Arbitrary Lagrangian-Eulerian Method Research Articles

Interaction between underwater explosion bubbles and soil–water interface: A numerical and experimental study

To explore the interaction between underwater explosion bubbles and soil–water interface, a near soil–water interface underwater explosion model based on the arbitrary Lagrangian–Eulerian method was established in this work. The peak pressure of the shock wave, maximum bubble radius, and bubble evolution in free-field and bottom-charge underwater explosions determined from the proposed simulation were highly consistent with the experimental results, thereby validating the proposed numerical model. The effects of the explosion distance and amount of explosive charge on the bubble–soil surface interaction were evaluated. The results showed that the reflection coefficient of the soil–water interface was in the range of 1.204–1.250, suggesting that it was hardly affected by the explosion distance and amount of explosive charge. The attenuation coefficient of the saturated soil was found to be 1.058. With the decrease in the explosion distance, the period and maximum radius of the bubbles slightly increased, and soil deformation increased as the lower surface of the bubbles was closer to the soil surface. For explosion distances of 0.3 and 0.4 m, only an overall movement of the soil surface was observed. When the explosion distance was 0.2 m or lower, a powerful downward jet was generated upon the pulsation of the first bubble, resulting in craters and slender depressions in the soil. With the increase in the amount of explosive charge, the period and maximum radius of the bubbles increased, and soil deformation also increased. These findings are expected to help advance our understanding of underwater explosion dynamics.

Investigation on flooding dynamic response and mitigation measure of river bridge

Flood-induced failure of river bridges is intense due to frequently extreme and undesigned precipitation for global climate change. To reveal the dynamic characteristics and failure mechanism of bridges, flooding dynamic analysis is fully investigated via fluid–structure interaction simulation and Arbitrary Lagrangian-Eulerian method. Parametric analysis of different fluids and bridge configurations and pre-ballast mitigation measure are further conducted based on a simply-supported box-girder bridge. This study reveals several significant findings: the narrow channel can accelerate downstream flood velocity of the bridge piers to over double that of the upstream flow; moreover, unsubmerged piers experience vertical downward wave force surpassing buoyancy; the box girders exhibit three flood-response states, i.e., intact, slip and collapse, dependent on the hydraulic loading and bridge resistance capacity. Maximum horizontal wave force and displacement increase exponentially with the depth of water storage. Post-slip damage, bearing stress on the wave-facing side tends towards zero, while the wave-backing side presents a twofold increase. Maximum horizontal displacement (Xmax) distinguishes the failure states, such as 0 m ≤ Xmax ≤ 0.03 m (intact), 0.03 m < Xmax ≤ 1.39 m (slip), Xmax > 1.39 m (collapse), whose relation to the maximum horizontal wave force has been proposed for design reference and the inversion analysis of the bridge force. Applying a pre-ballast equivalent to 75 % of girder weight reduces Xmax by up to 91.5 %, shifting failure from collapse to slip. These insights offer crucial guidance for enhancing bridge safety amidst escalating flood risks.

Study on the jetting characteristics of an underwater explosion bubble collapsing near a floating body

This study explores the dynamic behavior and jet characteristics of underwater explosion (UNDEX) bubble oscillating near a rigid floating body using the arbitrary Lagrangian–Eulerian (ALE) method. Experiments on UNDEX bubble oscillating in a free field or oscillating near a rigid floating body in an explosion tank are used to validate the effectiveness of the ALE method in simulating the behaviors of high pressure bubble oscillating near a boundary in water. The numerical results are in good agreement with the experimental data. On this basis, the distribution of the field pressure and velocity of the oscillating bubble are further analyzed in detail. The evolution characteristics of the bubble jets are discussed for various values of the stand-off distance and explosion attack angle. The results reveal that a bubble produces two jet patterns for close stand-off distances (from γD=0.800 to γD=1.336) and attack angles of 0°, 45°, 75°, and 90°. The first bubble jet results in an annular splitting of the bubble, while the second jet is pointed toward the floating body. The aim of this study is to provide a reference for further understanding the jet dynamics of UNDEX bubble collapsing near a structure and the effective attack on ship sides.

A numerical model for the simulation of complex planar Newtonian interfaces

We present a numerical model for the simulation of complex planar interfaces at which moving solid objects can be immersed, reproducing a wide variety of experimental conditions. The mathematical model consists of the Navier-Stokes equations governing the incompressible viscous flow in the liquid subphase, the transport equation for the evolution of the surfactant concentration at the interface, and the interfacial stress balance equation. The equations are simplified by treating the problem as isothermal and the surfactant as insoluble. The bulk flow equations are discretized using a collocated finite volume method, while the interfacial flow equations are discretized using a finite area method. The Boussinesq-Scriven interface constitutive model and a variant form accounting for extensional viscosity are used to describe the extra surface stress tensor. The coupling between surfactant concentration, interfacial velocity, and bulk velocity is treated implicitly by solving the interfacial and bulk equations sequentially at each time step until a stopping criterion is satisfied. The motion of the solid is treated by an arbitrary Lagrangian-Eulerian method. The model has been implemented in the OpenFOAM framework and allows the incorporation of new interface models and solvers, making the developed new package a versatile and powerful tool in the field of computational rheology. Applications of the model include the numerical simulation of flow around objects, such as probes, immersed at a complex interface, reproducing given experimental conditions, and its use as a tool in the analysis and design of interfacial stress rheometers. Several test cases have been performed to validate the model by comparing the results obtained with analytical solutions and with numerical and experimental results available in the literature.

Dynamic response of spherical tanks subjected to the explosion of hydrogen-blended natural gas

Hydrogen is a renewable and clean energy and obtains increasing attention all around the world. Blending hydrogen into natural gas can promote hydrogen development and storage tank farms play an essential role in the storage of hydrogen-blended natural gas (HBNG). However, upon leakage from the tank, HBNG accumulates to create a vapor cloud and may explode, resulting in more severe consequences than natural gas. Furthermore, the explosion has the potential to trigger the domino effect in the spherical tank storage area, leading to multiple explosions. But little attention has been paid on this research issue. This article analyzes the dynamic response of the spherical tank exposed to HBNG explosions. The fluid–structure interaction theory is adopted to establish the whole finite element model. Meanwhile, the advanced Arbitrary Lagrangian-Eulerian (ALE) method can reduce mesh distortion and enhance computational accuracy, and the process of explosion is analyzed through the coupling of the Lagrangian mesh for the structure and the Eulerian mesh for the vapor cloud. Then, the algorithm is employed that couples shell elements with solid elements by utilizing a penalty function. Besides, the dynamic response of the spherical tank and pillar surfaces is analyzed in the trends of effective stress, displacement, velocity, and structural damage under various parameters, evaluating the energy absorbed by the spherical tank and pillar. Accordingly, the equipment damage caused by HBNG explosions considering possible damage caused by secondary explosions can be obtained. Then, the effects of the HBNG explosion chain on equipment are analyzed in tank areas. The dynamic response of structures in the explosion is closely related to the different hydrogen blended ratios, distances, and structural thickness, which significantly impact the effective stress of the spherical tank and pillar. Moreover, the damage caused by the HBNG explosion is more serious for pillars than the spherical tank, making the role of pillars crucial in supporting the spherical tank. The results obtained in this study can be used to support the design and safety operation of HBNG storage areas.

Experimental and numerical investigations on dynamic response of butt-welded plates subjected to blast load

Experimental and numerical investigations on the small-size butt-welded plates subjected to air blast loads were conducted to highlight the effect of welded joints on the blast proof structures. The inherent characteristics of welded joints, including geometry, mechanical properties and welding residual stress were evaluated and discussed in the computation of blast loading. The geometry shape was assessed through macrographic of the welded joints. The distribution of mechanical and thermal physics property was determined through basic experiments using the specimens extracted from different zones of a welded joint. Welding residual stress was calculated in a thermo-mechanical coupled model. Conventional Weapons Effects Program (CONWEP) is more economic but limited compared with Arbitrary-Lagrangian–Eulerian (ALE) method. ALE and CONWEP methods were applied to simulate the air blast load applied on the plates. Effectiveness and efficiency of the methods were discussed. The results of the two programs could both coincide well with the experiment measurements. The models under six conditions were calculated to uncouple and discuss the effect of material property distribution and welding residual stress on the dynamic response of the welded structure. Permanent deflections were considered to assess the capacity of welded structures. Welding residual stress fields and the local weak materials are advantageous to the bending deformation. The phenomenological expressions of permanent deflection across thickness under different welding conditions were established based on simulation results. The effect of aspect ratio of the welded structures was also be discussed.

Dynamic Seismic Probabilistic Risk Assessment of Nuclear Power Plants Using Advanced Structural Methodologies

The conditional core damage probability (CCDP) of a representative nuclear power plant is estimated for a beyond design basis earthquake (BDBE) using state-of-the-art structural models within a dynamic probabilistic risk assessment (DPRA) framework. Randomness of seismic excitation and uncertainty of structural parameters are considered using a simulation-based approach. Finite element models are developed for the structure and a liquid container (hydro-accumulator), and fluid–structure interaction is considered with the arbitrary Lagrangian-Eulerian method. The CCDP is evaluated through a time-dependent event tree. Also, correlation among multiple hydro-accumulators is investigated. The results show that operator action and implementation time of mobile safety equipment are critical under BDBE in case of loss of offsite power following an earthquake. It was also found necessary to adopt a DPRA approach to determine the available time for action and core damage timing probabilistically.

Pore-Scale Numerical Simulation of Acid-Rock Reaction Processes in Carbonate Reservoirs.

In the process of acidizing carbonate reservoirs, dissolution is employed for reservoir modification to enhance recovery rates. This study establishes a numerical model at the pore scale for acid-rock reaction flow based on a microscopic continuum medium model, integrating phase-field theory and component transport models. Subsequently, the results of the Darcy-Brinkman-Stokes model are compared to those of the arbitrary Lagrange-Euler method to validate the accuracy of the model. Finally, the flow behavior of the acid solution at the pore scale and the complex dissolution mechanisms in carbonate reservoirs are analyzed. The research indicates that the microscopic pore-scale dissolution in carbonate reservoirs mainly manifests as five dissolution modes: uniform dissolution, compact dissolution, conical wormholes, dominant wormhole, and ramified wormholes. Different distributions of microfractures will alter the flow state of the acid solution and the rock-acid reaction process within the pores. Once the wormhole breakthrough occurs, there is an increased probability of acid flow through the wormhole to the outlet, leading to a decrease in the effectiveness of the acidizing carbonate reservoirs. A proper understanding of pore-scale acid-rock reaction laws is of great significance for the development of carbonate oil and gas reservoirs.

High-order compact gas-kinetic scheme in arbitrary Lagrangian-Eulerian formulation

This study proposes an extension of the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulation in an arbitrary Lagrangian-Eulerian (ALE) formulation in unstructured mesh. The ALE method is achieved by subdividing arbitrary mesh into tetrahedrons and integrating flux function in a local coordinate system at the cell interface to ensure geometric conservation law. The scheme incorporates a compact reconstruction with third-order accuracy for updating both cell-averaged conservative flow variables and their gradients. HWENO-type nonlinear reconstruction and gradient compression factors are adopted to improve the accuracy and robustness of the scheme. A multi-stage multi-derivative (MSMD) time-stepping method is also implemented to achieve high-order time accuracy with fewer middle stages. The scheme is used to study problems involving moving boundaries. The numerical experiments demonstrate the effectiveness of the scheme in capturing the accurate solutions of both low-speed smooth flow and highly compressible ones with strong shock waves.

On the water entry impact characteristics of high-speed vehicle with an Arbitrary Lagrangian-Eulerian method

This paper investigates the fluid-structure interaction process of high-speed vehicles during water entry using the Arbitrary Lagrangian-Eulerian method. Through mesh independence verification and comparison of numerical simulation results with experimental data and empirical formulas, the reliability and accuracy of the computational method are confirmed. The study comprehensively analyzes flow field pressure distribution, cavity evolution characteristics, and vehicle force features, evaluating the impact of water-entry angle, Froude number (Fr), and cavitator dimension. The results indicate that during water entry, the instantaneous impact forces are mainly concentrated on the wetted surface at the bottom of the vehicle and the plane at the head. The peak stress at the entry point is significantly higher than at other locations, and stress waves propagate along the vehicle body, concentrating at the hollow structure due to the structural characteristics. The change in water-entry angle does not significantly affect the decay of Fr for the vehicle, but increasing the water-entry angle leads to an earlier and larger peak stress at the mid-point monitoring location of the vehicle. In addition, the study also found that the stress level increases with the increase of the Froude number, resulting in larger high-stress areas and peak stresses. However, the cavity evolution at the same water-entry depth is essentially independent of the variation in Fr. With the increase in cavitator dimension, the water-entry load and cavity profile will also significantly increase, and vehicles with larger cavitator dimension will generate larger stress waves upon impact.

Numerical Simulation of Electromagnetic-Thermal-Fluid Coupling for the Deformation Behavior of Titanium-Aluminum Alloy under Electromagnetic Levitation.

Electromagnetic levitation (EML) is a good method for high-temperature processing of reactive materials such as titanium-aluminum (Ti-Al) alloys. In this study, the oscillation and deformation processes of Ti-48Al-2Cr alloy specimens at different high-frequency currents during the EML process were simulated using the Finite Element Method and Arbitrary Lagrangian-Eulerian (ALE) methods. The data of oscillation, stabilization time, deformation, and distribution of electromagnetic-thermal-fluid fields were finally obtained. The accuracy of the simulation results was verified by EML experiments. The results show the following: the strength and distribution of the induced magnetic field inside the molten droplet are determined by the high-frequency current; under the coupling effect of the electromagnetic field, thermal field, and fluid field, the temperature rise of electromagnetic heating is rapid, and accompanied by strong stirring, resulting in a uniform distribution of the internal temperature and a small temperature difference. Under the joint action of gravity and Lorentz force, the molten droplets are first within a damped oscillation and then tend to stabilize with time, and finally maintain the "near rhombus" shape.

Pinch-off dynamics of an electrohydrodynamic tip streaming jet transforming into the microdroplet

The drop-on-demand electrohydrodynamic (EHD) printing is promising for manufacturing high-resolution dot arrays. Such dot fabrication is commonly achieved through two printing modes (jet/droplet mode), i.e., continuous jet directly flying to or broken jet induced droplet depositing in the substrate. The droplet mode commonly has a higher printing frequency than the jet mode, indicating the droplet mode's advantage in drop-on-demand EHD printing. However, most research on EHD printing focuses on the jet mode, which causes the mechanism of droplet production through jet pinch-off remains unclear. This study employs an arbitrary Lagrangian–Eulerian method capable of getting a sharp interface to reveal the pinch-off mechanism. First, the development of a tip streaming from a meniscus to the pinch-off is analyzed. It is found that the high pressure at the neck is the main reason for the pinch-off of the jet into the droplet. Second, the EHD phase diagram in the parameter space of We–Cae is plotted, where We is the Weber number and Cae is the electric capillary number. Finally, the important influences of the charge relaxation on the EHD tip streaming jet's breakup behavior and the generated droplets' properties are revealed. Evolutions of the droplet's properties, including radius, velocity, and charge, with varying charge relaxation parameters are offered. These properties of the droplet show their relationships with extreme values as a function of the charge relaxation parameter. This work can serve as the theoretical basis for tuning the EHD printing manufacturing performance.

A Survey of Multimaterial Treatments for Thermal Radiative Transfer

Arbitrary Lagrangian-Eulerian methods are a popular choice for hydrodynamic modeling in radiation (rad-hydro) simulations. Because these methods involve a relaxation step that moves the mesh relative to material boundaries, multimaterial spatial zones are generally present. Accurate treatments of these zones are needed to resolve various physical phenomena of interest for inertial confinement fusion applications. However, these codes are often paired with single-material, deterministic thermal radiative transfer (TRT) codes that are oblivious to the material compositions of each zone. These single-material TRT codes can only accept homogenized material properties (opacities, specific heats, etc.) from the hydrodynamic code and output homogenized solutions. After each TRT time step, the multimaterial hydrodynamic code must dehomogenize the quantities computed by the TRT package in order to update subzonal material temperatures. The process by which hydrodynamic codes perform this dehomogenization has not been well documented in previous literature, and the methods can vary significantly from code to code. The purpose of this paper is to document, study, and compare existing techniques used for rad-hydro simulations as well as present a new method with potentially promising results. We summarize several methods and give comparisons on infinite-medium problems as well a finite-medium problem for two of the methods.

A fluid-structure interaction simulation on the impact of transcatheter micro ventricular assist devices on aortic valves

Background and ObjectiveThe implantation of ventricular assist devices (VADs) has become an important treatment option for patients with heart failure. Aortic valve insufficiency is a common complication caused by VADs implantation. Currently, there is very little quantitative research on the effects of transcatheter micro VADs or the intervention pumps on the aortic valves. MethodsIn this study, the multi-component arbitrary Lagrange-Eulerian method is used to perform fluid-structure interaction simulations of the aortic valve model with and without intervention pumps. The effects of intervention pumps implantation on the opening area of the aortic valves, the stress distribution, and the flow characteristics are quantitatively analyzed. Statistical results are consistent with clinical guidelines and experiments. ResultsThe implantation of intervention pumps leads to the valve insufficiency and causes weak valve regurgitation. In the short-term treatment, the valve regurgitation is within a controllable range. The distribution and variation of stress on the leaflets are also affected by intervention pumps. The whirling flow in the flow direction affects the closing speed of the aortic valves and optimizes the stress distribution of the valves. In the models with whirling flow, the effects of intervention pumps implantation on valve motion and stress distribution differ from those without whirling flow. However, the valve insufficiency and valve regurgitation caused by intervention pumps still exist in the models with whirling flow. Conventional artificial bioprosthetic valves have limited effectiveness in treating the valve diseases caused by intervention pumps implantation. ConclusionsThis study quantitatively investigates the impact of intervention pumps on the aortic valves, and investigates the effect of blood rotation on the valve behavior, which is a gap in previous research. We suggest that in the short-term treatment, the implantation of intervention pumps has limited impact on aortic valves, caution should be exercised against valve regurgitation issues caused by intervention pumps.

Modelling the first droplet emission from an electrified liquid meniscus hanging at the nozzle tip

Electrohydrodynamic (EHD)-induced droplet emission is an efficient method for the production of micron- and submicron-sized droplets in technological applications. Existing studies propose several scaling laws to determine the size of the emitted droplet. However, they have usually focused on the tip streaming phenomena of a droplet when subjected to a uniform electric field. In most applications, a non-uniform distribution of the electric field is created owing to the nozzle-to-plate configuration. Here, we employ an arbitrary Lagrangian–Eulerian method to demonstrate the mechanism of the first droplet emission from an electrified liquid meniscus with a fixed volume hanging at the nozzle tip. The critical condition when tip streaming occurs is determined using our numerical results. A phase diagram in terms of the electric field and initial liquid volume is presented to obtain the commonly used jetting mode. The effects of the liquid volume, electric field strength and electrical conductivity of the liquid on the processes of jet formation and breakup are further investigated. We find a particularly non-monotonic dependence of the size of the emitted droplet on the electrical conductivity. These findings could be useful for generating microdroplets and improving injection frequency in EHD printing technology.

Numerical analysis of microwave-enhanced oil shale pyrolysis by rotation turntable based on the Arbitrary Lagrangian-Eulerian method

Microwave heating technology has great potential for efficient pyrolysis of oil shale. However, the inhomogeneous heating characteristics of microwave heating can lead to secondary cracking of pyrolysis products, thus reducing the overall oil yield. In order to address this issue, a rotational movement of oil shale under microwave heating has been proposed to obtain a uniform temperature distribution of the oil shale. Then, a new coupled three-dimensional electromagnetic-thermal-chemical-hydraulic model incorporating the Arbitrary Lagrangian-Eulerian (ALE) method was developed to investigate the temperature distribution and pyrolysis characteristics of oil shale under the rotational motion during microwave pyrolysis. The effects of rotational speed, rotational direction, and microwave power on the pyrolysis process of oil shale were explored through this model. The results showed that the introduction of rotational movement effectively addressed the uneven temperature distribution within the oil shale. Compared with the static condition, the rotational condition reduced the secondary reactions of oil products during microwave pyrolysis and increased the oil yield of oil shale to 50.12 %. As the rotation speed increased, the temperature distribution within the oil shale became more uniform, but the total oil yield reached its peak at a moderate speed of 180 s/r. Research on microwave power indicated that rotation increased the maximum usable power and highlighted that reducing the residence time of pyrolysis products within the oil shale was key to increasing oil yield. This study provides a novel approach and numerical simulation method for enhancing the microwave pyrolysis efficiency of oil shale, and the findings of this study are applicable to both the ex-situ and in-situ exploitation of oil shale.

Underwater implosion protection of a new concept composite structure for a deep-sea hollow ceramic sphere with CFRP shield

Carbon fiber–reinforced polymers (CFRP) and ceramics are lightweight, non-metallic materials with broad applications. However, their use in deep-sea engineering is limited owing to the potential risk of catastrophic implosions. This study introduces the concept of deep-sea ceramic-pressure-resistant hollow structures with CFRP shields for achieving a balance between safety and light weight. This research examines typical engineering cases, including the HROV Nereus and Titan accidents, and uses the Arbitrary Lagrangian–Eulerian method to investigate the fluid–structure interactions. First, the feasibility of the numerical method was verified, with the responses of the structure and flow field summarized. The advantages of ceramic hollow spheres with a CFRP shield were analyzed, leading to the development of a new implosion protection scheme with a composite structure. Furthermore, this study discusses the effects of the CFRP thickness, CFRP ratio, and trigger mode on implosion protection, with the results revealing that increasing the thickness and proportion of the CFRP shield considerably enhances the implosion suppression effect of the entire structure. These findings are valuable for designing pressure-resistant structures for practical engineering applications.

A comparative study on waveform prediction between SPH and S-ALE methods in impact welding

To explore the optimal method for simulating impact welding, we compared detailedly the smoothed particle hydrodynamics (SPH) and structured arbitrary Lagrangian-Eulerian (S-ALE) methods in predicting bonding interface. Based on the experimental results of Cu-Q235 steel atmospheric explosive welding, an in-depth analysis was presented. The results show that the SPH and S-ALE methods converged at element sizes of 2.5 and 2 μm, respectively. When the element size was further reduced to 0.5 % of the wavelength, the errors of both methods were less than 5 %. Benefiting from the gradient mesh, the efficiency of the S-ALE method was 2–4 times that of the SPH method at the same element size. With the addition of the gas medium, the S-ALE method derived the formation mechanism of the gap gas shockwave and indicated that the pressure distribution is not uniform. Furthermore, the local high pressure of the gas shockwave prevents the vortex closure during the wave formation, generating the pore. The calculated pressure and velocity of the wavefront were 20 MPa and 3500 m s−1, respectively. In conclusion, the SPH is suitable for fast previewing waveform interfaces, while the S-ALE method has the advantage of capturing fine waveform structures under various environmental conditions.

Lateral loading response of monopiles in sand considering installation effect

The effect of pile installation is a critical issue in the analysis and design of pile foundations but it is commonly ignored due to various numerical difficulties. In this paper, the installation process of an open-ended pipe pile into a sand deposit is simulated by using the zipper technique combined with the Arbitrary Lagrangian-Eulerian (ALE) method in the framework of three-dimensional (3D) finite element modeling. The subsequent lateral load response of the pile is also simulated and compared with that without consideration of the pile installation. The state dependent behavior of sand in associated with the pile installation and the subsequent lateral load is described using an advanced constitutive model. The study shows that for a relatively loose sand deposit, the sand surrounding the pile exhibits contraction and the disturbance zone takes the form of a trapezoid, whereas for a dense sand deposit, the sand near the pile will dilate and the disturbance zone takes the form of an inversed trapezoid. Furthermore, the deformation mode of the surrounding sand under the lateral load differs to some extent from that without consideration of the installation effect. Particularly, the location of the rotation point for the laterally loaded pile tends to move downwards when the pile installation process is considered.

Test and numerical analysis for water entry of elastic cabin from amphibious aircraft

Water-entry performance of amphibious aircraft is one of the main factors affecting the structural design. However, it is analyzed by rigid models in general, which is difficult to reflect the elastic characteristics of the structure. And it is difficult to obtain sufficient guidance for structural design from rigid-body analysis. In this study, water-entry model of an elastic cabin from amphibious aircraft was developed using the Arbitrary Lagrangian-Eulerian (ALE) method and validated by a designed 1:1 cabin water-entry test. Analysis under various conditions revealed the cabin's dynamic response in three steps: (1) the keel of the cabin section touches the water, (2) the bottom skin is wetted, and (3) the bottom skin is submerged. This study also compares the rigid-surface crashes and water-entry impacts of the cabin from the point of view of load and energy analysis. The results show that rigid-surface crash mainly affects bulkhead and keel, whereas water-entry energy is mainly absorbed by the skin, connectors, and stringers. Additionally, varying skin thicknesses showed a negative correlation with back surface deformation. The methodologies and conclusions presented in this study can offer valuable references for researchers in the field of water entry.