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Application of ABAQUS in numerical analysis of underwater explosion of ships

introduction

ships will inevitably be attacked by enemy weapons in battle. For underwater mines, deep-water bombs and other weapons, they usually explode several meters to hundreds of meters away from the ship, which is the so-called non-contact underwater explosion. This kind of explosion usually does not cause serious damage to the hull and cause the sinking of the ship, but it may cause severe vibration and large plastic deformation of the hull, resulting in extensive impact damage to various important equipment on the ship and damage to the overall structure of the ship, making the ship lose its combat effectiveness [1]. Therefore, the response of ships under non-contact underwater explosion has attracted more and more attention. In view of the huge amount of funds needed for the real ship explosion experiment, many countries have to flinch. However, it is difficult to use the existing similarity criterion theory to convert the model test results to real ships because of the certain scale effect and processing technology of the physical model. And the explosion pool is only suitable for the model test of small-scale objects with small charge, and the results of the model test also have certain errors and randomness

with the great progress of computing technology in recent years, many large-scale finite element dynamic analysis software (such as ABAQUS, ansys/ls-dyna, msc/dytran, etc.) have emerged in the world, which makes finite element simulation a practical method to calculate the impact response of ships. ABAQUS is widely regarded as a powerful nonlinear finite element software, which can analyze the mechanical system of solid mechanics structure that automatically stops after one cycle of complex electromechanical rotation, especially it can control very large and complex problems and simulate highly nonlinear problems. ABAQUS has some unique analytical capabilities in the numerical calculation of ship underwater explosion. The analysis content includes many linear and nonlinear problems, such as accurately simulating the impact of underwater explosion on the hull, underwater noise analysis, the design of the overall structure and components of the submarine, and the launch research of torpedo missiles, as well as the safety of nuclear power and nuclear safety devices. When dealing with the impact load of underwater explosion, ABAQUS uses empirical or theoretical formulas to calculate the pressure or acceleration time history curve at the point that first reaches the structural surface in the process of shock wave propagation in the flow field, and then ABAQUS automatically calculates the pressure distribution in the flow field, rather than through the flow field unit, so there is no problem of far-field explosion pressure attenuation. The same is true when calculating bubble pressure. ABAQUS bypasses the complex calculation of BASF's 2014 sales in Greater China of more than 5.5 billion euros, and directly loads the pressure field on the underwater structures of concern. Therefore, this method has fast calculation speed and reliable results

1 characteristics of underwater explosion load

explosion load generally presents two stages, shock wave stage and bubble pulsation stage. In the shock wave stage, the shock wave head has a sudden jump form, and the amplitude quickly reaches the maximum. After the sudden jump, it decays approximately according to the exponential law [2], and the duration after attenuation does not exceed a few milliseconds; In the bubble pulsation stage, the explosion products form expansion and contraction bubbles in the water. The effect of the fluctuating pressure on the ship is called whipping or oscillation effect. After the shock wave, the explosive gas products (bubbles) continue to expand at a gradually decaying rate after the shock wave radiation. The pressure in the bubble decreases continuously until it is less than the ambient pressure. When the bubble radius reaches the maximum, the internal pressure of the bubble is the minimum, and the bubble begins to shrink. At this time, the environment is much higher than the internal pressure of the bubble, and the bubble collapses rapidly to the minimum. At the same time, the bubble begins to expand, radiating secondary pressure waves to the outward flow field. Once the bubble radius reaches the maximum for the second time, the bubble begins to shrink again. The same expansion and contraction are repeated several times. During bubble pulsation, the bubble rises continuously due to buoyancy. The bubble bursts when it reaches the free surface. The former is easy to cause serious damage to the local plate of the ship structure; The latter is easy to make the hull vibrate, resulting in serious damage to the overall structure. Oscillation is a bending motion of the whole hull in the low-frequency vertical vibration mode. The analysis shows that for non-contact explosion, it is the expanding and contracting bubble pulsating pressure formed by the explosive gas that provides energy for this bending movement. Therefore, for the overall vibration damage of the hull, the bubble pulsation pressure is a significant reason. Since the residual energy in the bubble after a bubble pulsation is about 7% of the initial energy, generally, only the influence of a bubble pulsation on the hull damage is considered. The underwater explosion process and the resulting explosion load are shown in the following figure:

2 Application of ABAQUS in the numerical experiment of underwater explosion of ships

2.1 interface between ABAQUS and other software

in the process of numerical calculation of underwater explosion of ships, the industry often adopts the finite element method, and the use of finite element software also has different effects. The software that can carry out underwater explosion numerical experiment includes ABAQUS, ansys/ls-dyna, msc/dytran and so on. This paper focuses on the application of ABAQUS software in ship underwater explosion calculation. At the same time, for example, although three stars use plastic to give several typical underwater explosion models on the back shell of Galaxy note 3, they are analyzed and studied respectively:

ABAQUS/CAE provides a very convenient pre-processing function, which is easy to learn and understand. With the help of the script language Python embedded in ABAQUS, arbitrary complex finite element models are established. Of course, it can also be imported from other professional modeling software (such as pro/e, AutoCAD), or directly generated with ABAQUS template after dividing grids in other pre-processing software (such as HyperMesh) InP file. If there are other finite element models that have been built, you can also program and convert them yourself. This paper is to use programming means to transform the existing model under LS-DYNA into the model under ABAQUS. As shown in the figure:

the model in Figure 3 is the finite element model of a type I ship calculated by LS-DYNA, which can represent a series of surface ships. The model in Figure 4 is the transformed ABAQUS model. The converted ABAQUS model has the unit attributes set by the original software and the lattice characteristics divided by the original software, so it can be calculated directly in ABAQUS software. For other structures, corresponding conversion can be carried out

2.2 application of ABAQUS in underwater explosion of surface ships

below is a schematic diagram of surface ships subjected to explosion shock waves in infinite waters, as shown in Figure 5

the following features can be seen from Figure 5: free surface S0 (0 pressure boundary), seabed reflection boundary SSB, structural wet surface SSW connected with the flow field, fluid surface SFW connected with the structural surface, and fluid boundary sinf (no reflection boundary). Figure 5 shows the explosion load source point s, and the point that first reaches the structural surface in the process of shock wave propagation is set as point a. ABAQUS provides two methods to analyze underwater explosion: scattered wave formula and total wave formula. For the scattered wave formula, the fluid is all market prices, and it is difficult to return to a reasonable linear interval, ignoring the cavitation phenomenon of the fluid. The so-called cavitation phenomenon refers to that after the shock wave reaches the free surface, the water surface rises rapidly, and many cavitation layers are generated in a certain water area. The cavitation layer at the top is the thickest, and gradually becomes thinner downward. With the increase of hydrostatic pressure, cavitation will no longer occur after exceeding a certain depth; For the total wave formula, the cavitation phenomenon of the fluid can be considered, and the static pressure of the flow field can also be included. If you want to get the total pressure in the flow field, you can use the total wave formula. In this paper, the scattered wave formula is adopted, which ignores the cavitation phenomenon of fluid and the influence of hydrostatic pressure, and does not consider the bubble effect

2.2.1 the relationship between the size of outboard flow field and the added mass

the outboard flow field of a ship has particularity and importance to the impact response of the ship. Its influence can be divided into the following three aspects: gravity influence, damping influence and inertia influence. What the industry usually cares about is the inertial influence of the outboard flow field. At this time, the flow field will participate in the total vibration of the hull and change the equivalent mass of the hull, which is equivalent to a part of the outboard flow field vibrating with the ship. This part of the outboard flow field mass is called the attached water mass or virtual mass, which is of the same order of magnitude as the mass of the hull itself. Therefore, this part of the attached water mass can not be ignored. In order to obtain a more accurate low-frequency response of the ship, it is necessary to ensure that the outboard flow field is large enough when simulating and analyzing the underwater explosion of the ship in the infinite flow field. However, in engineering calculation, it is impossible to set the flow field large enough, otherwise the calculation cannot be carried out; As the ratio of the flow field radius to the structure radius changes, the change value of the increased added mass rate is given below, where the flow field radius represents the minimum distance from the flow field edge to the center of the model, and the structure radius represents half of the ship width, where the increased added mass rate represents the ratio of the added mass of the infinite flow field to the added mass of the finite element model flow field [6], as shown in Table 1. Table 1 Relationship between the size of outboard flow field and the increased added mass rate in the finite element model

it can be seen from table 1 that if the size of the modeled flow field is 32 times of the structural radius, it can accurately simulate the impact of the infinite flow field on the structure. However, even this will cost a lot of machine time. Considering the accuracy of the calculation results and the time factor of calculation, the flow field radius is taken as 6 times of the structural radius in this paper

2.2.2 influence of lattice division on finite element analysis

in the process of underwater explosion simulation of ships, the factor of lattice division plays a key role. The size of lattice division is related to the frequency component of impact load. However, it is difficult to determine the frequency component of impact load in time domain. At this time, spectral analysis of impact load is needed to determine the main frequency component of impact load. In practical work, it is often necessary to rely on the user's experience to judge the density of the lattice. This paper believes that if the analytical results are in good agreement with the experiment, the structure and the flow field around the structure generally have at least 10 to 25 grids in a shock wave length, while the external flow field has about 1 to 5 grids in a shock wave length. For large models, if the flow field lattice is too thin, it needs a lot of calculation time. In order to save calculation time and basically ensure calculation accuracy, high-precision grids are usually divided near the fluid solid interface, while the rest of the flow field grids can be slightly thicker. In this way, the external flow field of the ship is divided into two layers, as shown in Figure 6

2.2.3 theoretical calculation

in the finite element model shown in Figure 6, the type II ship has a length of 38.6m, a width of 7.5m and a draft of 1.5m. The coordinate system is: the intersection of the middle longitudinal section, the middle transverse section and the base plane is the coordinate origin, the bow of the x-axis is positive, the port of the y-axis is positive, and the vertical up of the z-axis is positive. The charge quantity of the cartridge is 162.5kgtnt, as shown in the figure. The explosion center position is x=3.5m, y=30.5m, z=-18.5m. The position of point a and the calculation basis of pressure time history curve in the calculation of ship underwater explosion model are given below. See Figure 7 and figure 8

in Figure 7, the time history curve of shock wave pressure at point a is calculated by Geers and Hunter model [5], and its formula is as follows:

in T3 conclusion

(1) ABAQUS software uses empirical or theoretical formulas to calculate the time history curve of pressure or acceleration at the point closest to the structure on the shock wave front in the flow field, and then automatically calculates the pressure distribution in the flow field, so the calculation speed is fast, and it can

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