Water pressure mapping method and analysis method based on slice grid and structural grid

Abstract

The invention relates to the technical field of water pressure mapping, in particular to a water pressure mapping method and analysis method based on slice grids and structural grids, and the water pressure mapping method comprises the following steps: obtaining a three-dimensional model, slicing the three-dimensional model to obtain a plurality of slice units, and performing grid division on each slice unit; calculating the speed potential of the grid center of each slice unit based on a source sink method, and calculating the pressure data of the grid center of each slice unit according to the speed potential; performing mesh division on the three-dimensional model to obtain a finite element model, acquiring coordinates of a mesh center of each slice unit and coordinates of a mesh center of the finite element model, and interpolating and mapping pressure data of the mesh center of each slice unit to the mesh center of the finite element model by using a radial basis function, and obtaining pressure data of the grid center of the finite element model. According to the method, the accurate transmission of the hydrodynamic grid pressure data to the structural grid is realized, and powerful data support is provided for subsequent fluid-structure interaction analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of water pressure mapping, and in particular to a water pressure mapping method and an analysis method based on a slice grid and a structure grid. Background Art

[0002] Mesh mapping technology is a technology based on mathematical interpolation, optimization methods and deformable meshes for data conversion and mapping between different meshes. Mesh mapping technology is usually most widely used in fluid-solid coupling problems. Usually, the fluid solver and the structural finite element solver will have meshes of different scales and sizes at the interface, so it is necessary to conduct mesh mapping research on the interface between the two sets of fluid-solid meshes.

[0003] Mesh mapping technology is mainly used for the transfer and alignment of results between different meshes to ensure the accuracy and reliability of simulation results. It is widely used in CAD / CAE software for data exchange and conversion between different meshes. For example, mature commercial software such as ANSYS and ABAQUS include mesh mapping related functions. The mesh mapping function in these software can be used for data transfer between meshes on both sides of different mesh interfaces, or to map the stress on a mesh with large distortion to a set of meshes with less distortion.

[0004] In the existing technology, data transfer between hydrodynamic grids and structural finite element grids is basically achieved based on commercial software and other methods. The process is relatively complicated. In addition, since slice grids (usually two-dimensional, used to analyze data of a specific plane or section) and finite element grids (usually three-dimensional, used to simulate the behavior of the entire physical system or structure) have significant differences in structure, accuracy, and data representation, achieving pressure data exchange between the two is indeed a technical challenge. Summary of the invention

[0005] The purpose of the present invention is to address the defects of the prior art and provide a water pressure mapping method and analysis method based on slice grids and structural grids, which successfully realizes the accurate transmission of hydrodynamic grid pressure data to the structural grid. The data transmission between the hydrodynamic grid and the structural grid becomes seamless and efficient, providing strong data support for subsequent fluid-solid coupling analysis.

[0006] In order to solve the above technical problems, in a first aspect, the present invention provides a water pressure mapping method based on a slice grid and a structure grid, comprising:

[0007] Acquire a three-dimensional model, slice the three-dimensional model to obtain a plurality of slice units, and mesh each slice unit;

[0008] The velocity potential of the grid center of each slice unit is calculated based on the source-sink method, and the pressure data of the grid center of each slice unit is calculated according to the velocity potential;

[0009] The three-dimensional model is meshed to form a finite element model, the coordinates of the mesh center of each slice unit and the coordinates of the mesh center of the finite element model are obtained, and the radial basis function is used to interpolate the pressure data of the mesh center of each slice unit to the mesh center of the finite element model to obtain the pressure data of the mesh center of the finite element model.

[0010] Furthermore, the pressure data of the grid center of each slice unit is interpolated and mapped to the grid center of the finite element model using the radial basis function to obtain the pressure data of the grid center of the finite element model, including:

[0011] Determine the interpolation calculation dimension;

[0012] According to the coordinates of the grid nodes of each slice unit, the envelope box corresponding to each slice unit is calculated;

[0013] Determine the interpolation method within the envelope box and the interpolation method outside the envelope box;

[0014] Determine the kernel function;

[0015] According to the interpolation method within the envelope box, the mesh center of the finite element model located within the envelope box is interpolated to obtain the pressure data of the mesh center of the finite element model within the envelope box; according to the interpolation method outside the envelope box, the mesh center of the finite element model located outside the envelope box is interpolated to obtain the pressure data of the mesh center of the finite element model outside the envelope box.

[0016] Furthermore, the interpolation calculation dimension is three-dimensional.

[0017] Furthermore, the interpolation method within the envelope box is to use radial basis function for interpolation, and the interpolation method outside the envelope box is to use radial basis function for interpolation or to select the pressure data of the grid center of the nearest slice unit for assignment.

[0018] Furthermore, the kernel function includes a Gaussian distribution function, a polynomial function, an inverse polynomial function, a spline function, and a thin plate spline function.

[0019] Furthermore, the calculation formula for interpolation using radial basis function is:

[0020] Where n means that the slice unit includes n grids, x n represents the coordinate point of the center of the nth grid, f n (x) is the kernel function corresponding to the nth coordinate point, ωn is the weight corresponding to the nth coordinate point, F j (x) is the interpolation result of the jth grid center of the finite element model;

[0021] The weights are obtained by solving the inverse of the matrix, and the original function can be obtained through the weights to perform interpolation calculations.

[0022] In a second aspect, the present invention provides an analysis method of the water pressure mapping method based on radial basis functions, comprising:

[0023] Establishing a three-dimensional model corresponding to the structure, slicing the three-dimensional model to obtain a plurality of slice units, meshing each slice unit, and calculating pressure data at the mesh center of each slice unit;

[0024] The three-dimensional model is meshed to obtain a finite element model, the coordinates of the mesh center of the finite element model are calculated, and the coordinates of the mesh center below the draft of the finite element model are screened out;

[0025] According to the pressure data of the grid center of each slice unit and using the radial basis function, the pressure data of the grid center below the draft of the finite element model is calculated;

[0026] The structural strength calculation is performed based on the pressure data at the grid center below the draft of the finite element model.

[0027] Furthermore, the calculation of the pressure data at the center of the grid below the draft of the finite element model includes:

[0028] Save the coordinates of the grid center of each slice unit and its corresponding pressure data as well as the coordinates of the grid center below the draft of the finite element model into two txt format files;

[0029] Import the two txt format files into MATLAB to generate a first data matrix and a second data matrix. The first data matrix includes the coordinates of the grid center of each slice unit and its corresponding pressure data, and the second data matrix includes the coordinates of the grid center below the draft of the finite element model.

[0030] Calculate the pressure data corresponding to each coordinate point of the second data matrix using the radial basis function and the first data matrix to obtain the second data matrix including the pressure data of the grid center below the draft of the finite element model;

[0031] The second data matrix is ​​input into the finite element Inp file through MATLAB, and the structural strength of the finite element model is analyzed and calculated using the finite element software ABAQUS.

[0032] In a third aspect, the present invention provides a non-transitory computer-readable storage medium for storing a computer program or instruction. When the computer program or instruction is executed by a computer, the water pressure mapping method based on a slice grid and a structured grid and / or the analysis method are implemented.

[0033] In a fourth aspect, the present invention provides a computer program product, which includes computer instructions; when part or all of the computer instructions are run on a computer, the water pressure mapping method based on slice grid and structure grid and / or the analysis method are executed.

[0034] The beneficial effects of the present invention are:

[0035] 1. The present invention applies radial basis function interpolation technology to the grid mapping process, and successfully realizes the accurate transmission of hydrodynamic grid pressure data to the structural grid (i.e., the grid of the finite element model). The data transmission between the hydrodynamic grid and the structural grid becomes seamless and efficient, providing strong data support for subsequent fluid-solid coupling analysis.

[0036] 2. The present invention introduces the radial basis function interpolation method and constructs an interpolation function that accurately reflects the spatial distribution law of data based on the known hydrodynamic slice grid pressure data. This function not only has a high degree of accuracy and continuity, but also can effectively avoid the error accumulation problem in traditional interpolation methods. On this basis, the constructed interpolation function is applied to the structural grid to achieve accurate mapping of pressure data. In addition, RBF has a simple form and usually only involves a center point and a scale parameter, which makes RBF easy to implement and adjust in practice, and can be applied to a variety of different problem areas.

[0037] 3. The present invention uses MATLAB to realize fast mapping between grid data, uses MATLAB to extract data of slice grids and grids of finite element models and generate a data matrix, and uses radial basis functions to perform interpolation calculations on grid center pressure data of the finite element model to obtain a data matrix containing grid center coordinates and pressure data of the finite element model, and finally forms a new finite element model file containing accurate pressure mapping data. Compared with traditional grid mapping methods, the transmission efficiency between grid data is greatly improved, and there is no need for cumbersome input parameters, and mapping data can be input with one click. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a schematic diagram of the radial basis function interpolation of the present invention;

[0039] Figure 2 This is a schematic diagram of the pressure mapping principle of the present invention;

[0040] Figure 3It is a schematic diagram of pressure mapping of the present invention;

[0041] Figure 4 Flow chart of the structural analysis method of the present invention. DETAILED DESCRIPTION

[0042] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0043] The radial basis function is a real-valued function whose value depends only on the distance from the origin, that is, the distance to any point c, where point c is called the center point. Any function that satisfies this property is called a radial basis function, and the standard one generally uses the Euclidean distance (also called the Euclidean radial basis function).

[0044] The radial basis function space is more suitable for isotropic problems. Krige, who first proposed the radial basis function, regarded the deposition of mineral deposits as the realization of an isotropic stable random function and proposed the Kriging method. At this time, people first made a stretching transformation perpendicular to the river direction, and then approximated it with the radial basis function, and then used compression transformation to compensate for the radial basis function.

[0045] The general principle of the radial basis function is to use a series of functions to fit the original function, as shown in the following formula: F(x) = ∑ω i *f i (x c ,x)

[0046] Where f(x c ,x) is the basis function, which is a central symmetric function with the center point at x c ω is the weight of each function. So we only need to find the weight, and we can use the value of the basis function at each point to calculate the function of the entire domain. Solving the weight is also a simple linear algebra problem, which can be obtained directly by inverting the linear equation system.

[0047] As shown in the above formula, when interpolating, we must first select a kernel function as the interpolation kernel function. By selecting different kernel functions, we can construct a function space. This function space can approximate almost all functions with high accuracy. The following introduces some commonly used kernel functions.

[0048] (1) Gaussian distribution function

[0049] The Gaussian kernel function can realize nonlinear mapping of data and has good processing capabilities for nonlinearly separable data sets. In addition, the Gaussian kernel function has fewer parameters, which helps reduce the complexity of the model and the risk of overfitting.

[0050] (2) Multi-Quadric Function

[0051] Polynomial functions usually have a smooth property, which helps to reduce the impact of noise and outliers during data processing and fitting, but polynomial functions often have locality, that is, they only focus on local information near the data points, which helps to deal with complex data structures and local features.

[0052] (3) Inverse Multi-Quadric function

[0053] The inverse polynomial function is often used to describe physical phenomena with long-range forces, such as gravity, etc. It can capture the characteristics of such long-range forces and play an important role in the corresponding application fields.

[0054] (4) Spline function

[0055] The spline function can preserve the detailed features of the local terrain during the interpolation and fitting process, which is very important for terrain analysis, surface reconstruction and other fields. In addition, the spline function can generate continuous and smooth fitting surfaces with good numerical stability and convergence, which helps to ensure the accuracy and reliability of the solution process.

[0056] (5) Thin plate spline function

[0057] The thin plate spline function has a clear physical meaning, and its energy function can be interpreted as the minimum energy of bending a thin plate. Only a small number of transformation parameters and marking points are needed when solving it, and there is only one solution.

[0058] An embodiment of the present invention provides a water pressure mapping method based on radial basis function, comprising:

[0059] Acquire a three-dimensional model, slice the three-dimensional model to obtain a plurality of slice units, and mesh each slice unit;

[0060] The velocity potential of the grid center of each slice unit is calculated based on the source-sink method, and the pressure data of the grid center of each slice unit is calculated according to the velocity potential;

[0061] The finite element model is obtained by meshing the three-dimensional model, and the coordinates of the mesh center of each slice unit and the mesh center of the finite element model are obtained. The pressure data of the mesh center of each slice unit is interpolated and mapped to the mesh center of the finite element model using the radial basis function to obtain the pressure data of the mesh center of the finite element model.

[0062] The present invention divides the three-dimensional model into multiple slice units, uses the source-sink method to calculate the pressure data of the grid center of each slice unit, and uses the radial basis function to perform spatial interpolation according to the coordinates of the grid center of the finite element model to obtain the pressure data of the grid center of the finite element model, thereby successfully realizing the accurate transmission of the hydrodynamic grid pressure data to the structural grid.

[0063] In some embodiments, Figure 1 As shown, the pressure data for calculating the mesh center of the finite element model includes:

[0064] Determine the interpolation calculation dimension; generally, the interpolation calculation dimension includes one dimension, two dimensions, and three dimensions. In the present invention, the interpolation calculation dimension adopts three dimensions;

[0065] According to the coordinates of the grid nodes of each slice unit, the envelope box corresponding to each slice unit (i.e. Figure 1 The envelope box is a box formed by connecting the grid nodes of the slice unit close to the boundary, which is generally a cuboid.

[0066] Determine the interpolation method within the envelope box and the interpolation method outside the envelope box; since the mesh division of the slice unit is sparser than that of the finite element model, part of the mesh of the finite element model will be outside the envelope box, so it is necessary to perform interpolation calculations within the envelope box and outside the envelope box respectively, among which the interpolation method within the envelope box is to use radial basis function for interpolation, and the interpolation method outside the envelope box is to use radial basis function for interpolation or to select the pressure data of the grid center of the nearest slice unit for assignment.

[0067] Determine a kernel function, the kernel function includes a Gaussian distribution function, a polynomial function, an inverse polynomial function, a spline function, and a thin plate spline function;

[0068] According to the interpolation method within the envelope box, the mesh center of the finite element model located within the envelope box is interpolated to obtain the pressure data of the mesh center of the finite element model within the envelope box; according to the interpolation method outside the envelope box, the mesh center of the finite element model located outside the envelope box is interpolated to obtain the pressure data of the mesh center of the finite element model outside the envelope box.

[0069] The specific calculation formula is: Where n means that the slice unit includes n grids, x n represents the coordinate point of the center of the nth grid, f n (x) is the kernel function corresponding to the nth coordinate point, ω n is the weight corresponding to the nth coordinate point, F j (x) is the interpolation result of the jth grid center of the finite element model;

[0070] The weights are obtained by solving the inverse of the matrix, and the original function can be obtained through the weights to perform interpolation calculations.

[0071] like Figure 4 As shown, an embodiment of the present invention further provides an analysis method, which is described by taking a seaplane as an example, comprising:

[0072] Use Abaqus to build the corresponding three-dimensional model of the seaplane and get the Inp file, such as Figure 2 As shown, the Inp file includes PART data block, Assembly data block, and Step data block;

[0073] Slice the corresponding part of the fuselage of the three-dimensional model along the length direction to obtain multiple slice units, mesh each slice unit, calculate the pressure data of the mesh center of each slice unit, correspond the mesh center coordinates of the slice unit with the pressure data and save them as a first txt format file;

[0074] Meshing the three-dimensional model to obtain a finite element model; extracting the Node and Element data of the finite element model (e.g., the node and element information will be extracted in the form of a matrix, and geometric elements such as triangular face elements and quadrilateral face elements will be identified accordingly), and obtaining the coordinates of the mesh center of the finite element model; screening out the coordinates of the mesh center below the draft of the seaplane, and saving the screened coordinates as a second txt format file;

[0075] Import the first txt format file and the second txt format file into MATLAB to generate a first data matrix and a second data matrix, wherein the first data matrix includes the coordinates of the grid center of each slice unit and its corresponding pressure data, and the second data matrix includes the coordinates of the grid center below the draft of the finite element model;

[0076] The radial basis function and the first data matrix are used to calculate the pressure data corresponding to each coordinate in the second data matrix, and the second data matrix containing the pressure data of the grid center below the draft of the finite element model is obtained, so as to realize the rapid mapping of water pressure from the slice grid to the structure grid;

[0077] Generate the second data matrix as a txt file and input it into the Inp file through MATLAB to obtain a new Inp file containing accurate pressure mapping data, such as Figure 3 As shown, Abaqus is used to set the mesh parameters, such as material density, Poisson's ratio, mesh properties and other related properties, and Abaqus is used to analyze and calculate the structural strength of the seaplane.

[0078] An embodiment of the present invention also provides a non-transitory computer-readable storage medium for storing a computer program or instruction. When the computer program or instruction is executed by a computer, the radial basis function-based water pressure mapping method and / or the structural analysis method are implemented.

[0079] An embodiment of the present invention also provides a computer program product, which includes computer instructions; when part or all of the computer instructions are run on a computer, the radial basis function-based water pressure mapping method and / or the structural analysis method are executed.

[0080] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions may be transmitted from one website, computer, server or data center to another website, computer, server or data center via wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium may be any available medium that can be accessed by a computer or a data storage device such as a server or data center that includes one or more available media integrated therein. The available medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a magnetic tape), an optical medium (e.g., a high-density digital video disc (DVD)), or a semiconductor medium (e.g., a solid state disk (SSD)), etc.

[0081] The embodiments described above are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A water pressure mapping method based on slice grid and structure grid, characterized by: include: Acquire a three-dimensional model, slice the three-dimensional model to obtain a plurality of slice units, and mesh each slice unit; The velocity potential of the grid center of each slice unit is calculated based on the source-sink method, and the pressure data of the grid center of each slice unit is calculated according to the velocity potential; The three-dimensional model is meshed to form a finite element model, the coordinates of the mesh center of each slice unit and the coordinates of the mesh center of the finite element model are obtained, and the radial basis function is used to interpolate the pressure data of the mesh center of each slice unit to the mesh center of the finite element model to obtain the pressure data of the mesh center of the finite element model.

2. The water pressure mapping method based on slice grid and structure grid according to claim 1, characterized in that: The radial basis function is used to interpolate the pressure data of the grid center of each slice unit to the grid center of the finite element model to obtain the pressure data of the grid center of the finite element model, including: Determine the interpolation calculation dimension; According to the coordinates of the grid nodes of each slice unit, the envelope box corresponding to each slice unit is calculated; Determine the interpolation method within the envelope box and the interpolation method outside the envelope box; Determine the kernel function; According to the interpolation method within the envelope box, the mesh center of the finite element model located within the envelope box is interpolated to obtain the pressure data of the mesh center of the finite element model within the envelope box; according to the interpolation method outside the envelope box, the mesh center of the finite element model located outside the envelope box is interpolated to obtain the pressure data of the mesh center of the finite element model outside the envelope box.

3. The water pressure mapping method based on slice grid and structure grid according to claim 2, characterized in that: The interpolation calculation dimension is three-dimensional.

4. The water pressure mapping method based on slice grid and structure grid according to claim 2, characterized in that: The interpolation method within the envelope box is to use radial basis function for interpolation, and the interpolation method outside the envelope box is to use radial basis function for interpolation or to select the pressure data of the grid center of the nearest slice unit for assignment.

5. The water pressure mapping method based on slice grid and structure grid according to claim 2, characterized in that: The kernel function includes a Gaussian distribution function, a polynomial function, an inverse polynomial function, a spline function, and a thin plate spline function.

6. The water pressure mapping method based on slice grid and structure grid according to claim 5, characterized in that: The calculation formula for interpolation using radial basis function is: Where n means that the slice unit includes n grids, x n represents the coordinate point of the center of the nth grid, f n (x) is the kernel function corresponding to the nth coordinate point, ω n is the weight corresponding to the nth coordinate point, F j (x) is the interpolation result of the jth grid center of the finite element model; The weights are obtained by solving the inverse of the matrix, and the original function can be obtained through the weights to perform interpolation calculations.

7. An analysis method for the water pressure mapping method based on radial basis function according to any one of claims 1 to 6, characterized in that: include: Establishing a three-dimensional model corresponding to the structure, slicing the three-dimensional model to obtain a plurality of slice units, meshing each slice unit, and calculating pressure data at the mesh center of each slice unit; The three-dimensional model is meshed to obtain a finite element model, the coordinates of the mesh center of the finite element model are calculated, and the coordinates of the mesh center below the draft of the finite element model are screened out; According to the pressure data of the grid center of each slice unit and using the radial basis function, the pressure data of the grid center below the draft of the finite element model is calculated; The structural strength calculation is performed based on the pressure data at the grid center below the draft of the finite element model.

8. The analysis method according to claim 7, characterized in that: Calculation of pressure data at the center of the mesh below the draft of the finite element model includes: Save the coordinates of the grid center of each slice unit and its corresponding pressure data as well as the coordinates of the grid center below the draft of the finite element model into two txt format files; Import the two txt format files into MATLAB to generate a first data matrix and a second data matrix. The first data matrix includes the coordinates of the grid center of each slice unit and its corresponding pressure data, and the second data matrix includes the coordinates of the grid center below the draft of the finite element model. Calculate the pressure data corresponding to each coordinate point of the second data matrix using the radial basis function and the first data matrix to obtain the second data matrix including the pressure data of the grid center below the draft of the finite element model; The second data matrix is ​​input into the finite element Inp file through MATLAB, and the structural strength of the finite element model is analyzed and calculated using the finite element software ABAQUS.

9. A non-transitory computer-readable storage medium, characterized in that: Used to store computer programs or instructions, when the computer programs or instructions are executed by a computer, the water pressure mapping method based on slice grids and structure grids as described in any one of claims 1 to 6 and / or the analysis method as described in any one of claims 7 and 8 are implemented.

10. A computer program product, characterized in that The computer program product includes computer instructions; when part or all of the computer instructions are run on a computer, the water pressure mapping method based on slice grid and structure grid as described in any one of claims 1 to 6 and / or the analysis method as described in any one of claims 7 and 8 are executed.

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