Analysis of fuel tank collision structure based on defense point method


 Aiming at the impact process of a fuel tank, which is a transient energy conversion process, the material absorbs energy through deformation to analyze the mechanical properties of the fuel tank during the impact process. The defense node method is adopted to simulate the dynamic response of the fuel tank during impact. The results show that it can accurately evaluate the safety of the container.


28
The fuel tank impact test is a simulated impact test of the product. The purpose of this test is to verify whether the product or 29 equipment is qualified in all aspects of the product when it subjected to external force shock or external force under normal 30 operating conditions. Because collision is a complex process, it is affected by many factors, such as the constraints of the collision 31 body, the relative speed of contact, the geometry and duration of the contact surface, local plastic deformation, etc. [1][2][3] Aiming at 32 the collision model of the system, Stronge analyzed the energy change during the oblique collision and the velocity relationship 33 before and after the collision, and established the dynamic model of viscous/sliding friction contact [4] . The CEL method used to 34 simulating the dynamic response of liquid storage vessel in the process of drop collision and the space motion state of liquid at 35 different times. By comparing with the results of previous literature, the dynamic response and space state in the process of drop 36 2 collision are discussed in four cases. Namely, different drop angle, drop height, vessel thickness, and liquid storage capacity, and 37 the impact of factors on the vessel is also discussed [5] . The composite structure is vulnerable to all kinds of low energy impact 38 during the process of production and application, which will make invisible visual damage in the laminates and degenerate the 39 mechanical properties of the composite. Composite laminate is closely related to structural safety and life expectancy. So it is 40 significant to evaluate the low-energy impact resistance and damage prediction of composite structures.

41
In a variety of collision detection algorithms, the oriented bounding box algorithm had widely used. By using the characteristics 42 of the triangle surrounded by the rectangle in the leaf node and the value calculated in the rectangle-rectangle intersection test 43 phase, the new algorithm contains a better triangle-triangle intersection algorithm in the oriented bounding box. In the original 44 algorithm, to convert the two triangles into the same coordinate system before the two triangles were to test, but this step could 45 omit by using the coordinates of the bounding boxes to replaces the coordinates of the triangles. This method reduces a lot of 46 redundant coordinate transformation operations compared to the original algorithm [6] . Chai Lin established a single-degree-of-47 freedom collision vibration model and studied the effects of parameters such as collision clearance, damping, stiffness, and 48 excitation frequency on the bifurcation and chaos phenomena of the system motion using non-linear dynamic analysis and 49 numerical simulation [7] . Fan Jianping uses the penalty stiffness method in the contact algorithm. By adjusting the penalty stiffness 50 value reasonably, controlling the penetration distance effectively, and avoiding the ill-conditioned stiffness matrix, which makes 51 the calculation result approach the true value [8] . Collision detection is a hot topic in computer graphics, augmented reality, human-52 computer interaction, and other fields. In recent years, real-time simulation of large-scale complex scenes has attracted many 53 scholars' attention, especially the emergence of cloud computing and big data technology, which puts forward higher requirements 54 for real-time scene simulation, which also brings unprecedented opportunities and challenges to researchers. As the geometric 55 complexity of the virtual environment increases, the computational complexity of collision detection greatly improved, and the 56 interaction of complex scenes consumes a lot of computer resources. Therefore, the fast collision detection problem has become 57 a bottleneck in the virtual environment. How to design an efficient collision detection algorithm to meet the requirements of real-58 time and accuracy has become a current problem to be solved. Qu had put forward a multiple date parallel collision algorithm 59 based on optimization operator. The search space confined in a non-uniform local minimum area to reduce the colony search time. [9] . Chen Chengjun based on the local search algorithm of surface, characterized the contact sheet by the coordinates of the center 61 of the face and the length of the feature, carried out pre-search to quickly eliminate potential contact pairs that would not occur 62 contact, eliminated the blind area of contact search, and had good robustness and calculation accuracy [10] . Li Zhao proposes an 63 improved collision detection algorithm based on deformable objects, which is difficult to solve the real-time and fidelity problems 64 of deformable objects. To improve the efficiency of collision detection, an improved particle selection method and the idea of a  different drop angle). The variation of stress and impact duration, impact force, and peak overload (impact acceleration) are 71 discussed [12] . An algorithm for simulating friction contact between soil and rigid or flexible structure in the SPH frame is 72 proposed [13] . The calculation domain divides into several subdomains, and the contact force is used as a bridge to establish the 73 connection between the subdomains, to finally realize the global solution. When the SPH discretizes governing equations of soil 74 motion in each subdomain, the inherent boundary defects of SPH are corrected. It makes the SPH particles near the contact 75 boundary have accurate acceleration, which ensures the accuracy of contact detection. It assumed that the soil SPH particles are 76 allowed to invade the structure locally. According to the allowable residual invasion amount and the principle of momentum.

3
Normal and tangential contact forces of the contact surface are corrected by the slip condition so that they do not exceed the limit 78 friction. Compared with the existing methods which usually use "particle-particle" contact or ignore friction slip in SPH, the 79 method has higher calculation efficiency and accuracy. It is suitable for the simulation of the interaction between geotechnical 80 materials and rigid or deformable structures. The accuracy and stability of this method verifies in many examples. The calculation 81 shows that the SPH bases on a contact algorithm. The results are in good agreement with the theoretical solution or the finite 82 element solution. The algorithm is effective and can be used to expand the calculation ability and application scope of the SPH.

83
Considered the fluid-structure interaction effects in the analysis of liquid storage container dropping [14] , CEL method simulates 84 the inertia effect of fluid and the lateral hydraulic pressure to the container, and the fluid-structure interaction effects on the 85 deformation and dynamic response of the container during the process of dropping are considered. The numerical result shows 86 that the method can provide a more accurate evaluation of vessel safety and structural design. Therefore, the CEL mentioned in 87 the paper also provides a reference design evaluation method for the same structure. Considered particularity and uncertainty of

93
The collision of the fuel tank is a transient energy conversion process in which the material absorbs energy through deformation.

94
However, the structure of the fuel tank is sophisticated, which will lead to long calculation time and difficulty to ensure accuracy 95 in collision operation. Aimed at the structural characteristics of the fuel tank, this paper adopts a defense node algorithm that 96 avoids solving simultaneous equations and ensures constraints and accurately calculates contact force.

2.1Material collision mechanical properties 99
For the collision body made of the fuel tank, the maximum shear stress is related to the surface pressure. The following 100 simple formula expresses their relationship [16] .
Among them, is the velocity at contact.

103
The maximum value of occurs at ≈ 2/(1 + ) and 0 ( ) is the maximum surface pressure at given time t. For 104 materials with low shear strength, collision will cause shear failure near the surface. The maximum value occurs at 0.5 0 , and the 105 its duration occurs at 0 . The equivalent plastic strain criterion is used for the failure of fuel tank structural materials. When the 106 equivalent plastic strain of the element reaches the threshold, the material is destroyed, and the corresponding part be deleted.

Fluid-solid Coupling Analysis 108
The dynamic characteristics of liquids are affected by the geometrical its, filling height, internal structure distribution,

114
In the formula， is mass, is density.

115
For the mass conservation is satisfied in the Lagrangian fluid unit, the mass does not change with time, that is to say, the 116 following equation is satisfied.

117
The fluid is a uniform, non-viscous, and incompressible theoretical fluid, ignored the fluid-solid momentum transfer and the 119 local pressure-density linear relationship [18] . The coupling equation is:

124
On the coupling interface , the displacement and load balance conditions meet the following formula:

3.1Research on contact problems during collision contact 132
The collision process of the fuel tank has nonlinear characteristics. When the collision height is short, and the impact energy 133 is small, the elastic force ( ) of the cushioning material has a linear relationship with the deformation . That is to say;

134
Simplified the buffer material becomes a single-degree-of-freedom spring-mass system with a constant stiffness coefficient in the 135 process of drop impact.

136
The dynamic impact process is a series of dynamic processes varying with time. Subjected to shock excitation, the system will 137 produce a corresponding shock response. It proves theoretically that the maximum value is related to the duration of shock 138 and the inherent period of the system itself after shock excitation. When < , the maximum shock response of the system 139 may be twice the peak value of the shock wave, while when > , the shock response will be weakened. The impact process 140 is a transient energy conversion process, and the buffer material absorbs energy through deformation.

142
The contact and collision structure of the fuel tank shows in Fig. 1. When two contacts are in contact, two points 2 and 1 143 coincide at the contact interface. Point 2 is the orthogonal projection of point 1 on boundary 1 of contact 1 on boundary 144 2 . According to kinematic constraints, the formula is as follows: [19] 145 5 ( 1 − 2 ) • 1 ≥ 0 (7)

146
Among them, 1 is the usual unit vector.

150
The contact force on the unit contact surface is pressure, and its pressure value should be satisfied.

152
The tangential friction on the contact surface is the resultant force of the tangential contact forces in the other two 153 directions.

155
Among them, 2 and 3 are the tangential friction forces of unit tangent vectors 2 and 3 , respectively.

156
If the Coulomb friction model is adopted, when the maximum static friction force is less than the maximum static friction force, 157 the points on the two contact surfaces are relatively static, that is, the relative tangential velocity A of the points on the two contact 158 faces is

160
Among them, 1 and 2 are the tangential relative speeds of points 1 and 2 , respectively.

161
When it is equal to the sliding friction, point 1 and point 2 are relatively slipped

163
Because the collision time is short and the tangential force is relatively small relative to the normal force, ignored the influence 164 of the tangential force during the collision.

3.2Contact force algorithm for contact collision 166
Found out the contact point after the analysis of the contact interface, and then calculated the contact force using the motion 167 law of the object. Limited the value of the contact force contact constraints. The contact point is not allowed to penetrate the 168 contact boundary, and the contact force cannot be a tensile.

169
The usual methods to calculate contact force are the penalty function method and the Lagrange multiplier method. These two

207
According to the same magnitude of the defense point force and the force from the contact point, the normal distance is 0, and 208 the defense node force is 0.
7 Among them, is the total gap between the defensive point and the contact point.

211
The contact search algorithm plays an significant role in reducing calculation time and improving calculation accuracy. Any

3Stress Failure Criteria 226
The surface pressure caused by collision, the failure form caused by three-dimensional internal stress, and the time sequence 227 of various failure forms. Therefore, appropriate failure criteria can be adopted for the three-dimensional stress state caused by a

237
For the plane stress-strain state, the improved maximum stress failure criterion is used to judge the failure of the matrix material. In terms of displacement, the front end with relatively large deformation is taken. As the fuel tank is a curved part, it is 9 convenient to fix the sensor. The sensor is placed on the plane of the fuel tank in the front section. After measuring its position, 258 the collision and simulation experiments are carried out ( fig. 4). In the process of impact test, the major deformation is in the x-259 axis direction, so this test also mainly considers the impact on the x-axis, and the simulation results are consistent with the 260 experimental results, meeting our impact requirements.

267
In this paper, the structure of the fuel tank is analyzed, and the mechanical analysis of the collision body made of the fuel tank is 268 carried out. In the collision operation, the problems such as long calculation time and difficult to guarantee accuracy are caused.

269
The collision impact process of the fuel tank is analyzed, and the deformation process of the fuel tank is simulated and analyzed 270 by the defense node algorithm. This study has important practical significance for the actual collision process of the fuel tank.