Application of structural rapid simulation technology in railway wagon equipment

. In the traditional finite element simulation analysis, the designer spend a lot of time and energy to establish a reasonable finite element model. This approach is not suitable for rapid iterative updates and optimizations of products . Therefore, for the needs of rapid simulation of structure,this article introduced the basic principle of implicit boundary method and the characteristics of different analytical methods.The author explored and practiced the application of structural rapid simulation technology based on meshless method.Through the comparative study of simulation examples, The results of meshless analysis and finite element analysis are consistent. But the meshless method increase analysis efficiency by 92.5%.The research results have certain practical guiding significance for the application of structural rapid simulation in the engineering field.


Introduction
At present, the mainstream simulation software is based on the theory of finite element analysis.The most critical link in the traditional finite element simulation analysis is to establish a reasonable finite element model.The quality of the finite element model directly determines the accuracy of the result and the calculation run time [1] .For specific analysis objects, a finite element model of appropriate scale should be established in line with the actual situation.It is necessary to comprehensively consider the structural design, force transmission path, working conditions, material properties and other aspects of the equipment.The time taken is longer and typically accounts for about 70% of the entire finite element analysis process.Therefore, how to achieve rapid structural simulation by improving the efficiency of preprocessing is the key to shortening the entire structural simulation cycle.It is also an urgent problem to be solved in the field of engineering at present [2] .
In view of the requirements of rapid structural simulation, this paper introduces the rapid structural simulation technology based on meshing.Taking the typical railway wagon body structure as the object, the result accuracy and solution efficiency of meshless fast simulation and traditional finite element simulation are compared [3] .It provides an https://doi.org/10.1051/shsconf/202316601067SHS Web of Conferences 166, 01067 (2023) EIMM 2022 engineering practice basis for the rapid simulation of complex railway wagon equipment structures.

The need for structural rapid simulation
At present, the complexity of railway freight car products is getting higher and higher, and the time span of the development process will be longer, and it will generally go through the process of scheme demonstration, preliminary design, detailed design, and test verification [4] .In the process of continuous refinement and iteration of product design schemes, multiple rounds of simulation analysis are generally carried out to ensure that the performance of the product is fully verified at the design stage.However, traditional finite element analysis methods require a lot of time and effort to build a suitable finite element model [5] .Once the design changes, it needs to be remodeled.This results in a great waste of manpower and material resources and time.
In the early stage of product development, it is the stage with the fastest frequency and the largest number of iterations of the design plan.Simulation analysis takes too long to affect the development progress of the entire product.Through the early rapid simulation iteration to drive the continuous optimization and improvement of the structural design, this stage does not have to be too rigid to the high precision requirements of the simulation results.The simulation results obtained quickly can verify the rationality of the design and make a preliminary evaluation of the structural performance of the product.
Therefore, in the early stage of product development where the scheme has not yet converged, the structure has subversive changes, and the design needs to be continuously updated and refined, a more time-saving structure rapid simulation technology is required than the traditional finite element simulation method.Faster and shorter analysis processes accelerate iterative optimization of designs.It can effectively improve the development efficiency of products and reduce the cost of manpower and material resources [6] .

Structural rapid simulation technology based on meshless method 3.1 Simulation software based on meshless technology
MIDAS MeshFree is a new simulation design software developed based on the implicit boundary method (IBM) [7] .The software now supports static analysis, modal analysis, linear dynamic analysis, thermodynamic analysis and materials or geometric nonlinear analysis [8] .
The software is mesh-free for the user.However, the software still meshes when it runs internally, but it uses a structured mesh generated based on the principle of implicit boundary method.As shown in Figure 1, the software generates a background area based on the size of the geometry and divides the mesh elements on this area.According to the different positions of the grid elements, they are divided into external elements, boundary elements and internal elements [9] .Among them, the external element does not participate in the calculation, the internal element adopts the processing method consistent with the finite element method, and the boundary element adopts the implicit boundary method.This method can solve the problem that the mesh is difficult to handle during the finite element analysis of complex structures.Very regular mesh elements can be generated without simplifying the model, greatly reducing the analysis cycle.(1) a u is the boundary value function; D Is Dirichlet function; N Is a shape function; g q Is the mesh variable approximated on the mesh; a q is the forced displacement of the node.The purpose of the constructor is to satisfy the boundary conditions.The expression of the D function is as follows: In the D function, ϕ function is an implicit equation used to describe the boundary.
When this expression is 0 ≤ ϕ , the value of the function is 0, indicating that the grid is on the boundary or outside the analysis domain; When this expression is or smaller, indicating that the grid is in a narrow band near the boundary; When this expression is δ ϕ ≥ , it indicates that the mesh is inside the analytical domain.
The calculation process of stiffness matrix is as follows.According to the virtual work equation, the following expression can be obtained.
In the above expression, { } σ represents the stress tensor; { } t represents quantity oriented; { } b represents a force vector.Bring this expression into formula (2) to get the following expression: The stiffness matrix expression can be obtained from the above formula.If the analysis problem is linear elastic, the strain matrix expression is as follows:

[ ] [ ] [ ][ ]dV
For the internal grid element, since the value of D function is 1, the strain matrix becomes the following formula: In the above expression, i N is a shape function.m represents the number of grid element nodes.Therefore, the general finite element method is used to deal with the internal elements [10] .
For boundary elements without boundary conditions, the value of D function is 1.This kind of element is divided into two parts, with and without materials.The element stiffness matrix is calculated by adjusting the weight coefficient and the position of the Gaussian integration point.The Gaussian integral formula of the stiffness matrix is as follows.
In the above expression, y x n n 、 is the number of Gaussian integration points in the x direction and y direction of the element; ( ) is the position of the Gaussian integration point.
For boundary elements with boundary conditions, the displacement expression contains the D function, so the strain matrix contains the derivative of the D function.Because the value of δ is very small, the influence of the derivative of D function and D function on the stiffness matrix cannot be ignored.The strain matrix is converted into two parts, and the B is as follows [11] : K is related to D function itself and derivative of shape function.Only the entity part of the element is not zero.Therefore, the same calculation method as that of element matrix without boundary conditions can be adopted.
The [ ]  K , the sum of these matrices is the stiffness matrix of the boundary element with boundary conditions.In fact, for the of MIDAS MeshFree soft, the problems to be solved are all three-dimensional.The above derivation method can be extended to three-dimensional space.
The function of boundary function is to make the constructed displacement function meet the forced displacement.Using shape function to construct displacement function can ensure the completeness of solution.) is imposed on the boundary of the structure, it is necessary to impose a forced displacement on all the element nodes through which the boundary passes.The forced displacement imposed by other irrelevant element nodes is zero.

Comparison with traditional finite element simulation analysis methods
In order to meet the requirements of rapid structural simulation, the meshless simulation has been reformed in principle.The pre-processing content in traditional finite element simulation is greatly reduced.As shown in Table 1, the finite element simulation is compared with the meshless simulation from the perspectives of method principle, specific operation, application occasions, etc.As shown in Figure 2, geometric simplification and mesh generation in traditional finite element simulation require a lot of time.However, meshless simulation avoids these two tasks, so the time required for simulation has been greatly reduced as a whole.Designers can test more design iterations in a shorter time to analyze and verify the feasibility of more solutions [12] .

Application examples of rapid structural simulation 4.1 Simulation analysis object
Taking the C70E body of railway freight car as the simulation analysis object, the car body has a typical railway freight car equipment structure.The car body is mainly composed of underframe, side wall, end wall and other structures.The car body is of welded structure.As shown in Figure 3.The equipment structure is made of stainless steel.

Precision comparison of simulation results
According to TB/T3550.2-2019Specification for Strength Design and Test Appraisal of Rolling Stock -Body, the calculation analysis of the static strength of the body are carried out [13][14] .ANSYS and MIDAS MeshFree were used to calculate and analyze the static strength and stiffness of the model.In this specification, there are mainly four calculation conditions [15] .The stress nephogram and displacement nephogram of calculation results are shown in Table 2 and Table 3.The maximum values of the four working conditions are compared in Table 4, and the relative error is calculated.It can be seen from the table that the stress distribution and the maximum stress position under different simulation methods are consistent, and the error of the maximum stress result is 5.81%.The results of structural stiffness calculated by the two methods are basically consistent.However, for strength analysis, the error of stress results is slightly larger, but within an acceptable range.There are several reasons for the large stress error of these two calculation methods.On the one hand, it may be that the shell element is used in the calculation of ANSYS, ignoring the influence of normal stress, while MeshFree fully considers the three-dimensional stress in the solid calculation.On the other hand, the accuracy of the stress results of traditional finite element simulation analysis is greatly affected by the number of grids and the quality of elements, and there may be some errors between the calculated stress and the actual stress.The displacement results tend to be more stable.In a word, the calculation error can meet the requirements of structural feasibility analysis in engineering design.

Timeliness comparison of simulation calculation
The simulation calculation time of different calculation methods is statistically compared, as shown in Table 5.Because there is no need to simplify the geometric model and mesh generation, and the optimization of the solution algorithm, the meshless simulation method is 92.5% more efficient than the traditional finite element simulation method.The time of the pretreatment process has been greatly shortened, from 1687 min to 85 min, and the efficiency has been improved by 95%; The analysis solution time increased from 15 min to 28 min, and the efficiency decreased by 46.4%;The time of post-treatment process was reduced from 20 min to 17 min, and the efficiency was increased by 15%; The overall analysis time was reduced from 1722 min to 130 min.The time of each stage and the total time are shown in Figure 4.

Conclusion
In the early stage of the development of complex railway wagon equipment, due to the rapid iteration speed of the scheme and the great changes in structural design, the traditional finite element simulation method requires a lot of time and energy, which seriously affects the product development progress and design cost.In this paper, the calculation principle of MIDAS MeshFree software developed on the basis of implicit boundary method and the fast simulation technology of the structure are introduced to meet the requirements of fast structure simulation.Through the analysis of examples, the meshless analysis method greatly reduces the pre-processing time of traditional finite element simulation analysis while ensuring the analysis accuracy, and the overall simulation time efficiency is improved by 92.5%.The simulation analysis time is greatly saved, and the product design and development cycle is effectively shortened.

3. 2
The principle of implicit boundary method MIDAS MeshFree uses the implicit boundary method.Firstly this method requires the construction of the D function.The D function is constructed as follows.

2 K 2 K 3 K 1 K 、 [ ] 2 K
matrix contains the derivatives of the D function and shape function, while the D function is non-zero only in the narrow band region, and its width isδ .The calculation of the [ ] matrix can be converted into line integral.The calculation method of the [ ] matrix is similar to the [ ] 2 K matrix.After calculating [ ] and [ ]

N
is the shape function of the element;

u
is the forced displacement of the i node of the element.When a forced displacement(

Fig. 3 .
Fig. 3. Three dimensional model of C70E railway freight car body.The stiffness and strength performance of the object are analyzed and verified by using the meshless simulation analysis tool MIDAS MeshFree and the traditional finite element https://doi.org/10.1051/shsconf/202316601067SHS Web of Conferences 166, 01067 (2023) EIMM 2022

Fig. 4 .
Fig. 4. Comparison of time consumed in each simulation stage.
12)Accordingly, the stiffness matrix becomes as follows:

Table 1 .
Comparison between finite element simulation and meshless simulation.

Table 4 .
Comparison of maximum displacement and maximum stress.