\rm N}\) was used for all directional damping forces [23]. The \(T_{\rm N}\) represents the natural period of the blast wall obtained from modal analysis. Surface-to-surface contact between the corrugated panel and the angle-type support, as well as single-surface contact on the corrugated panel, were defined to capture potential interactions between structural components. A static friction coefficient of 0.55 and a dynamic friction coefficient of 0.45 were used to define the contact conditions. These values represent the median values within the typical range for dry contact between clean stainless steel surfaces. Simply supported and symmetric boundary conditions were applied to the ends of supports and corrugated panels, respectively. For the blast load, a time-varying pressure was applied over the entire surface of the blast wall in the direction indicated by the red arrow (-Y direction) in Figure 5, without conducting separate Computational Fluid Dynamics (CFD) or Fluid-Structure Interaction (FSI) simulations. This time-varying pressure corresponds to the blast load scenario described in Section 3.2. four-node fully integrated shell elements were used in the numerical model, and the size of elements was determined based on existing literature [62] and the mesh convergence study presented in Figure 6. In the mesh convergence study, maximum and permanent displacements at the center of the corrugated blast wall were compared for different element sizes. Computation time was also compared due to the large number of simulations required. When the element size was set to 30 mm, the displacements converged while having a reasonable computation time. Therefore, an element size of 30 mm was determined for analyzing the dynamic structural response of the blast wall. The characteristic length used for time step calculation was defined as the element area divided by the maximum element edge length. Termination times were set to three times the blast load durations to observe complete structural responses, including the effect of inertia force. The blast load durations are described in detail in Section 3.2. An explicit solver in LS-DYNA was used for the simulations, employing the numerical model described previously and shown in Figure 5. The numerical model was entirely implemented by the authors, and no pre-defined numerical procedures provided by the software were utilized.