Material coordinate system transformation method for anisotropic materials in impact analysis

Abstract

The present application provides a material coordinate system transformation method for anisotropic materials during impact analysis, which belongs to the technical field of aviation structure testing, and comprises: establishing a local oblique coordinate system with the center of the anisotropic material unit as the origin, and obtaining the local oblique coordinate system according to the relationship between the global coordinate system and the local oblique coordinate system; obtaining the material coordinate system of the anisotropic material unit at the initial configuration, obtaining the material coordinate system initial vector of the material coordinate system at the initial configuration in the global coordinate system according to the relationship between the material coordinate system at the initial configuration and the global coordinate system, and transforming the material coordinate system initial vector to obtain its material coordinate system transformation vector in the local oblique coordinate system; obtaining the material coordinate system vector of the anisotropic material unit after deformation, calculating the Jacobian matrix of the center of the anisotropic material unit after deformation according to the deformed material coordinate system vector, and obtaining the actual material coordinate system vector after deformation through the material coordinate system transformation vector transformation.

Description

Technical Field

[0001] The present application belongs to the technical field of aviation structure testing, and in particular relates to a material coordinate system transformation method for anisotropic materials during impact analysis. Background Art

[0002] Composite materials are increasingly used in the aerospace field. Composite materials are typical orthotropic or fully anisotropic materials. When analyzing the impact dynamics of composite structures, the discrete units will not only produce rigid body motion, but also undergo large deformations, and their material coordinate systems will also change accordingly. Accurately tracking the changes in the material coordinate system is the key to calculating stress using the material constitutive relationship.

[0003] The traditional impact analysis calculation method is to save the material coordinate system of the initial configuration of the discrete unit and the inverse matrix of the initial Jacobian matrix of the discrete unit, calculate the deformed Jacobian matrix after the discrete unit is deformed, and further obtain the deformation gradient matrix and Green-St.Venant strain of the discrete unit, obtain the PK2 stress through the initial material coordinate system, and finally obtain the Cauchy stress through the deformation gradient matrix. This method requires multiple conversions, has low calculation efficiency, and requires additional space to save the initial information of the discrete unit, and is only suitable for elastic materials.

[0004] In order to ensure the efficiency and versatility of the calculation method, the stress update should adopt an incremental algorithm, which requires determining a new material coordinate system at each incremental step to directly obtain the incremental Cauchy stress. Summary of the invention

[0005] The purpose of the present application is to provide a material coordinate system transformation method for anisotropic materials during impact analysis, so as to solve or alleviate at least one problem in the background technology.

[0006] The technical solution of the present application is: a material coordinate system transformation method for anisotropic materials during impact analysis, including:

[0007] A local oblique coordinate system is established with the center of the anisotropic material unit as the origin, and the local oblique coordinate system is obtained according to the relationship between the global coordinate system and the local oblique coordinate system;

[0008] Obtaining the material coordinate system of the anisotropic material unit at the initial configuration, obtaining the material coordinate system initial vector of the material coordinate system of the anisotropic material unit at the initial configuration in the global coordinate system according to the relationship between the material coordinate system of the anisotropic material unit at the initial configuration and the global coordinate system, and transforming the material coordinate system initial vector to obtain its material coordinate system transformation vector in the local oblique coordinate system;

[0009] The material coordinate system vector of the anisotropic material unit after deformation is obtained, and the Jacobian matrix of the center of the anisotropic material unit after deformation is calculated according to the material coordinate system vector of the anisotropic material unit after deformation. Assuming that the material coordinate system in the local oblique coordinate system does not change with the material deformation, the actual material coordinate system vector after deformation is obtained through the material coordinate system conversion vector transformation to complete the transformation of the material coordinate system.

[0010] Preferably, the relationship between the global coordinate system and the local oblique coordinate system satisfies:

[0011] ;

[0012] In the formula, ( ) are local oblique coordinate system coordinates;

[0013] ( x , y ) are the coordinates of the global coordinate system;

[0014] A is the transformation matrix between the local oblique coordinate system and the global coordinate system;

[0015] ( a , b ) are the center coordinates of the anisotropic material unit.

[0016] Preferably, obtaining the material coordinate system of the anisotropic material unit at the initial configuration includes obtaining the material coordinate system corresponding to the anisotropic material unit at the initial configuration by specifying the unit node number, by directly giving a vector, or by the unit center and a given position point.

[0017] Preferably, the material coordinate system transformation vector satisfies:

[0018] , ;

[0019] In the formula, ( ) is the material coordinate system transformation vector;

[0020] ( e 1 , e 2 ) is the initial vector of the material coordinate system.

[0021] Preferably, the actual material coordinate system vector is ( ), where J 0 is the Jacobian matrix of the center of the anisotropic material unit after deformation, T Represents the transpose of a matrix.

[0022] The material coordinate system transformation method for anisotropic materials in impact analysis proposed in the present application establishes a local oblique coordinate system at the center of the anisotropic material unit, and binds the material coordinate system to the deformation of the anisotropic material unit. After the anisotropic material unit is deformed, the material coordinate system is transformed accordingly. In structural impact analysis, it is only necessary to save the material coordinate system in the local oblique coordinate system of the initial configuration. After deformation, the actual material coordinate system can be obtained by conversion and used for stress update. When solving Cauchy stress, there is no need for multiple conversions and storage of unit information, which greatly improves the calculation efficiency. At the same time, it meets the solution accuracy required for structural impact analysis, which is of great significance for the efficient and high-precision calculation of complex impact / collision problems of composite materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the technical solution provided by the present application, the following is a brief introduction to the accompanying drawings. Obviously, the accompanying drawings described below are only some embodiments of the present application.

[0024] Figure 1 This is a schematic diagram of the material coordinate system transformation method used in the impact analysis of anisotropic materials in the present application.

[0025] Figure 2 It is a schematic diagram of a quadrilateral 2D anisotropic material unit formed by four nodes in an embodiment of the present application in a global coordinate system. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solutions and advantages of the implementation of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below in conjunction with the drawings in the embodiments of this application.

[0027] The present application proposes a material coordinate system transformation method for anisotropic materials during impact analysis. By establishing a material coordinate system for anisotropic materials and continuously updating it as the unit is deformed, it can be used for high-precision simulation of impact problems of anisotropic materials such as composite materials.

[0028] like Figure 1 As shown, the material coordinate system transformation method for anisotropic materials in impact analysis provided by the present application includes the following steps:

[0029] S10, a local oblique coordinate system (Oblique Coordinate System) is established with the center of the anisotropic material unit as the origin. The local oblique coordinate system is bound to the anisotropic material unit. After the anisotropic material unit is deformed, the local oblique coordinate system also changes accordingly. The local oblique coordinate system is obtained according to the relationship between the global coordinate system and the local oblique coordinate system.

[0030] Among them, the local oblique coordinate system ( ) and the global coordinate system ( x , y ) relationship satisfies:

[0031] ;

[0032] Where A is the transformation matrix between the local oblique coordinate system and the global coordinate system, ( a , b ) are the center coordinates of the anisotropic material unit.

[0033] This application takes the anisotropic material unit with 2D properties as an example for explanation. The calculation of the anisotropic material unit with 3D properties is similar to that of the anisotropic material unit with 2D properties, and will not be repeated here. Figure 2 The quadrilateral 2D anisotropic material unit formed by four nodes in this embodiment of the present application is shown in FIG. , which has four nodes N1 to N4. A local oblique coordinate system ( ), local oblique coordinate system ( ) and the global coordinate system ( x , y ) is as follows:

[0034] ;

[0035] Among them, (ζ,η) are isoparametric local coordinates; ( a 4, b 4) is the coordinate of the center point of the anisotropic material unit of the four-node quadrilateral. The coordinate of the anisotropic material unit is obtained by four-node isoparametric interpolation; J -T | ζ=η=0 Represents the transpose of the inverse matrix of the Jacobian matrix of the anisotropic material unit center, also known as the transformation matrix between two coordinate systems A .

[0036] S20, obtaining the material coordinate system of the anisotropic material unit at the initial configuration, and obtaining the material coordinate system initial vector ( e 1 , e 2 ), transform the initial vector of the material coordinate system to obtain its material coordinate system transformation vector in the local oblique coordinate system ( ),in:

[0037] , .

[0038] There are many ways to obtain the material coordinate system of the initial configuration of anisotropic material units. Usually, the material coordinate system corresponding to the initial configuration of anisotropic material units can be obtained by, for example, specifying the unit node number, directly giving a vector, or by the unit center and a given position point.

[0039] S30, obtaining the material coordinate system vector of the anisotropic material unit after deformation, and calculating the Jacobian matrix of the center of the anisotropic material unit after deformation according to the material coordinate system vector of the anisotropic material unit after deformation J 0 , it is approximately assumed that the material coordinate system in the local oblique coordinate system does not change with the material deformation, and the actual material coordinate system vector after deformation is obtained by transforming the material coordinate system transformation vector ( ), T Represents the transpose of a matrix.

[0040] The material coordinate system transformation method for anisotropic materials in impact analysis proposed in the present application establishes a local oblique coordinate system at the center of the anisotropic material unit, and binds the material coordinate system to the deformation of the anisotropic material unit. After the anisotropic material unit is deformed, the material coordinate system is transformed accordingly. In structural impact analysis, it is only necessary to save the material coordinate system in the local oblique coordinate system of the initial configuration. After deformation, the actual material coordinate system can be obtained by conversion and used for stress update. When solving Cauchy stress, there is no need for multiple conversions and storage of unit information, which greatly improves the calculation efficiency. At the same time, it meets the solution accuracy required for structural impact analysis, which is of great significance for efficient and high-precision calculation of complex impact / collision problems of composite materials.

[0041] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A material coordinate system transformation method for anisotropic materials in impact analysis, characterized in that: include: A local oblique coordinate system is established with the center of the anisotropic material unit as the origin, and the local oblique coordinate system is obtained according to the relationship between the global coordinate system and the local oblique coordinate system; Obtaining the material coordinate system of the anisotropic material unit at the initial configuration, obtaining the material coordinate system initial vector of the material coordinate system of the anisotropic material unit at the initial configuration in the global coordinate system according to the relationship between the material coordinate system of the anisotropic material unit at the initial configuration and the global coordinate system, and transforming the material coordinate system initial vector to obtain its material coordinate system transformation vector in the local oblique coordinate system; The material coordinate system vector of the anisotropic material unit after deformation is obtained, and the Jacobian matrix of the center of the anisotropic material unit after deformation is calculated according to the material coordinate system vector of the anisotropic material unit after deformation. Assuming that the material coordinate system in the local oblique coordinate system does not change with the material deformation, the actual material coordinate system vector after deformation is obtained through the material coordinate system conversion vector transformation to complete the transformation of the material coordinate system.

2. The material coordinate system transformation method for anisotropic materials in impact analysis according to claim 1, characterized in that: The relationship between the global coordinate system and the local oblique coordinate system satisfies: ； In the formula, ( ) is the coordinate of the local oblique coordinate system; ( x , y ) are the coordinates of the global coordinate system; A is the transformation matrix between the local oblique coordinate system and the global coordinate system; ( a , b ) are the center coordinates of the anisotropic material unit.

3. The material coordinate system transformation method for anisotropic materials in impact analysis according to claim 2, characterized in that: Obtaining the material coordinate system of the initial configuration of the anisotropic material unit includes obtaining the material coordinate system corresponding to the initial configuration of the anisotropic material unit by specifying the unit node number, by directly giving a vector, or by the unit center and a given position point.

4. The material coordinate system transformation method for anisotropic materials in impact analysis according to claim 3, characterized in that: The material coordinate system transformation vector satisfies: ， ； In the formula, ( ) is the material coordinate system transformation vector; ( e 1 , e 2 ) is the initial vector of the material coordinate system.

5. The material coordinate system transformation method for anisotropic materials in impact analysis according to claim 4, characterized in that: The actual material coordinate system vector is ( ), where J 0 is the Jacobian matrix of the center of the anisotropic material unit after deformation, T Represents the transpose of a matrix.

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