Method for characterizing spatial variability of mechanical properties of curved-surface-containing composite material structure

Abstract

The invention discloses a spatial variability characterization method for mechanical properties of a curved-surface-containing composite material structure, and belongs to the field of characterization of mechanical properties of composite materials. The method comprises the following steps: firstly, dividing a manifold structure into three-dimensional discrete units and acquiring central point coordinates of each unit; the center point coordinates are converted into two-dimensional plane coordinates through a dimension reduction mapping means. And then, acquiring the mechanical properties of part of discrete units, selecting a proper kernel function by using a Gaussian random field in combination with the two-dimensional plane coordinates corresponding to the central points of the units, and acquiring the mechanical properties of the two-dimensional central points of other discrete units. And finally, mapping a performance characterization result of the two-dimensional plane to the curved surface structure to realize characterization of spatial variability of the mechanical properties of the curved surface composite material structure. According to the method, the distance measurement in the covariance kernel function is replaced by the geodesic distance on the curved surface, and the problem that manifold features are not met due to the fact that spatial mapping is directly established based on the Euclidean distance is avoided.

Description

Technical Field

[0001] The present invention belongs to the field of composite material mechanical property characterization, and specifically relates to a method for characterizing the spatial variability of composite material structural mechanical properties by combining a plane mapping method of a curved structure manifold with a Gaussian random field. Background Art

[0002] Composite materials with curved surfaces are widely used in aerospace and other fields. However, the performance of composite materials is affected by the randomness of the microstructure and the non-uniformity of fiber weaving. Especially in curved structures, the mechanical properties of the materials at different positions of the structure have obvious randomness and differences. The complex geometric characteristics of the surface itself bring challenges to accurately characterizing the spatial variability of the mechanical properties of the above materials.

[0003] Current modeling and analysis of composite structures containing curved surfaces typically employs the same material mechanical properties at different locations within the structure, with limited research examining the spatial variability of these properties. Even when differences in mechanical properties between different locations are considered, different locations are often assigned different properties based on destructive sampling test results, lacking effective characterization of the correlation between mechanical properties at different locations. Simultaneously, studies have shown that spatial variability in material properties significantly impacts the modal and vibration characteristics, stress localization, and damage evolution of the structure. For specific material systems, the spatial variability of moduli can reach over 20%, resulting in differences in structural strength exceeding 15%. The lack of methods to characterize the spatial variability of composite structures containing curved surfaces severely restricts the accurate analysis of the response of composite structures containing curved surfaces and the reliable assessment of their load-bearing capacity.

[0004] Therefore, establishing a method for characterizing the spatial variability of mechanical properties of composite materials that can be used for curved surface structures, fully considering the impact of the differences and correlations between mechanical properties at different positions of the structure on the mechanical behavior of the structure, is of great value for the refined design of composite structures and the reliable evaluation of the structural status during service. Summary of the Invention

[0005] The purpose of the present invention is to solve the above-mentioned problems existing in the background technology and to provide a method for characterizing the spatial variability of the mechanical properties of composite materials by combining the planar mapping method of curved structure manifolds with Gaussian random fields.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A method for characterizing the spatial variability of mechanical properties of composite materials containing curved surfaces, the method comprising:

[0008] Step 1: Two-dimensional plane mapping of the surface structure manifold; this step avoids the problem of large errors in the results of complex surfaces caused by directly using the Euclidean distance to characterize in the traditional method, and better maintains the positional relationship in the structure.

[0009] Step 2: Mechanical property characterization based on the planar Gaussian random field; this step improves the traditional method of destructive sampling to assign different properties to different positions, and can better effectively characterize the correlation of mechanical properties between different positions.

[0010] Step 3: Characterization of the spatial variability of the mechanical properties of the surface structure based on the mapping correspondence.

[0011] Furthermore, the specific content of Step 1 is as follows:

[0012] Step 1-1: Discretize the three-dimensional surface manifold structure into n units , and represent the center point of each unit with a three-dimensional coordinate point (1 ≤ i ≤ n, and the superscripts 1, 2, and 3 respectively represent the abscissa, ordinate, and vertical coordinate), that is, obtain three-dimensional coordinate data from the manifold space;

[0013] Step 1-2: Adopt a neighborhood search algorithm (such as k-nearest neighbor or ε-neighborhood) to construct the local adjacency graph of each point, calculate the local tangent space of each point to characterize the local geometric features of the manifold; connect all the local adjacency graphs to construct a global manifold graph structure, and represent the distance between points with the adjacency distance l;

[0014] Step 1-3: Based on the graph embedding algorithm (such as Laplacian eigenmaps, Diffusion Maps or a customized topology-preserving algorithm), perform two-dimensional unfolding on the three-dimensional manifold, and map it to the two-dimensional plane to obtain two-dimensional coordinate points (1 ≤ i ≤ n), which corresponds one-to-one with the three-dimensional point (1 ≤ i ≤ n).

[0015] Furthermore, the specific content of Step 2 is as follows:

[0016] Step 2-1: Obtain the material mechanical property data of m (m < n) typical positions of the structure , and the typical positions correspond to two-dimensional coordinate points , and it is required that the selection of typical positions is representative and covers the entire structure as much as possible;

[0017] ​​Step 2: Combine the dimensionality-reduced data points with the mechanical properties data of typical locations, select the appropriate kernel function form (such as linear kernel function, exponential kernel function, square exponential kernel function, periodic kernel function) according to whether the data has periodicity, monotonicity and other characteristics, and establish a Gaussian random field model

[0018]

[0019] Where GP is a Gaussian random field, f(x) represents the mechanical properties at x in two-dimensional coordinates, is the mean function, which is usually set to 0. is the kernel function, used to represent Point and The correlation between two points can be expressed in different forms according to the actual situation. Where E is the expectation.

[0020] Furthermore, the step three is specifically as follows:

[0021] Step 31: Based on the selected kernel function, use the typical position coordinate vector to calculate the covariance matrix between different typical positions:

[0022]

[0023] Step 32: Using the calculated covariance matrix, according to the Gaussian random field model solution process, solve the mechanical properties of atypical positions and establish a joint Gaussian distribution:

[0024]

[0025] Where N is Gaussian distribution, is the two-dimensional coordinate vector of the atypical position, yes The corresponding mechanical properties, , , through conditioning, we get The result:

[0026]

[0027]

[0028]

[0029] in, It can be considered that the mechanical properties at atypical locations For atypical locations The confidence level (variance), is the noise variance of the training point data (the general sensor noise variance is 0.1, which can also be optimized by maximum likelihood estimation), and I is the unit matrix;

[0030] The distribution of mechanical properties in space can be described by the generated Gaussian random field;

[0031] Step 3: Through the correspondence between two-dimensional points and three-dimensional discrete elements, the generated Gaussian random field data is mapped to specific discrete elements to obtain the mechanical property distribution of the entire structure.

[0032] The advantages of this invention over the prior art are as follows: 1. The present invention replaces the distance metric in the covariance kernel function with the geodesic distance on the surface, avoiding the problem of not satisfying manifold characteristics when directly establishing spatial mapping based on Euclidean distance. 2. The present invention utilizes the statistical method of Gaussian random fields to characterize overall performance based on the performance of partial positions, effectively characterizing the correlation between mechanical properties at different positions. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flow chart of the present invention.

[0034] Figure 2 The following is a specific flow chart for the example. DETAILED DESCRIPTION

[0035] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention that does not depart from the spirit and scope of the technical solution of the present invention should be included in the scope of protection of the present invention.

[0036] The present invention provides a method for characterizing the spatial variability of the mechanical properties of a curved composite material structure by combining a plane mapping method of a curved structure manifold with a Gaussian random field. First, the manifold structure is divided into three-dimensional discrete units and the coordinates of the center point of each unit are obtained; the center point coordinates are converted into two-dimensional plane coordinates by means of dimensionality reduction mapping. Subsequently, the mechanical properties of some discrete units are obtained, and combined with the two-dimensional plane coordinates corresponding to the unit center points, a suitable kernel function is selected using the Gaussian random field to obtain the mechanical properties at the two-dimensional center points of other discrete units. Finally, the performance characterization results of the two-dimensional plane are mapped to the curved structure to achieve the characterization of the spatial variability of the mechanical properties of the curved composite material structure. The present invention provides a complete method from two-dimensional plane mapping of the curved structure manifold to mechanical property characterization based on a plane Gaussian random process model and then to characterization of the spatial variability of the mechanical properties of the curved structure based on the mapping correspondence, which provides support for the characterization of the spatial variability of the mechanical properties of composite materials containing curved surfaces.

[0037] Example 1:

[0038] like Figure 1 The present invention shown comprises the following stages:

[0039] Stage 1: Two-dimensional plane mapping of the curved surface structure manifold;

[0040] Stage 2: Mechanical property characterization based on the planar Gaussian random field;

[0041] Stage 3: Characterization of the spatial variability of the mechanical properties of the curved surface structure based on the mapping correspondence;

[0042] Among them, Stage 1 includes the following steps:

[0043] Step 1: Discretize the three-dimensional curved surface manifold structure into n units , and represent the center point of each unit with a three-dimensional coordinate vector (1 ≤ i ≤ n and i ∈ N), that is, obtain three-dimensional coordinate data from the manifold space; in this example, the curved surface shell structure is taken as an example for illustration, and the overall process framework is as Figure 2 shown. Divide the curved surface shell structure into three-dimensional discrete units of 6×23 , and take the center point of each unit to represent each discrete unit, as Figure 2 shown.

[0044] Step 2: Use the neighborhood search algorithm (such as k-nearest neighbor or neighborhood) to construct the local adjacency graph of each point, calculate the local tangent space of each point to characterize the local geometric features of the manifold. Connect all the local adjacency graphs to construct the global manifold graph structure, and represent the distance between points with the adjacency distance l; in this example, the discrete points are , use k-nearest neighbor to obtain the adjacency graph of each point, and then connect the adjacency graphs of each point to construct the global manifold graph structure.

[0045] Step 3: Based on the graph embedding algorithm (such as Laplacian eigenmaps, Diffusion Maps or customized topology-preserving algorithms), perform two-dimensional expansion on the three-dimensional manifold, and map it to the two-dimensional plane to obtain two-dimensional points (1 ≤ i ≤ n) while keeping the adjacency distance l between all points unchanged to the greatest extent, and it corresponds one-to-one with the three-dimensional points (1 ≤ i ≤ n); in this example, the Maps algorithm is used, input the adjacency distance matrix of the discrete points, and output the Euclidean distance matrix of the points after dimensionality reduction, so as to reduce the curved surface to the two-dimensional plane.

[0046] Stage 2 includes the following steps:

[0047] Step 4: Obtain the material mechanical property data of m (m < n) typical positions of the structure , and the typical positions correspond to two-dimensional coordinate points , the selection of typical positions is required to be representative and cover the entire structure as much as possible; in this example, the typical positions of the structure are selected , its three-dimensional coordinate point is ,in , corresponding to the two-dimensional coordinate vector ,in Typical positions correspond to elastic modulus data .

[0048] Step 5: Combine the dimensionality-reduced data points with the mechanical properties data of typical locations, select the appropriate kernel function form (such as linear kernel function, exponential kernel function, square exponential kernel function, periodic kernel function) according to whether the data has periodicity, monotonicity and other characteristics, and establish a Gaussian random field model

[0049]

[0050] Where GP is a Gaussian random field, f(x) represents the mechanical properties at x in two-dimensional coordinates, is the mean function, which is usually set to 0. is the kernel function, used to represent the x point and x ’ The correlation between two points can be expressed in different forms depending on the actual situation. Where E is the expectation; in this example, the Young's modulus of elasticity of the material is selected as the characterization target, and the square exponential kernel function is selected:

[0051]

[0052] in, is the signal variance, , are the coordinate vectors of the two points, is the relevant length scale, is the noise variance, is the Kronecker delta function. 、 、 It can be jointly optimized via maximum likelihood estimation.

[0053] Phase 3 includes the following steps:

[0054] Step 6: Based on the selected covariance function, calculate the covariance matrix between different typical positions; in this example, the covariance matrix of different typical sites is:

[0055]

[0056] Step 7: Using the calculated covariance matrix, according to the Gaussian random field model solution process, solve the mechanical properties of atypical positions and establish a joint Gaussian distribution:

[0057]

[0058] In this example, is the two-dimensional coordinate vector of the atypical position, yes The corresponding Young's modulus of elasticity is, , , through conditioning, we can get The result:

[0059]

[0060]

[0061]

[0062] in, It can be considered that the elastic modulus at the atypical position, For atypical locations The confidence level (variance) of .

[0063] The generated Gaussian random field can be used to characterize the distribution of elastic modulus in a two-dimensional plane.

[0064] Step 8: Through the correspondence between two-dimensional points and three-dimensional discrete elements, the generated Gaussian random field data is mapped to specific discrete elements to obtain the mechanical properties distribution of the entire structure; in this example, the two-dimensional dimensionality reduction coordinate point , 3D original coordinate points , three-dimensional discrete elements The numbers are consistent and can be mapped directly.

Claims

1. A method for characterizing the spatial variability of mechanical properties of composite materials containing curved surfaces, characterized by: The method is Step 1: 2D plane mapping of the surface structure manifold; Step 2: Mechanical properties characterization based on planar Gaussian random field; Step 3: Characterization of the spatial variability of mechanical properties of surface structures based on mapping correspondence.

2. The method for characterizing the spatial variability of mechanical properties of composite materials containing curved surfaces according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1: Discretize the three-dimensional surface manifold structure into n units , use a three-dimensional coordinate point for each unit center point (1≤i≤n, the superscripts 1, 2, and 3 represent the horizontal coordinate, vertical coordinate, and vertical coordinate, respectively), that is, obtaining three-dimensional coordinate data from the manifold space; Step 1 and 2: Use neighborhood search algorithm (such as Neighbor or Neighborhood) constructs a local adjacency graph for each point and calculates the local tangent space of each point to characterize the local geometric characteristics of the manifold; all local adjacency graphs are connected to construct the global manifold graph structure, and the distance between points is represented by the adjacency distance l; Step 13: Based on a graph embedding algorithm (such as Laplace Eigenmap, Diffusion Maps, or a customized topology-preserving algorithm), the 3D manifold is expanded into 2D, and the 2D coordinate points are obtained by mapping it to a 2D plane while keeping the adjacent distance l between all points unchanged to the greatest extent possible. (1≤i≤n), which is consistent with the three-dimensional point (1≤i≤n) one-to-one correspondence.

3. The method for characterizing the spatial variability of mechanical properties of composite materials containing curved surfaces according to claim 1, characterized in that: The step 2 is specifically as follows: Step 2-1: Obtain the material mechanical property data of m (m < n) structurally typical positions , where the typical positions correspond to two-dimensional coordinate points , and it is required that the selection of typical positions be representative and cover the entire structure as much as possible; ​ Step 2: Combine the dimensionality-reduced data points with the mechanical properties data of typical locations, select the appropriate kernel function form (such as linear kernel function, exponential kernel function, square exponential kernel function, periodic kernel function) according to whether the data has periodicity, monotonicity and other characteristics, and establish a Gaussian random field model Where GP is a Gaussian random field, f(x) represents the mechanical properties at x in two-dimensional coordinates, is the mean function, which is usually set to 0. is the kernel function, which is used to represent Dot and The correlation between two points can be expressed in different forms according to the actual situation. Where E is the expectation.

4. The method for characterizing the spatial variability of mechanical properties of composite materials containing curved surfaces according to claim 1, characterized in that: The step three is specifically as follows: Step 31: Based on the selected kernel function, use the typical position coordinate vector to calculate the covariance matrix between different typical positions: Step 32: Using the calculated covariance matrix, according to the Gaussian random field model solution process, solve the mechanical properties of atypical positions and establish a joint Gaussian distribution: Where N is Gaussian distribution, is the two-dimensional coordinate vector of the atypical position, yes The corresponding mechanical properties, , , through conditioning, we get The result: in, It can be considered that the mechanical properties at atypical locations For atypical locations The confidence level (variance), is the noise variance of the training point data (the general sensor noise variance is 0.1, which can also be optimized by maximum likelihood estimation), and I is the unit matrix; The distribution of mechanical properties in space can be described by the generated Gaussian random field; Step 3: Through the correspondence between two-dimensional points and three-dimensional discrete elements, the generated Gaussian random field data is mapped to specific discrete elements to obtain the mechanical property distribution of the entire structure.

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