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

Abstract

The present application relates to the technical field of water pressure mapping, and particularly relates to a water pressure mapping method and analysis method based on slice grids and structural grids, the water pressure mapping method comprising: 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 velocity potential of the grid center of each slice unit based on the source-sink method, and calculating the pressure data of the grid center of each slice unit according to the velocity potential; performing grid division on the three-dimensional model to obtain a finite element model, obtaining the coordinates of the grid center of each slice unit and the coordinates of the grid center of the finite element model, and using a radial basis function to interpolate and map 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. The present application realizes accurate transmission of hydrodynamic grid pressure data to structural grids, and provides strong data support for subsequent fluid-structure coupling analysis.

Description

TECHNICAL FIELD

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

[0002] Grid mapping technology is a technology based on mathematical interpolation, optimization method and deformed grid for data conversion and mapping between different grids. Grid mapping technology is most widely used in fluid-structure coupling problems. Generally, fluid solver and structure finite element solver have different scale and size of grids on the interface, so it is necessary to carry out grid mapping research of fluid-structure two sets of grids on the interface.

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

[0004] In the existing technology, the data transmission between hydrodynamic grid and structure finite element grid is basically realized based on commercial software method, which is complex. And due to the significant differences in structure, precision and data representation between slice grid (usually two-dimensional, used for analyzing data of a certain plane or section) and finite element grid (usually three-dimensional, used for simulating the behavior of the entire physical system or structure), it is indeed a technical challenge to realize the pressure data exchange between the two. SUMMARY

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

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

[0007] obtaining a three-dimensional model, slicing the three-dimensional model to obtain a plurality of slice units, and dividing the slice units into grids;

[0008] The velocity potential of the grid center of each slice unit is calculated based on the source and 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 grid center of each slice unit and the coordinates of the grid center of the finite element model are obtained, the pressure data of the grid center of each slice unit is interpolated and mapped to the grid center of the finite element model by using the radial basis function, and the pressure data of the grid center of the finite element model is obtained.

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

[0011] Determine the interpolation calculation dimension;

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

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

[0014] Determine the kernel function;

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

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

[0017] Further, the interpolation method within the envelope box range is interpolation by using the radial basis function, and the interpolation method outside the envelope box range is interpolation by using the radial basis function or assigning the pressure data of the grid center of the nearest slice unit.

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

[0019] Further, the calculation formula of interpolation by using the radial basis function is:

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

[0021] According to the inverse solution of the matrix, the weight is obtained, and the original function is obtained through the weight, so as to perform interpolation calculation.

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

[0023] A three-dimensional model corresponding to the structure is established, a plurality of slice units are obtained by slicing the three-dimensional model, each slice unit is meshed, and the pressure data of the grid center of each slice unit is calculated;

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

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

[0026] According to the pressure data of the grid center below the waterline of the finite element model, the structural strength is calculated.

[0027] Further, the calculation of the pressure data of the grid center below the waterline of the finite element model comprises:

[0028] The coordinates of the grid center of each slice unit and the corresponding pressure data and the coordinates of the grid center below the waterline of the finite element model are saved as two txt format files;

[0029] The two txt format files are imported into MATLAB to generate a first data matrix and a second data matrix, the first data matrix comprising the coordinates of the grid center of each slice unit and the corresponding pressure data, and the second data matrix comprising the coordinates of the grid center below the waterline of the finite element model;

[0030] The pressure data corresponding to each coordinate point of the second data matrix is calculated by using the radial basis function and the first data matrix, so as to obtain the second data matrix comprising the pressure data of the grid center below the waterline 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 by using the finite element software ABAQUS.

[0032] In a third aspect, the present application provides a non-transitory computer readable storage medium for storing a computer program or instructions, which when executed by a computer, cause the slice grid and structure grid based water pressure mapping method and / or the analysis method to be implemented.

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

[0034] The present application has the following beneficial effects:

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

[0036] 2. The present application introduces the radial basis function interpolation method, constructs an interpolation function that accurately reflects the data space distribution law according to the known hydrodynamic slice grid pressure data. This function not only has high 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 structure grid, realizing the accurate mapping of pressure data. In addition, the form of RBF is simple, usually only involving a center point and a scale parameter, which makes RBF easy to implement and adjust in practice, and can be applied to various problem fields.

[0037] 3. The present application realizes the rapid mapping between grid data by using MATLAB, extracts the data of the slice grid and the grid of the finite element model by using MATLAB and generates a data matrix, and performs interpolation calculation of the grid center pressure data of the finite element model by using the radial basis function, to obtain a data matrix containing the grid center coordinates and pressure data of the finite element model, and finally form a new finite element model file containing accurate pressure mapping data. Compared with the traditional grid mapping method, the transmission efficiency between grid data is greatly improved, and there is no need for tedious input parameters, only one key input mapping data is needed. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 The principle diagram of the radial basis function interpolation of the present application;

[0039] Figure 2 The principle diagram of the pressure mapping of the present application;

[0040] Figure 3A pressure mapping schematic diagram of the present application;

[0041] Figure 4 A flow chart of the structure analysis method of the present application. DETAILED DESCRIPTION

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

[0043] A radial basis function is a real-valued function whose value depends only on the distance from the origin, i.e. the distance to any point c, which 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 resources as the realization of a stable random function in all directions, and proposed the Kriging method. At this time, people first make a stretching transformation perpendicular to the river direction in space, and then use the radial basis function to approximate, and then make a compression transformation to make up for the.

[0045] The approximate principle of the radial basis function is to use a series of functions to superimpose and 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 center-symmetric function, and the function center point is at x c . ω is the weight of each function. Therefore, only the weight needs to be solved, and the value of the basis function at each point can be used to calculate the function of the entire domain. And solving the weight is also a simple linear algebra problem, which can be obtained directly by using the inverse of linear equations.

[0047] As shown in the above formula, when interpolating, a kernel function is first selected as the kernel function for interpolation. By selecting different kernel functions, a function space can be constructed, which can almost approximate all functions with high accuracy. Some commonly used kernel functions are introduced below.

[0048] (1) Gaussian (Gauss) distribution function

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

[0050] (2) Multi-Quadric function

[0051] The polynomial function generally has the property of smoothness, which helps to reduce the influence of noise and outliers in the data processing and fitting process, but the polynomial function often has locality, that is, it only focuses on the local information near the data points, which helps to process complex data structures and local features.

[0052] (3) Inverse Multi-Quadric function

[0053] The inverse polynomial function is usually used to describe physical phenomena with long-range forces, such as universal gravitation, 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 local terrain in the interpolation and fitting process, which is very important for terrain analysis, surface reconstruction, etc. Moreover, the spline function can generate a continuous and smooth fitting surface, with good numerical stability and convergence, which helps to ensure the accuracy and reliability in the solving process.

[0056] (5) Thin plate spline function

[0057] The thin plate spline function has a clear physical meaning, and its energy function can be explained as the minimum energy of bending a thin plate. Moreover, only a small number of transformation parameters and marker points are needed in solving, and there is only one unique solution.

[0058] Embodiments of the present application provide a water pressure mapping method based on radial basis function, comprising:

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

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

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

[0062] The present application divides the three-dimensional model into a plurality of slice units, calculates pressure data of the grid centers of each slice unit by using a source-sink method, and obtains pressure data of the grid centers of the finite element model by using a radial basis function and spatial interpolation according to the coordinates of the grid centers of the finite element model, thereby successfully realizing accurate transmission of hydrodynamic grid pressure data to structural grid.

[0063] In some embodiments, as shown in Figure 1 calculating pressure data of the grid centers of the finite element model comprises:

[0064] determining an interpolation calculation dimension; generally, the interpolation calculation dimension includes one dimension, two dimensions and three dimensions, and in the present application, the interpolation calculation dimension is three dimensions;

[0065] calculating an envelope box (i.e., a package line in Figure 1 ) corresponding to each slice unit according to the coordinates of the grid nodes of each slice unit; the envelope box is a box body formed by connecting the grid nodes of the slice unit close to the boundary, and is generally a cuboid;

[0066] determining an interpolation method within the envelope box range and an interpolation method outside the envelope box range; since the mesh division of the slice unit is more sparse than the mesh division of the finite element model, part of the grid of the finite element model is located outside the envelope box range, and therefore interpolation calculation is required within and outside the envelope box range, wherein the interpolation method within the envelope box range is interpolation by using a radial basis function, and the interpolation method outside the envelope box range is interpolation by using a radial basis function or assigning pressure data of the grid center of the nearest slice unit.

[0067] determining a kernel function, the kernel function including a Gaussian distribution function, a polynomial function, an inverse polynomial function, a spline function and a thin-plate spline function;

[0068] interpolating and calculating the grid centers of the finite element model within the envelope box range according to the interpolation method within the envelope box range, to obtain pressure data of the grid centers of the finite element model within the envelope box range; interpolating and calculating the grid centers of the finite element model outside the envelope box range according to the interpolation method outside the envelope box range, to obtain pressure data of the grid centers of the finite element model outside the envelope box range.

[0069] The specific calculation formula is: Wherein, n represents 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] According to the inverse solution of the matrix, the weight can be obtained, and the original function can be obtained through the weight, so as to carry out interpolation calculation.

[0071] As Figure 4 shown, the embodiment of the application also provides an analysis method, taking a seaplane as an example, comprising:

[0072] Abaqus is used to establish a three-dimensional model corresponding to the seaplane, and an Inp file is obtained, as shown in Figure 2 , the Inp file includes PART data block, Assembly data block and Step data block.

[0073] The corresponding part of the fuselage of the three-dimensional model is sliced along the length direction to obtain a plurality of slice units, the grid division is carried out on each slice unit, the pressure data of the grid center of each slice unit is calculated, the grid center coordinates of the slice unit are corresponded with the pressure data and saved as a first txt format file.

[0074] The three-dimensional model is meshed to obtain a finite element model; the Node and Element data (such as node and element information which are extracted in the form of a matrix, and the triangular and quadrilateral geometric elements are identified according to the matrix) of the finite element model are extracted, the coordinates of the grid center of the finite element model are obtained; the coordinates of the grid center below the waterline of the seaplane are screened out, and the screened coordinates are saved as a second txt format file.

[0075] The first txt format file and the second txt format file are imported 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 the corresponding pressure data, and the second data matrix includes the coordinates of the grid center below the waterline 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, so as to obtain the second data matrix containing the pressure data of the grid center below the waterline of the finite element model, and the water pressure rapid mapping from slice grid to structure grid is realized.

[0077] The second data matrix is generated as a txt file, input into an Inp file through MATLAB, and an entirely new Inp file containing accurate pressure mapping data is obtained, as shown in Figure 3 The grid parameters are set by using Abaqus, such as material density, Poisson's ratio, and grid attributes and other related attributes, and the structural strength of the seaplane is analyzed and calculated by using Abaqus.

[0078] The embodiment of the present application also provides a non-transitory computer readable storage medium for storing a computer program or instructions, which, when executed by a computer, causes the water pressure mapping method based on a radial basis function and / or the structural analysis method to be implemented.

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

[0080] In the above embodiment, all or part of the embodiment can be realized by software, hardware, firmware or any combination thereof. When realized by software, all or part of the embodiment can be realized in the form of a computer program product. The computer program product comprises one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiment of the present application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network or other programmable devices. The computer instructions can be stored in a computer readable storage medium or transferred from one computer readable storage medium to another computer readable storage medium, for example, the computer instructions can be transmitted from one website, computer, server or data center to another website, computer, server or data center through a wired (such as coaxial cable, optical fiber, digital subscriber line (DSL) or wireless (such as infrared, wireless, microwave, etc.)) way. The computer readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server, data center, etc. integrated with one or more available media. The available medium can be a magnetic medium (such as a floppy disk, a hard disk, a magnetic tape), an optical medium (such as a high-density digital video disc (digital video disc, DVD)) or a semiconductor medium (such as a solid state disk (solid state disk, SSD)) and the like.

[0081] The above-described embodiments are only used to illustrate the technical solutions of the present application, but not limit them; although the present application is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the protection scope of the present application.

Claims

1. A water pressure mapping method based on slice grids and structured grids, 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 based on the velocity potential; Meshing the three-dimensional model to form a finite element model, obtaining the coordinates of the grid center of each slice unit and the coordinates of the grid center of the finite element model, and using radial basis functions 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; 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; Calculate the envelope box corresponding to each slice unit according to the coordinates of the grid nodes of each slice unit; Determine the interpolation method within the envelope box and the interpolation method outside the envelope box; Determine the kernel function; The mesh center of the finite element model within the envelope box is interpolated according to the interpolation method within the envelope box to obtain the pressure data of the mesh center of the finite element model within the envelope box; the mesh center of the finite element model outside the envelope box is interpolated according to the interpolation method outside the envelope box to obtain the pressure data of the mesh center of the finite element model outside the envelope box.

2. The water pressure mapping method based on slice grid and structure grid according to claim 1, characterized in that: The interpolation calculation dimension is three-dimensional.

3. The water pressure mapping method based on slice grid and structure grid according to claim 1, characterized in that: The interpolation method within the envelope is to use radial basis function for interpolation, and the interpolation method outside the envelope 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.

4. An analysis method for water pressure mapping based on a slice grid and a structured grid according to any one of claims 1 to 3, characterized in that: include: Establish a three-dimensional model corresponding to the structure, slice the three-dimensional model to obtain multiple slice units, mesh each slice unit, and calculate the pressure data at the mesh center of each slice unit; Meshing the three-dimensional model to obtain a finite element model, calculating the coordinates of the mesh centers of the finite element model, and selecting the coordinates of the mesh centers below the waterline of the finite element model; Based on 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; Structural strength calculations are performed based on the pressure data at the grid center below the draft of the finite element model.

5. The analysis method according to claim 4, characterized in that: Calculating the pressure data at the mesh center below the draft of the finite element model includes: The grid center coordinates of the slice unit are matched with the pressure data and saved as a first txt format file, the coordinates of the grid center below the draft of the finite element model are screened out, and the screened coordinates are saved as a second txt format file; Import the two txt files into MATLAB to generate the first data matrix and the second data matrix. The first data matrix includes the coordinates of the grid center of each slice unit and its corresponding pressure data. The second data matrix includes the coordinates of the grid center below the draft of the finite element model. Calculating pressure data corresponding to each coordinate point of the second data matrix using a radial basis function and the first data matrix to obtain a second data matrix including 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.

6. 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 structured grids as described in any one of claims 1 to 3 and / or the analysis method as described in any one of claims 4 and 5 are implemented.

7. 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 according to any one of claims 1 to 3 and / or the analysis method according to any one of claims 4 and 5 are executed.

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