A modeling method of time-varying moving load in finite element method

Abstract

The application provides a modeling method of time-varying moving load in finite element method, comprising the following steps: establishing an initial mechanical finite element model of a structure to be calculated, and performing initial finite element mesh division; calculating the radius R of a contact spot between a force application surface and a force receiving surface by using a finite element method; selecting contact points within a width R range along a load moving path, and sequentially renumbering the contact points according to a load action time sequence to obtain finite element mesh nodes; establishing independent unit time load base functions at the finite element mesh nodes; calculating a total load F(t) of the structure at a time t; obtaining a coefficient item in a base function weighting coefficient vector at the time t by using a linear interpolation method; and decomposing the moving load F(t) to a plurality of mesh nodes near the load contact points based on an equation L(t) = f t ·W(t) to obtain a time-varying moving load loading result within a time [0, t1]. The method solves the moving load problem in the finite element environment.

Description

Technical Field

[0001] This invention belongs to the field of mechanical modeling, and in particular to a modeling method for time-varying moving loads in the finite element method. Background Technology

[0002] In recent years, with the rapid development of computer simulation technology, modeling and simulation analysis of engineering structures based on this technology has gradually become a new direction for structural design and technological improvement. The advantages of finite element modeling and simulation analysis are that it allows for understanding the characteristics of a structure during the structural redesign phase and provides reasonable guidance for related experiments, leading to its widespread application in many engineering fields. However, due to the limitations of its mathematical principles, it is usually extremely inefficient or even unsolvable when dealing with structural mechanics problems involving relative motion within a system.

[0003] Analyzing the force state of the ground when a wheel rolls on it involves a region that moves with the wheel's movement, potentially changing over time—a dynamic moving load. Solving this problem using the contact algorithm in the finite element method (FEM) involves time-consuming nonlinear iterations. Solutions to such problems are frequently reported, such as multibody dynamics, but these methods only assume the wheel and ground are indeformable rigid bodies, failing to consider the structure's inherent elasticity. Rigid-flexible coupling dynamics, building upon rigid body dynamics, incorporates the structure's flexibility; however, the flexible body needs to be simplified through modal truncation and model reduction in the FEM software, significantly reducing computational accuracy. Therefore, how to handle moving load problems within the FEM environment is a pressing issue. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention discloses a modeling method for time-varying moving loads in the finite element method. It performs movement path analysis on the time-varying moving load in the finite element model, selects the load timing nodes on the structure based on the size of the contact surface, establishes the load basis function for each node, and decomposes the spatial load at each moment to the nodes in the contact area based on the principle of linear interpolation. By replacing the time field with the spatial field, the problem of moving loads in the finite element environment is solved.

[0005] This invention discloses a modeling method for time-varying moving loads in the finite element method, the modeling method comprising the following steps:

[0006] Step 1: Establish the initial mechanical finite element model of the structure to be calculated. The finite element model includes the force application surface and the force receiving surface, and assign them material properties and element properties. Perform initial finite element mesh generation on the structure to be calculated.

[0007] Step 2: Calculate the radius R of the contact patch between the force-applying surface and the force-receiving surface using the finite element method;

[0008] Step 3: Along the load movement path, within the width R range, contact points G1 to G... N Selected nodes and renumbered sequentially according to the load application time; each node is then assigned a node in the finite element mesh G. i For i = 1, 2, 3, ..., N, establish an independent unit-time load basis function f. i (t) = 1, i = 1, 2, 3, ..., N; grid node G 1～N All basis functions form a unit vector f(t) = [f1(t), f2(t), ..., f N (t)];

[0009] Step 4: The total load F(t) of the structure at time t, where t∈[0,t1], and the position of the total load F(t) at time t is P(t), at the contact point G1~G N Search for all m grid nodes G within a radius R centered at P(t). n ~G n+m-1 ; Compute grid node G n ~G n+m-1 The distance S from the load application point P(t) n ~S n+m-1 ;

[0010] Step 5: Obtain the weighted coefficient vector W(t) = [w1(t), w2(t), ..., w] of the basis functions at time t using linear interpolation. N The coefficient term w in (t)] n ~w n+m-1 The remaining weighting coefficients are 0;

[0011] Step 6, based on the equation L(t) = f t W(t) decomposes the moving load F(t) onto several grid nodes near the load contact point;

[0012] Step 7: For the time-varying moving load F(t) acting on the structure at other times, perform interpolation decomposition loading according to steps 4 to 6 to obtain L(t), where t∈[0,t1]; then obtain the time-varying moving load loading result in the time interval [0,t1] based on L(t).

[0013] Furthermore, in the initial finite element mesh generation in step one, the mesh near the load movement path is refined.

[0014] Furthermore, in step two, the radius of the contact patch between the force-applying surface and the force-receiving surface is calculated using the implicit nonlinear method in the finite element method.

[0015] Furthermore, in step three, the unit time load basis function fi (t) Direction and node G i The normals of the corresponding mesh cells are opposite.

[0016] Furthermore, in step four, network node G n ~G n+m-1 The distance S from the load application point P(t) n ~S n+m-1 It represents the Euclidean distance in three-dimensional space.

[0017] Furthermore, in step five, the linear interpolation equation system is as follows:

[0018] When S n ~S n+m-1 When neither is 0:

[0019]

[0020] When S n ~S n+m-1 When one of them is 0, set S. n =0, the linear interpolation equation system is:

[0021]

[0022] Furthermore, in step six, if the direction of F(t) is time-varying, it is decomposed into each coordinate axis for separate calculation.

[0023] Furthermore, in step seven, the sum of L(t) to obtain L=L(0)+…+L(t)+…+L(t1) is a vector linear sum to obtain the time-varying moving load loading result in the time interval [0,t1].

[0024] Beneficial Effects: This invention addresses the shortcomings of existing technologies by disclosing a modeling method for time-varying moving loads in the finite element method. It analyzes the movement path of the time-varying moving load in the finite element model, selects the load timing nodes on the structure based on the dimensions of the contact surface, establishes the load basis function for each node, and decomposes the spatial load at each moment to the nodes within the contact area using linear interpolation. Within the full loading time [0, t1], the sum of the loads at each loading node at any moment has the same magnitude and direction as P(t), and the point of application of the resultant load force is consistent with P(t). This method is effective. Attached Figure Description

[0025] Figure 1 This is a flowchart of a modeling method for time-varying moving loads in the finite element method of the present invention;

[0026] Figure 2 This is a schematic diagram of the wheel and ground contact area in a modeling method for time-varying moving loads using the finite element method of the present invention.

[0027] Figure 3 This is a schematic diagram of the mechanical synthesis at time t in a modeling method for time-varying moving loads using the finite element method of the present invention.

[0028] Figure 4 This is a schematic diagram of the mechanical synthesis of time-varying moving loads from 0 to t1 in the finite element method of this invention. Detailed Implementation

[0029] This application provides a modeling method for time-varying moving loads in the finite element method, the modeling method comprising the following steps:

[0030] Step 1: Establish the initial mechanical finite element model of the structure to be calculated. The finite element model includes the force application surface and the force receiving surface, and assign them material properties and element properties. Perform initial finite element mesh generation on the structure to be calculated.

[0031] Step 2: Calculate the radius R of the contact patch between the force-applying surface and the force-receiving surface using the finite element method;

[0032] Step 3: Select the contact points within the width R along the load movement path and renumber them sequentially according to the load application time to obtain finite element mesh nodes; establish an independent unit time load basis function for each finite element mesh node.

[0033] Step 4: The total load F(t) of the structure at time t, where t∈[0,t1], and the position of the total load F(t) at time t is P(t). Find all m grid nodes within the range of P(t) as the center and R as the radius of the contact point; calculate the distance of these m grid nodes from the load position P(t).

[0034] Step 5: Obtain the coefficient terms in the weighted coefficient vector of the basis functions at time t using linear interpolation, with the remaining weighted coefficients set to 0;

[0035] Step 6, based on the equation L(t) = f t W(t) decomposes the moving load F(t) onto several grid nodes near the load contact point;

[0036] Step 7: For the time-varying moving load F(t) acting on the structure at other times, perform interpolation decomposition loading according to steps 4 to 6 to obtain L(t), where t∈[0,t1]; then obtain the time-varying moving load loading result in the time interval [0,t1] based on L(t).

[0037] This embodiment utilizes a wheel rolling from one end of a bridge to the other; its finite element model comprises 2730 hexahedral elements. For example... Figure 1 The diagram shows a flowchart of a specific implementation of the present invention, and the specific steps are as follows:

[0038] 1) Establish an initial mechanical finite element model of the structure to be calculated, and assign it material properties and element properties;

[0039] 2) such as Figure 2 As shown, the radius R of the contact patch between the force-applying surface and the force-receiving surface is calculated using the finite element method and is 5 mm.

[0040] 3) Contact points G1 to G2 along the load path, within a width R range. N Selected and renumbered according to the load application time sequence, N=180; each one is then processed at the finite element mesh node G. i (i = 1, 2, 3, ..., N) Establish an independent unit-time load basis function f i (t) = 1; Grid node G 1～N The matrix composed of all basis functions is f(t) = [f1(t), f2(t), ..., f N (t)];

[0041] 4) The total load on the structure at time t is F(t) = 8N, where t∈[0,t1], and the load is applied at point P(t), between contact points G1 and G2. N Find all m nodes (m=5) within a radius R centered at P(t) in G. n ~G n+m-1 Computation node G n ~G n+m-1 The distance S from the load application point P(t) n ~S n+m-1 (Distances are 1, 1, 1, 1, 0 mm respectively);

[0042] 5) The basis function weighted coefficient vector W(t) at time t = [w1(t), w2(t), ..., w N w in (t)] n ~w n+m-1 The linear interpolation method was used to obtain the result, with all other coefficients being 0. The linear interpolation equation is as follows:

[0043] When S n ~S n+m-1 When neither is 0:

[0044]

[0045] When S n ~S n+m-1 When one of them is 0, assume S n =0, the linear interpolation equation system is:

[0046]

[0047] We obtain W(t) = [w1(t), w2(t), ..., w N The weighting coefficients for [t] are [1 1 1 1 4], and the rest are 0;

[0048] 6) The time-varying moving load F(t) acting on the structure at time t can be expressed by the equation L(t) = f t W(t) is decomposed onto several grid nodes near the load contact point;

[0049] 7) At other times, F(t) is interpolated and decomposed according to steps 4 to 6 to obtain L(t), where t∈[0,t1]; then L(t) is added together to obtain L=L(0)+…+L(t)+…+L(t1), which is the time-varying moving load loading result in the time interval [0,t1].

[0050] This embodiment discloses a modeling method for time-varying moving loads in the finite element method. It performs movement path analysis on the time-varying moving load in the finite element model, selects the nodes on the structure where the load applies sequentially based on the dimensions of the contact surface, establishes the load basis function for each node, and decomposes the spatial load at each moment to the nodes within the contact area using linear interpolation. Numerical examples demonstrate the effectiveness of this method.

[0051] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make several improvements and adjustments without departing from the principle of the present invention, and these improvements and adjustments should also be considered within the scope of protection of the present invention.

Claims

1. A modeling method for time-varying moving loads in the finite element method, characterized in that, The modeling method includes the following steps: Step 1: Establish the initial mechanical finite element model of the structure to be calculated. The finite element model includes the force application surface and the force receiving surface, and assign them material properties and element properties. Perform initial finite element mesh generation on the structure to be calculated. Step 2: Calculate the radius R of the contact patch between the force-applying surface and the force-receiving surface using the finite element method; Step 3: Select the contact points within the width R along the load movement path and renumber them sequentially according to the load application time to obtain finite element mesh nodes; establish an independent unit time load basis function for each finite element mesh node. Step 4: The total load F(t) of the structure at time t, where t∈[0,t1], and the position of the total load F(t) at time t is P(t). Find all m grid nodes within the range of P(t) as the center and R as the radius of the contact point; calculate the distance of these m grid nodes from the load position P(t). Step 5: Obtain the coefficient terms in the weighted coefficient vector of the basis functions at time t using linear interpolation, with the remaining weighted coefficients set to 0; Step 6, based on the equation L(t) = f t W(t) decomposes the moving load F(t) onto several grid nodes near the load contact point; Step 7: For the time-varying moving load F(t) acting on the structure at other times, perform interpolation decomposition loading according to steps 4 to 6 to obtain L(t), where t∈[0,t1]; then obtain the time-varying moving load loading result in the time interval [0,t1] based on L(t).

2. The modeling method for time-varying moving loads in the finite element method according to claim 1, characterized in that, In the initial finite element mesh generation in step one, the mesh near the load movement path is refined.

3. The modeling method for time-varying moving loads in the finite element method according to claim 1, characterized in that, In step two, the radius of the contact patch between the force-applying surface and the force-receiving surface is calculated using the implicit nonlinear method in the finite element method.

4. The modeling method for time-varying moving loads in the finite element method according to claim 1, characterized in that, In step three, the unit time load basis function f i (t) Direction and node G i The normals of the corresponding mesh cells are opposite.

5. The modeling method for time-varying moving loads in the finite element method according to claim 1, characterized in that, In step four, network node G n ~G n+m-1 The distance S from the load application point P(t) n ~S n+m-1 It represents the Euclidean distance in three-dimensional space.

6. The modeling method for time-varying moving loads in the finite element method according to claim 1, characterized in that, In step five, the linear interpolation equations are as follows: When S n ~S n+m-1 When neither is 0: When S n ~S n+m-1 When one of them is 0, set S. n =0, the linear interpolation equation system is:

7. The modeling method for time-varying moving loads in the finite element method according to claim 1, characterized in that, In step six, if the direction of F(t) is time-varying, it is decomposed into each coordinate axis for separate calculation.

8. The modeling method for time-varying moving loads in the finite element method according to claim 1, characterized in that, In step seven, the sum of L(t) yields L=L(0)+…+L(t)+…+L(t1), which is a linear sum of vectors to obtain the time-varying moving load loading result within the time interval [0,t1].

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