Method for calculating shaking restoring force of liquid in liquid tank and storage medium

Abstract

The invention provides a method for calculating shaking restoring force of liquid in a liquid tank, and belongs to the technical field of numerical analysis. The method comprises the following steps: constructing a tank box structural domain and a tank box inner liquid domain grid, and extracting a tank box inner liquid domain surface grid as a liquid free liquid level domain grid; the structural domain, the liquid domain in the tank and the free liquid level domain are connected in a grid combination mode, and a liquid shaking model in the tank is obtained; grid node initialization restoring force is calculated according to the free liquid level domain grid area, a liquid shaking characteristic analysis model in the tank is generated, a unit set and a node set of a free liquid level domain grid are extracted, and a unit area matrix is constructed; and calculating the actual coverage area of each node in the free liquid level domain grid through the unit area matrix to obtain the actual restoring force applied to each node in the free liquid level domain grid. The contribution value of the surrounding unit area of the shared node to the node restoring force is considered, the restoring force is calculated according to the actual coverage area of the node, the calculation precision is high, and the result is accurate and reliable.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical analysis, and particularly to a method for calculating the restoring force of liquid sloshing in a liquid tank container. Background Art

[0002] The problem of liquid sloshing in a liquid tank container widely occurs in various fields of engineering. The liquid sloshing causes additional forces on the load-bearing structure of the liquid tank container, affecting the dynamic characteristics of the structure. On the one hand, the vibration generated by the liquid sloshing may lead to the instability of the load-bearing structure. On the other hand, once the coupled vibration of the liquid and the structure resonates with the structure, it will cause the fatigue failure of the structure. Therefore, to avoid the occurrence of the coupled vibration of the liquid and the load-bearing structure, it is necessary to analyze the dynamic characteristics of the liquid to obtain the sloshing frequency of the liquid. Usually, the sloshing parameters of the liquid in the tank are obtained by using the restoring force of the liquid sloshing in the liquid tank container. Therefore, the restoring force of the liquid sloshing in the liquid tank container directly affects the accuracy of the sloshing parameters of the liquid in the tank.

[0003] In the prior art, after constructing the free surface domain grid, based on the divided grid nodes and the average area of each grid cell, an average restoring force is applied to the nodes in the overall free surface domain grid, so as to obtain the sloshing parameters of the liquid in the tank. However, in actual engineering, a regular grid form cannot be obtained when dividing the grid for a more complex liquid surface, resulting in inaccurate restoring forces obtained by the equal-sized restoring force assignment method, and the vibration mode is prone to singular phenomena.

[0004] Therefore, a method for calculating the restoring force of liquid sloshing in a liquid tank container that considers the contribution of the area of each grid cell in the actual free surface domain to the sloshing restoring force is needed. Summary of the Invention

[0005] In view of this, the present invention provides a method for calculating the restoring force of liquid sloshing in a liquid tank container, which overcomes the problems of insufficient accuracy of the calculation results and singular phenomena in the vibration mode caused by applying equal-sized restoring forces to each node in the free surface domain grid in the existing method.

[0006] For this purpose, the present invention provides the following technical solutions:

[0007] A method for calculating the restoring force of liquid sloshing in a liquid tank container includes:

[0008] Construct a structural domain and a liquid domain in the tank container, and use the surface grid of the liquid domain in the tank container as the free surface domain grid;

[0009] Combine the structural domain, the liquid domain in the tank container, and the free surface domain grid to obtain a liquid sloshing model in the tank container;

[0010] Based on the liquid sloshing model in the tank container, initialize the restoring force of each node in the free surface domain grid to obtain a dynamic liquid sloshing analysis model in the tank container;

[0011] Extract the dynamic free surface domain grid cell set and node set through preset keywords based on the dynamic liquid sloshing analysis model in the tank container;

[0012] Construct an element area matrix by using the dynamic free surface domain grid cell set and node set;

[0013] Obtain the actual covered area of each node in the dynamic free surface domain grid through the element area matrix;

[0014] Calculate the actual restoring force applied to each node in the dynamic free surface domain grid by using the actual covered area of each node in the dynamic free surface domain grid.

[0015] Further, initialize the restoring force of each node in the free surface domain grid based on the liquid sloshing model in the tank container, including:

[0016] Calculate the average restoring force of each node in the free surface domain grid:

[0017] F 恢复力 = ρgA

[0018] In the formula, ρ is the liquid density, g is the acceleration of gravity, and A is the area of a free surface domain grid, that is, the ratio of the free surface domain grid area to the number of cells;

[0019] Use the average restoring force of each node in the free surface domain grid as the initial value of the restoring force of each node in the free surface domain grid.

[0020] Further, construct an element area matrix by using the dynamic free surface domain grid cell set and node set, including:

[0021] Construct a node space coordinate matrix with node numbers and node space coordinates as rows and columns by using the numbers of all nodes included in each element in the dynamic free surface and the positions of these nodes in the node set;

[0022] Calculate the area of any element by the space coordinates of all nodes included in this element:

[0023]

[0024] p = (a + b + c + d) / 2

[0025] In the formula, a, b, c, and d are the side lengths of the four sides of the element;

[0026] Construct an element area matrix by using the numbers of all elements and the areas of these elements.

[0027] Further, obtaining the actual covered area of each node of the dynamic free liquid surface domain grid through the unit area matrix includes:

[0028] Converting the grid node into a shared node of all grid cells containing this grid node;

[0029] Calculating the actual covered area of each shared node:

[0030]

[0031] In the formula, A 1 ~A j are the unit areas of each cell containing this shared node, A i is the actual covered area corresponding to this shared node, and n is the total number of cells containing this shared node.

[0032] Further, calculating the actual restoring force of each node in the dynamic free liquid surface domain grid by using the actual covered area of each node of the dynamic free liquid surface domain grid includes:

[0033] Calculating the restoring force of each shared node based on the actual covered area of each shared node, and taking it as the actual restoring force applied by each grid node.

[0034] Further, constructing the structural domain and the liquid domain inside the tank container, and taking the surface grid of the liquid domain inside the tank container as the free liquid surface domain grid includes:

[0035] Dividing the grid of the three-dimensional model structure domain of the tank container, and setting the structural material properties and boundary conditions;

[0036] Dividing the grid of the liquid domain, and setting the bulk modulus of the liquid material and the liquid density parameter;

[0037] Taking the surface grid of the liquid domain inside the tank container as the free liquid surface domain grid, and setting the material properties of the free liquid surface domain grid;

[0038] The unit type of the free liquid surface domain grid is different from that of the liquid domain grid.

[0039] Further, the unit of the structural domain grid is a solid unit or a shell unit;

[0040] The unit of the liquid domain grid is an AC3D8 acoustic unit;

[0041] The unit type of the liquid surface grid is an M3D4 membrane unit.

[0042] Further, combining the structural domain, the liquid domain inside the tank container, and the free liquid surface domain grid includes:

[0043] Connect the liquid domain with the structural domain mesh and connect the liquid domain with the free surface domain mesh. A storage medium, characterized in that the storage medium includes a stored program, wherein when the program runs, it executes the method according to any one of claims 1 to 8.

[0044] Advantages and positive effects of the present invention:

[0045] By introducing shared nodes and calculating the liquid sloshing restoring force based on the actual covered area of the shared nodes, reassigning values to the nodes of the free surface domain mesh, and considering the contribution of the area of each surrounding unit to the node restoring force, the calculation result of the liquid sloshing frequency of the present invention is more accurate; and the singularity phenomenon of the vibration mode is avoided.

[0046] The present invention calculates the actual covered area of the shared nodes by constructing a unit area matrix, with high calculation efficiency and convenient operation. Description of the drawings

[0047] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0048] Figure 1 It is a flowchart of the method according to an embodiment of the present invention;

[0049] Figure 2 It is a schematic diagram of a tank container model in an embodiment of the present invention;

[0050] Figure 3 It is a schematic diagram of the shared nodes of the free surface domain mesh in an embodiment of the present invention;

[0051] Figure 4 It is a comparison diagram of the liquid sloshing vibration modes of the free liquid surface in a tank in an embodiment of the present invention;

[0052] Figure 5 It is a flowchart of the method according to an application embodiment of the present invention;

[0053] Figure 6 It is a schematic diagram of the input device for calculating the liquid restoring force according to an application embodiment of the invention. Detailed implementation manners

[0054] To enable those skilled in the art to better understand the solution of the present invention, the following will clearly and completely describe the technical solution in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0055] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and do not necessarily need to be used to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0056] S1. Construct a structural domain;

[0057] Establish a three-dimensional model of the tank container to be analyzed;

[0058] Divide the grid of the three-dimensional model structure domain of the tank container. After completing the grid division of the structure domain, set the structural material properties and relevant boundary conditions to obtain the structure domain.

[0059] In this embodiment, the element type of the structure domain grid is a solid element or a shell element;

[0060] S2. Construct the liquid domain inside the tank container;

[0061] Divide the grid of the liquid domain;

[0062] In this embodiment, the element type of the liquid domain grid is an AC3D8 acoustic element;

[0063] After completing the grid division of the liquid domain, set the bulk modulus of the liquid material and the liquid density parameter to obtain the liquid domain.

[0064] S3. Obtain the grid of the free liquid surface domain, and construct a set of free liquid surface domain grid elements and a set of free liquid surface domain grid element nodes;

[0065] In this embodiment, the surface grid of the liquid domain is used as the grid component of the free liquid surface domain; when the model is established, the liquid domain and the free liquid surface domain grid are set in different components respectively;

[0066] In this embodiment, the element type of the free liquid surface domain mesh is the M3D4 membrane element;

[0067] Set the material properties of the free liquid surface domain mesh membrane elements according to the requirements of the liquid material properties to obtain the free liquid surface domain mesh element set and the free liquid surface domain mesh node set.

[0068] S4. Combine the analysis domains to obtain the liquid sloshing model inside the tank container;

[0069] Connect the liquid domain mesh with the structural domain mesh; connect the liquid domain mesh with the free surface domain mesh to obtain the liquid sloshing model inside the tank container.

[0070] S5. Initialize the restoring forces of each node in the free liquid surface domain mesh based on the liquid sloshing model inside the tank container to obtain the dynamic liquid sloshing analysis model inside the tank container

[0071] In this embodiment, calculate the average restoring force of the free liquid surface domain mesh nodes using the free liquid surface domain mesh element set and the free liquid surface domain mesh node set:

[0072] F 恢复力 = ρgA

[0073] In the formula, ρ is the liquid density, g is the acceleration due to gravity, and A is the area of a free liquid surface domain mesh.

[0074] Use the average restoring force of the free liquid surface domain mesh nodes as the initial restoring force assignment for the free liquid surface domain mesh nodes.

[0075] S6. Construct the element area matrix of the dynamic free liquid surface domain mesh;

[0076] Use the numbers of all the nodes included in each element in the dynamic free liquid surface domain mesh and their positions in the node set to construct a node space coordinate matrix with the node numbers and node information as rows and columns;

[0077] Calculate the area of any element by forming the node numbers and node information included in the element, that is, the spatial coordinates of the nodes:

[0078]

[0079] p = (a + b + c + d) / 2

[0080] In the formula, a, b, c, and d are the side lengths of the four sides of the element.

[0081] Use the numbers of all the elements and the area of each element to construct the element area matrix.

[0082] S7. Introduce shared nodes;

[0083] Taking each grid node as the shared node of all grid cells containing this grid node, as Figure 2 shown; the number and cell numbers of the cells sharing a node in multiple free surface domain grid cells, that is, node i is the shared node of grid cells 1, 2, 3, and 4.

[0084] S8. Obtain the actual restoring force of each node in the free surface domain grid through the shared node and the cell area matrix of the free surface domain grid;

[0085] Calculate the actual covered area of each shared node:

[0086]

[0087] In the formula, A 1 ~A j are the areas of each cell containing this shared node, A i is the actual covered area corresponding to this shared node, and n is the total number of cells containing this shared node.

[0088] Calculate the restoring force of each shared node with the actual covered area of each shared node as the actual restoring force of each dynamic free surface domain grid node.

[0089] Combined with Figure 3 shown below, the method of the present invention will be further described with the following application embodiments:

[0090] Step 1. Import the geometric model of the tank box into ABAQUS, perform mesh division on each region part, as Figure 2 shown in the mesh model. Define the structural element types, material properties, and connection relationships of each region part, initialize the free surface restoring force value, create an analysis step and output a *.INP file;

[0091] Step 2. Use MATLAB software to create a *.m file, write a statement to open the *.INP file and read the free surface domain grid cells and grid cell nodes through keywords. The statements written in MATLAB are as follows:

[0092] fin=fopen('*.INP','r');Nset='*Part,name=FREE_SURFACE_NODE_SET';

[0093] Nset1='*Node';

[0094] The above statement opens a *.INP file through the fopen function, locates it according to the keyword "FREE_SURFACE_NODE_SET" established in ABAQUS and the formats (Nset and Nset1) in the INP file, and stores the free surface domain mesh node set in an array; use the same sentence pattern:

[0095] fin = fopen('*.INP', 'r'); MED5 = '*Element,type=M3D4';

[0096] MED4 = '*Nset,nset=FREE_SURFACE_ELEMENT_SET,generate';

[0097] Store the free surface domain mesh element set in an array.

[0098] Step 3: Write statements using a loop structure: for jj = 1:N_Node, where N_Node is the number of nodes and jj is the loop variable representing the node number currently being processed, to traverse all nodes. Write statements using the find function: [m,n] = find(Element(:,2:5) == Node(jj,1)), which is used to find the elements in columns 2 to 5 of the Element matrix that match the node Node(jj,1). m and n are the results returned by the find function, m represents the row number of the element related to the node, and n represents the column number. Write statements: Size_m = size(m), where size(m) returns the size of the matrix m, and Size_m(1) represents the number of elements related to node jj. Use an if-else statement to process the restoring force of the node with multiple mesh elements sharing the node in sequence. When there are 7 mesh elements associated with the shared node, write the following statements:

[0099] If Size_m(1) == 7,

[0100] Node_Force(jj) = 1 / 7.*(EA(m(1)) + EA(m(2)) + EA(m(3)) + EA(m(4)) + EA(m(5)) + EA(m(6)) + EA(m(7)))*Rou*g

[0101] The restoring force value of the shared node can be solved respectively according to the number of mesh elements associated with the shared node.

[0102] Step 4: Reassign the nodal restoring forces calculated in MATLAB in the following format: fprintf(fid,'*Spring,elset=SPRINGS / DASHPOTS-%d-SPRING-spring\n%d\n%f\n*Element,type=Spring1,elset=SPRINGS / DASHPOTS-%d-SPRING-spring\n%d,%s,%d\n',Node(kk,1),3,Node_Force(kk),Node(kk,1),Node(kk,1),'Part-2-1',Node(kk,1));

[0103] Automatically reassign the initial values of the restoring forces in the format of the INP file and save them as a new INP file for ABAQUS calculation and analysis.

[0104] In the application embodiment of this application, the liquid restoring force calculation input device is as Figure 6 shown.

[0105] The following simulation experiment is used to further verify the effect of the method of the present invention:

[0106] Analysis results are obtained by using the method of the average restoring force of each node in the traditional free liquid surface domain grid, the method of the present invention, and the liquid sloshing frequency formula in the cylindrical tank container, as shown in Table 1 and Figure 4 shown:

[0107] According to the calculation results of the liquid sloshing frequency of the free liquid surface in the tank shown in Table 1, it can be seen that the error of calculating the liquid sloshing frequency parameters by using the method of the present invention is lower than that of the traditional method, and the calculation accuracy is higher.

[0108] According to Figure 4 shown in the comparison of the vibration mode results calculated by the two methods, it can be seen that the liquid sloshing vibration mode of the method of the present invention avoids the singular phenomenon of the vibration mode and the singular points on the boundary. In Figure 4 the comparison result of the third-order vibration mode is particularly obvious, which is precisely because the method of the present invention can calculate the liquid restoring force according to the actual covered area of the shared nodes of the grid elements and quickly load, solving the problem that the traditional method can only apply equal liquid restoring forces at the grid nodes for calculation and analysis and the calculation result accuracy is relatively low.

[0109] Among them, the liquid sloshing frequency formula in the cylindrical tank container:

[0110]

[0111] In the formula, w i is the i-th order frequency of liquid sloshing; λ iis the i-th root of the derivative of the first-order Bessel function, a is the semi-major axis of the tank container, and H is the liquid level height in the tank container.

[0112] Table 1

[0113]

[0114]

[0115] In summary, the present invention obtains the contribution of the actual covered area of the free liquid surface domain grid unit to the nodal restoring force by introducing shared nodes, calculates the more accurate nodal restoring force of the free liquid surface domain by applying the actual covered area of the shared nodes, and further improves the accuracy of analyzing the liquid sloshing parameters in the tank.

[0116] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the restoring force of liquid sloshing in a liquid tank, characterized in that: include: Constructing a structure domain and a liquid domain in a tank, and using the surface mesh of the liquid domain in the tank as a free liquid surface mesh; Combining the structural domain, the liquid domain in the tank, and the free liquid surface domain grids to obtain a liquid sloshing model in the tank; Initializing the restoring force of each node of the free liquid surface domain grid based on the liquid sloshing model in the tank container, and obtaining a dynamic liquid sloshing analysis model in the tank container; Based on the dynamic tank liquid sloshing analysis model, the dynamic free liquid surface domain grid unit set and node set are extracted by preset keywords; Constructing a unit area matrix using the dynamic free liquid surface domain grid unit set and node set; Obtaining the actual coverage area of ​​each node of the dynamic free liquid surface domain grid through the unit area matrix; The actual restoring force exerted by each node in the dynamic free liquid surface domain grid is calculated using the actual coverage area of ​​each node in the dynamic free liquid surface domain grid.

2. According to claim 1, a method for calculating the restoring force of liquid sloshing in a liquid tank is characterized in that: Initialize the restoring force of each node of the free surface domain grid based on the liquid sloshing model in the tank, including: Calculate the average restoring force at each node of the free surface domain mesh: F 恢复力 =ρgA Where ρ is the liquid density, g is the gravitational acceleration, and A is the mesh area of ​​a free liquid surface domain, that is, the ratio of the mesh area of ​​the free liquid surface domain to the number of cells; The average restoring force of each node in the free surface domain grid is taken as the initial value of the restoring force of each node in the free surface domain grid.

3. According to claim 1, a method for calculating the restoring force of liquid sloshing in a liquid tank is characterized in that: The unit area matrix is ​​constructed using the dynamic free liquid surface domain grid unit set and node set, including: Using the numbers of all nodes included in each unit in the dynamic free liquid surface and the positions of the nodes in the node set, a node space coordinate matrix with node numbers and node space coordinates as rows and columns is constructed; The area of ​​any unit is calculated by the spatial coordinates of all the nodes that make up the unit: p=(a+b+c+d) / 2 In the formula, a, b, c, d are the lengths of the four sides of the unit; Construct a cell area matrix using the numbers of all cells and the area of ​​the cell.

4. According to claim 1, a method for calculating the restoring force of liquid sloshing in a liquid tank is characterized in that: The actual coverage area of ​​each node of the dynamic free liquid surface domain grid is obtained through the unit area matrix, including: Convert a grid node into a shared node of all grid cells containing the grid node; Calculate the actual coverage area of ​​each shared node: In the formula, A1~A j is the area of ​​each unit containing the shared node, A i is the actual coverage area corresponding to the shared node, and n is the total number of units containing the shared node.

5. According to claim 1, a method for calculating the restoring force of liquid sloshing in a liquid tank is characterized in that: Calculating the actual restoring force of each node in the dynamic free liquid surface domain grid using the actual coverage area of ​​each node in the dynamic free liquid surface domain grid comprises: The restoring force of each shared node is calculated based on the actual coverage area of ​​each shared node, which is used as the actual restoring force applied by each grid node.

6. According to claim 1, a method for calculating the restoring force of liquid sloshing in a liquid tank is characterized in that: The construction of the structure domain and the liquid domain in the tank, and using the surface mesh of the liquid domain in the tank as the free liquid surface domain mesh, includes: Divide the structural domain mesh of the tank container 3D model and set the structural material properties and boundary conditions; Divide the liquid domain grid and set the bulk modulus and liquid density parameters of the liquid material; Using the surface mesh of the liquid domain in the tank as the free liquid surface mesh, and setting the material properties of the free liquid surface mesh; The free surface domain grid cell type is different from the liquid domain grid cell type.

7. A method for calculating the restoring force of liquid sloshing in a liquid tank according to claim 6, characterized in that: The unit of the structural domain grid is a solid unit or a shell unit; The unit of the liquid domain grid is AC3D8 acoustic unit; The unit type of the liquid surface grid is M3D4 membrane unit.

8. According to claim 6, a method for calculating the restoring force of liquid sloshing in a liquid tank is characterized in that: The combined structure domain, the liquid domain in the tank container and the free liquid surface domain grid include: Connect the liquid domain to the structure domain mesh and connect the liquid domain to the free surface domain mesh.

9. A storage medium, characterized in that: The storage medium includes a stored program, wherein when the program is run, the method according to any one of claims 1 to 8 is executed.

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