A method for generating a wheel disc rectangular plate suitable for structured mesh in fracture mechanics analysis

Abstract

This invention discloses a rapid generation method for rectangular disks suitable for structured meshes. This method simplifies crack propagation calculations of the disk into a parametric fracture mechanics model, enabling the calculation of stress intensity factor and crack propagation life. Specifically, finite element modeling is employed to extract the geometric boundaries of the disk and its partitions, considering the influence of geometric dimensions and boundary effects on crack propagation. Based on coordinate system transformation, using the crack initiation point and stress gradient direction as a reference, the rectangular plate can be accurately located, improving modeling efficiency. This invention simplifies the crack propagation plane into a finite-size rectangular plate. Based on boundary intersection point capture, it achieves high-fidelity equivalence between the rectangular plate model and the actual complex contour of the disk, reducing calculation errors in the boundary region using traditional methods. Furthermore, by extracting the crack-free stress distribution along the crack propagation direction on the rectangular plate, the stress intensity factor at the crack tip and crack propagation life can be calculated using the weighted function method.

Description

Technical Field

[0001] This invention relates to the field of probabilistic fracture mechanics technology for aero-engines, and in particular to a method for generating a disc-shaped rectangular plate with a structured mesh suitable for fracture mechanics analysis. Background Technology

[0002] Life-limited components in aero-engines refer to rotors and major stator structural components whose primary failure could jeopardize engine safety. To ensure the service safety of these components, the U.S. aerospace industry has proposed an enhanced life management process. Its core lies in considering potential initial defects in these components and conducting probabilistic damage tolerance assessments. This assessment method comprehensively considers random factors such as defects, loads, material properties, and non-destructive testing, and performs fracture mechanics calculations to quantify failure risks and guide design and service management.

[0003] Taking a roulette wheel as an example, since the size and location of initial defects are random, a zoning study based on the stress distribution of the wheel is necessary. A common method is to perform stress analysis on the wheel using finite element method (FEM) software, then establish a zoning algorithm based on certain zoning criteria, and conduct failure risk assessment based on this. Existing techniques typically divide the wheel into several zones with similar risks based on finite element calculation results, and perform crack propagation calculations within each zone. However, due to the complex geometry of the wheel and the existence of significant boundary effects, the calculation process for the stress intensity factor at the crack tip is cumbersome, making it difficult to balance computational efficiency and accuracy.

[0004] A common international approach simplifies the crack propagation plane into a model combining an infinitely large plate and a finite-size plate. This simplified model, when dealing with non-rectangular boundaries, typically selects the narrowest cross-section as the rectangular plate size. This leads to an overestimation of the stress intensity factor in the boundary transition zone, resulting in conservative results and reduced prediction accuracy. Based on this, a novel method for establishing a rectangular plate model in fracture mechanics is proposed. This method accurately extracts geometric boundary and stress gradient features through disk stress partitioning, reducing errors in the boundary transition zone. Furthermore, it extracts the crack-free stress distribution along the crack propagation direction and combines this with a weighted function method to more accurately calculate the stress intensity factor, thus providing reliable support for probabilistic damage tolerance assessment of life-limited components. Summary of the Invention

[0005] This invention discloses a method for generating a rectangular plate of a disk with a structured mesh suitable for fracture mechanics analysis. This method simplifies the crack propagation calculation of the disk into a parametric fracture mechanics model, thereby enabling the calculation of the stress intensity factor and crack propagation life of the disk. Specifically, finite element modeling is employed to extract the geometric boundaries of the wheel and its partitions, taking into account the influence of geometric dimensions and boundary effects on crack propagation. Based on coordinate system transformation, using the crack initiation point and stress gradient direction as a reference, the rectangular plate can be accurately located, improving its modeling efficiency. Currently, many foreign methods combine infinitely large plates with finite-size plates. This method classifies the size of the rectangular plate according to the distance from the crack initiation point to the boundary. However, when dealing with complex boundaries, this conservative correction strategy based on distance classification is difficult to accurately capture the geometric features of the wheel, making the calculation results of the boundary transition zone too conservative. Compared with foreign research methods, the fast generation method for wheel rectangles suitable for structured meshes established in this invention simplifies the crack propagation plane to a finite-size rectangular plate. Based on boundary intersection point capture, it achieves high-fidelity equivalence between the rectangular plate model and the actual complex contour of the wheel, reducing the calculation error of traditional methods in the boundary region. At the same time, by extracting the crack-free stress distribution in the crack propagation direction on the rectangular plate, the stress intensity factor at the crack tip and the crack propagation life can be calculated by combining the weight function method. The method for rapid generation of disk rectangles applicable to structured grids provided by this invention provides technical support for the probabilistic damage tolerance assessment of aero-engine disks, and has significant engineering significance and practical value.

[0006] This invention provides a method for generating a disk-shaped rectangular plate with structured meshes suitable for fracture mechanics analysis, comprising: S1: For the wheel structure that requires fracture mechanics analysis, establish a wheel finite element model, divide the wheel finite element model into stress zones, obtain multiple stress zones of the wheel structure and the corresponding zone information, and calculate the characteristic parameters of each zone. S2: Identify the boundary nodes of the wheel structure and each element in each stress zone, obtain the boundary nodes of the wheel structure and each stress zone, and draw the outer boundary of the wheel structure and the outer boundary of each stress zone respectively. Each stress zone is classified based on its outer boundary to obtain the type of each stress zone; S3: Determine the crack propagation direction of each stress zone based on the stress zone type; Draw an initial rectangular plate with the crack initiation point as the origin, the crack propagation direction as the initial direction, and the four intersection points of the four orthogonal directions with the outer boundary of the wheel structure as edge points; S4: Transform the Cartesian coordinate system of the wheel into a polar coordinate system with the crack initiation point as the origin and the crack propagation direction as the positive direction. Divide the initial rectangular plate into four sectors along the four angular rays and obtain the polar radius of the intersection point of the ray of each sector with the boundary of the wheel structure. The shortest distance from the origin to the boundary of the disk within the sector is taken as the width of the rectangular plate in the main direction of each sector. The rectangular plate is drawn according to the width of the rectangular plate in the main direction of each sector to obtain the fracture mechanics rectangular plate. S5: Take samples at equal intervals along the crack propagation direction of the rectangular plate used for fracture mechanics analysis. Extract the crack-free stress of the rectangular plate.

[0007] Optionally, the partitioning information of the finite element model of the wheel in step S1 includes the partitioning stress, temperature, number of elements, volume, center x-coordinate, center y-coordinate, partitioning type, and x-coordinate and y-coordinate of the stress maximum point for all stress partitions on the principal stress orthogonal plane of the wheel.

[0008] Optionally, step S3 specifically includes: S31. Based on the stress zone type, determine the crack propagation direction of each stress zone; The stress partitioning types include internal stress partitioning, surface stress partitioning, and corner element stress partitioning; S32. Using the crack initiation point as the origin, and the crack propagation direction as the origin. D i As the initial direction, construct a Cartesian coordinate system. x ' Oy '; Get+ x - x + y - y The four intersection points of the four orthogonal directions with the outer boundary of the wheel structure are represented as points in the Cartesian coordinate system. x + , 0), point ( x - , 0), point (0, y + ) and point (0, y - ); S33, in Cartesian coordinate system x ' Oy 'the point below' As the initial geometric center, with ( x + - x - ) as the initial length, with ( y + - y - Draw a rectangle with the initial width to obtain the initial rectangular plate.

[0009] Optionally, step 31 includes the following specific steps: S311, Selecting stress zones i A group of points formed by several points of maximum stress in the inner front S max, i The point group formed by the first few stress minimum points S min, i The average coordinates of each are taken as the center of the stress maximum point group and the stress minimum point group; Optionally, the stress of each node within the stress partition is known. The node sequence is sorted according to the stress value, and the node indexed by the maximum stress value is the point of maximum stress, and the node indexed by the minimum stress value is the point of minimum stress.

[0010] S312, the vector pointing from the center of the stress minimum point group to the center of the stress minimum point group. G i As stress zone i The stress gradient direction serves as the crack propagation direction for internal stress zones; S313, When stress partitioning i When a stress zone is identified, the surface boundary segment closest to the geometric center within that stress zone is located, and the corresponding normal vector is used as the stress zone. i Crack propagation direction S ⊥, i ; S314, When stress partitioning i When a stress partition is defined as a corner element, the normal of the boundary segment connecting the corner node and its two surrounding surface nodes within the stress partition is taken as the partition line. i Crack propagation direction C ⊥, i .

[0011] Optionally, the crack initiation point can be the point of maximum stress or the geometric center of the zone.

[0012] Optionally, step S4 includes the following specific steps: Cartesian coordinate system x ' Oy Transform it into a polar coordinate system with the crack initiation point as the origin and the crack propagation direction as the positive direction. r , θ ), r Polar radius, θ Polar angle; With the origin of the polar coordinate system O Starting from the initial point, draw rays to the four vertices of the initial rectangular plate. OE ,ray OF ,ray OG and rays OH The finite element model of the roulette wheel is divided into sectors. HOE sectorEOF sector FOG and sectors GOH Their principal directions are the Cartesian coordinate system. x ' Oy 'of+ x Direction, + y direction,- x Direction and - y direction; Within each sector, by sector HOE For example, find the rays respectively OH Intersection with the outer boundary of the wheel structure H '( r H’ , θ H’ Record the corresponding polar radius of the intersection point. r H’ Find the ray OE Intersection with the outer boundary of the wheel structure E ' ( r E’ , θ E’ Record the corresponding polar radius of the intersection point. r E’ ; In sector HOE Within, iterate through all the roulette wheel boundary segments to obtain the boundary segments and points of each roulette wheel. O The distance between the points and the polar radius of the intersection. r H’ and the polar radius of the intersection point r E’ Merge the values ​​and take the minimum value as the sector. HOE Width of rectangular plate in the main direction d +x ; Similarly, sectors can be obtained. EOF Corresponding rectangular plate width d +y , FOG Corresponding rectangular plate width d -x and GOH Corresponding rectangular plate width d -y ; In the Cartesian coordinate system x ' Oy 'Next, determine the geometric center as The length of the rectangular plate is ( d +x + d -x The width of the rectangular plate is ( d +y +d -y A rectangular plate for fracture mechanics analysis is obtained according to the stated geometric center, length, and width.

[0013] Optionally, step S5 includes the following specific steps: Equally spaced samples are taken along the crack propagation direction of the rectangular plate used for fracture mechanics analysis. For each sampling point, the stress value in the crack-free state is extracted from the finite element analysis results or stress field interpolation, that is, the stress at that point is not considered when a crack exists. The stress values ​​in the crack-free state are derived from the elastic or elastoplastic stress analysis of the wheel under rated operating conditions, reflecting the stress distribution along the crack propagation direction near the crack initiation point. Pair the sampling point locations with the corresponding stress values ​​in the crack-free state to plot a stress-location curve. This curve can be used to calculate the stress intensity factor at the crack tip using the weighted function method.

[0014] Compared with the prior art, the present invention has at least the following beneficial effects: (1) The present invention uses finite element modeling to extract the geometric boundaries of the wheel and its partitions, which can take into account the influence of geometric dimensions and boundary effects on crack propagation; (2) Based on the coordinate system transformation method, the present invention uses the crack initiation point and stress gradient direction as the reference, which can accurately locate the rectangular plate and improve its modeling efficiency; (3) The fast generation method for wheel rectangular bodies suitable for structured meshes established in this invention simplifies the crack propagation plane into a rectangular plate of finite size. Based on the boundary intersection capture, the rectangular plate model and the actual complex contour of the wheel are realized with high fidelity equivalence, which reduces the calculation error in the boundary area of ​​the traditional method. At the same time, by extracting the crack-free stress distribution in the crack propagation direction on the rectangular plate, the stress intensity factor at the crack tip and the crack propagation life can be calculated by combining the weight function method. (4) The above-mentioned method for rapid generation of disk rectangles applicable to structured grids provided by the present invention provides technical support for the probabilistic damage tolerance assessment of aero-engine disks and has important engineering significance and practical value. Attached Figure Description

[0015] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0016] Figure 1 A flowchart of a method for rapidly generating wheel rectangles suitable for structured meshes provided by the present invention; Figure 2 In one embodiment of the present invention, rays drawn from the origin of the coordinate system to the four vertices of the initial rectangular plate divide the model into four sectors and their main directions; Figure 3In one embodiment of the present invention, the wheel boundary, the boundary of section 64, and the final rectangular plate shape are provided. Figure 4 A crack-free stress-location curve extracted from the final rectangular plate of partition 64 in one embodiment of the present invention; Figure 5 A schematic diagram of the wheel structure in one embodiment of the present invention; Figure 6 This is a schematic diagram of node types in one embodiment of the present invention. Detailed Implementation

[0017] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0018] A specific embodiment of the present invention, such as Figures 1 - 6 A method for generating a disk-shaped rectangular plate with structured meshes suitable for fracture mechanics analysis is disclosed, comprising the following steps: S1: For the wheel structure that requires fracture mechanics analysis, establish a wheel finite element model, divide the wheel finite element model into stress zones, obtain multiple stress zones of the wheel structure and the corresponding zone information, and calculate the characteristic parameters of each zone. Optionally, the partitioning information of the wheel structure is established based on stress distribution.

[0019] Optionally, the specific steps for obtaining multiple stress zones of the wheel structure include: Step S11: Apply periodic external forces to the finite element model of the wheel structure; Step S12: Determine the crack initiation location and principal stress orthogonal plane direction of the wheel structure and extract the crack propagation plane, which is characterized as the principal stress orthogonal plane; Obtain the three-dimensional coordinates of each node in the principal stress orthogonal plane and the principal stress values ​​of each node; Step S13: Reduce the dimensionality of the three-dimensional coordinates of each node in the principal stress orthogonal plane to obtain the two-dimensional coordinates of each node; Step S14: Divide the principal stress orthogonal plane after dimensionality reduction into elements. Each element includes multiple nodes, two-dimensional coordinates of each node, the correspondence between each node, and the stress value of each node. Step S15: Identify the unit type of each unit; Step S16: Obtain the maximum stress value of each element, and obtain the maximum stress value of the principal stress orthogonal plane based on the maximum stress value of each element; The stress value range of the principal stress orthogonal plane is set based on the maximum stress value of the principal stress orthogonal plane; Step S17: Set the stress gradient and perform the first stress partitioning of the stress value range according to the stress gradient; the first stress partitioning is to divide nodes with similar stress values ​​into corresponding stress partitions. Step S18: According to the element type, perform a second stress partitioning on the stress interval after the first stress partitioning to obtain multiple stress partitions; It also includes: step S19, order n =1, when n When =1, it indicates the first stress zone; Step S20: Based on the principle of geometric continuity, the first... n Each element in the stress partition is processed to determine whether the corresponding stress partition contains geometrically discontinuous elements. If so, a first stress partition is created based on the geometrically discontinuous elements. n +1 stress zone, let n = n +1, and update the total number of stress intervals. N Return to step S9; If not, obtain the first n Update the stress partition, record it, and proceed to the next step; Step S21: Repeat steps S19-S20 to traverse each stress zone and obtain multiple updated stress zones. Based on the multiple updated stress zones, obtain multiple partitions of the wheel structure.

[0020] Optionally, the partitioning information of the finite element model of the wheel disk in step S1 includes the partitioning stress, temperature, number of elements, volume, center x-coordinate, center y-coordinate, partitioning type, and x-coordinate and y-coordinate of the stress maximum point for all stress partitions on the principal stress orthogonal plane of the wheel disk. Among them, the partition stress is the partition i The maximum stress value borne by all nodes s i .

[0021] The number of elements in each partition is based on the finite element mesh generation. Each partition of the roulette finite element model consists of several quadrilateral elements, and the number of elements is... n e, i .

[0022] The partition volume is the partition i The volume obtained by rotating the disc around its axis once V i .

[0023] The coordinates of the partition center are the partition i Geometric center coordinates ( x i , y i ).

[0024] Stress zoning type according to zoning i The location is classified into internal stress zones, surface stress zones, and corner element stress zones.

[0025] The coordinates of the point of maximum stress in a given zone are the zone's coordinates. i Coordinates of the point of maximum stress ( x s,i , y s,i ).

[0026] Optionally, the element categories include internal elements, surface elements, and corner elements, and each element is traversed. The number of boundary nodes among the four nodes of an element is used to distinguish between internal and surface elements; if an element contains at least one corner node, then that element is defined as a corner element. Specifically: For each unit E r and its corresponding set of four nodes N Er ,have:

[0027] in, N Represents any node, It is unit E r The set of nodes, A It is a set of surface nodes. B It is a set of corner nodes.

[0028] Optionally, each element includes multiple nodes, two-dimensional coordinates of each node, the correspondence between each node, and stress values ​​of each node; Optionally, the specific steps for identifying the unit type of each unit include: Obtain the correspondence between nodes in each element and the boundary nodes. Determine whether the number of boundary nodes in each element is greater than 1. If yes, the corresponding element is a surface element; otherwise, the corresponding element is an internal element. Calculate the number of elements in a surface element or internal element where each node is shared; Determine if the number of shared units for each node is equal to 1. If yes, the corresponding node is a corner node and proceed to the next step. If no, proceed to the next step. Determine whether each element contains a corner node. If it does, then the corresponding element is determined to be a corner element; otherwise, the original element type is retained.

[0029] S2: Identify the boundary nodes of the wheel structure and each element in each stress zone, obtain the boundary nodes of the wheel structure and each stress zone, and draw the outer boundary of the wheel structure and the outer boundary of each stress zone respectively. Each stress zone is classified based on its outer boundary to obtain the type of each stress zone; For example, each unit has 4 nodes, and each unit has 0-4 boundary points; When there are two boundary points, the boundary points are distributed on the cell in a common-side or diagonal manner; in other cases, the distribution is uniquely determined. For example, when there is one boundary point, the boundary points are distributed only at the corners of the cell; when there are three boundary points, the boundary points are distributed in a triangular pattern; and when there are four boundary points, the boundary points are distributed on the four nodes of the cell.

[0030] Optionally, the distribution types of boundary nodes include distribution without boundary points, angular distribution with a single boundary point, common-side or diagonal distribution with two boundary points, triangular distribution with three boundary points, and full distribution with four boundary points; Optionally, the boundary node types include concave corner nodes, convex corner nodes, and surface nodes; Among them, concave corner nodes A Shared by 3 units, convex corner node B Dedicated to a single unit, surface nodes C It is shared by 2 units.

[0031] Optionally, step S2 specifically includes: Identify the number of boundary nodes and the corresponding boundary node types in each unit of the wheel structure; By determining the combination of boundary nodes, we obtain the set of roulette wheel boundary lines. B d Connect the boundary nodes in the boundary node combination in sequence to form a closed polygon, which serves as the outer contour of the wheel structure.

[0032] For example, in each unit of the roulette structure, there are a total of 1+3+6+10+15=35 possible combinations of boundary nodes. In a continuous roulette model, any unit has at least one adjacent unit, and the number and position of boundary points on the unit should satisfy geometric logic. Therefore, there are a total of 20 possible combinations of boundary points that meet the actual situation, listed below:

[0033] Note: There are 2 in this case. A Class boundary points A 1. A 2, A 1-A "2" indicates A 1 and A 2 are connected, and so on.

[0034] Based on the above combination of boundary nodes, by applying the corresponding boundary drawing method to each unit, a set of wheel boundary lines can be obtained. B d Its form is a closed polygon formed by connecting all boundary points in sequence, which is the outline of the wheel.

[0035] For each element within a stress partition, there may be four nodes that... n Each partition boundary point ( n = 0, 1, 2, 3 or 4), partition boundary points can be classified into concave corner nodes according to the geometric characteristics of the partition boundary. A (Shared by 3 units), convex corner node B There are three types: (exclusively owned by one element) and surface nodes C (shared by two elements).

[0036] In a single cell, there are a total of 1+3+6+10+15=35 possible combinations of partition boundary points. Since any cell in a continuous partition has at least one adjacent cell, and the number and position of partition boundary points in a cell should satisfy geometric logic, there are a total of 20 possible combinations of partition boundary points that meet the actual requirements. These are listed below:

[0037] *Note: There are 2 in this case. A Class partition boundary points A 1. A 2, A 1- A "2" indicates A 1 and A 2 are connected, and so on.

[0038] Based on the above combination of partition boundary points, by applying the corresponding boundary drawing method to each element within the partition, each stress partition can be obtained. i Set of boundary lines B i Its form is partitioned i A closed polygon formed by connecting all the boundary points of the partitions in sequence is called a partition. i The outer contour.

[0039] S3: Determine the crack propagation direction of each stress zone based on the stress zone type; Draw an initial rectangular plate with the crack initiation point as the origin, the crack propagation direction as the initial direction, and the four intersection points of the four orthogonal directions with the outer boundary of the wheel structure as edge points; Optionally, step S3 specifically includes: S31. Based on the stress zone type, determine the crack propagation direction of each stress zone; The stress partitioning types include internal stress partitioning, surface stress partitioning, and corner element stress partitioning; S32. Using the crack initiation point as the origin, and the crack propagation direction as the origin. D i As the initial direction, construct a Cartesian coordinate system. x ' Oy '; Get+ x - x + y - y The four intersection points of the four orthogonal directions with the outer boundary of the wheel structure are represented as points in the Cartesian coordinate system. x + , 0), point ( x - , 0), point (0, y + ) and point (0, y - ); S33, in Cartesian coordinate system x ' Oy 'the point below' As the initial geometric center, with ( x + - x - ) as the initial length, with ( y + - y - Draw a rectangle with the initial width to obtain the initial rectangular plate.

[0040] Step 31 includes the following specific steps: S311, Selecting stress zones i A group of points formed by several points of maximum stress in the inner front S max, i The point group formed by the first few stress minimum points S min, i The average coordinates of each are taken as the center of the stress maximum point group and the stress minimum point group; Optionally, the stress of each node within the stress partition is known. The node sequence is sorted according to the stress value, and the node indexed by the maximum stress value is the point of maximum stress, and the node indexed by the minimum stress value is the point of minimum stress.

[0041] S312, the vector pointing from the center of the stress minimum point group to the center of the stress minimum point group. Gi As stress zone i The stress gradient direction serves as the crack propagation direction for internal stress zones; S313, When stress partitioning i When a stress zone is identified, the surface boundary segment closest to the geometric center within that stress zone is located, and the corresponding normal vector is used as the stress zone. i Crack propagation direction S ⊥, i ; S314, When stress partitioning i When a stress partition is defined as a corner element, the normal of the boundary segment connecting the corner node and its two surrounding surface nodes within the stress partition is taken as the partition line. i Crack propagation direction C ⊥, i .

[0042] Optionally, the crack initiation point can be the point of maximum stress or the geometric center of the zone.

[0043] S4: Transform the Cartesian coordinate system of the wheel into a polar coordinate system with the crack initiation point as the origin and the crack propagation direction as the positive direction. Divide the initial rectangular plate into four sectors along the four angular rays and obtain the polar radius of the intersection point of the ray of each sector with the boundary of the wheel structure. The shortest distance from the origin to the boundary of the disk within the sector is taken as the width of the rectangular plate in the main direction of each sector. The rectangular plate is drawn according to the width of the rectangular plate in the main direction of each sector to obtain the fracture mechanics rectangular plate. Optionally, step S4 is as follows: Cartesian coordinate system x ' Oy Transform it into a polar coordinate system with the crack initiation point as the origin and the crack propagation direction as the positive direction. r , θ ), r Polar radius, θ Polar angle; With the origin of the polar coordinate system O Starting from the initial point, draw rays to the four vertices of the initial rectangular plate. OE ,ray OF ,ray OG and rays OH The finite element model of the roulette wheel is divided into sectors. HOE sector EOF sector FOG and sectors GOH Their principal directions are the Cartesian coordinate system. x ' Oy 'of+ x Direction, + y direction,- xDirection and - y direction; Within each sector, by sector HOE For example, find the rays respectively OH Intersection with the outer boundary of the wheel structure H '( r H’ , θ H’ Record the corresponding polar radius of the intersection point. r H’ Find the ray OE Intersection with the outer boundary of the wheel structure E ' ( r E’ , θ E’ Record the corresponding polar radius of the intersection point. r E’ ; In sector HOE Within, iterate through all the roulette wheel boundary segments to obtain the boundary segments and points of each roulette wheel. O distance d 1, d 2,…, and the polar radius of the intersection point r H’ and the polar radius of the intersection point r E’ Merge the values ​​and take the minimum value as the sector. HOE Width of rectangular plate in the main direction d +x ; Similarly, sectors can be obtained. EOF Corresponding rectangular plate width d +y , FOG Corresponding rectangular plate width d -x and GOH Corresponding rectangular plate width d -y ; In the Cartesian coordinate system x ' Oy 'Next, determine the geometric center as The length of the rectangular plate is ( d +x + d -x The width of the rectangular plate is ( d +y + d -y A rectangular plate for fracture mechanics analysis is obtained according to the stated geometric center, length, and width.

[0044] S5: Take samples at equal intervals along the crack propagation direction of the rectangular plate used for fracture mechanics analysis. For each sampling point, extract the stress value in the crack-free state from the finite element analysis results or stress field interpolation, i.e., the stress at that point when the crack exists is not considered. The stress values ​​in the crack-free state are derived from the elastic or elastoplastic stress analysis of the wheel under rated operating conditions, reflecting the stress distribution along the crack propagation direction near the crack initiation point. Pair the sampling point locations with the corresponding stress values ​​in the crack-free state to plot a stress-location curve. This curve can be used to calculate the stress intensity factor at the crack tip using the weighted function method.

[0045] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for generating a disk-shaped rectangular plate with structured meshes suitable for fracture mechanics analysis, characterized in that, include: S1: For the wheel structure that requires fracture mechanics analysis, establish a wheel finite element model, divide the wheel finite element model into stress zones, obtain multiple stress zones of the wheel structure and the corresponding zone information, and calculate the characteristic parameters of each zone. S2: Identify the boundary nodes of the wheel structure and each element in each stress zone, obtain the boundary nodes of the wheel structure and each stress zone, and draw the outer boundary of the wheel structure and the outer boundary of each stress zone respectively. Each stress zone is classified based on its outer boundary to obtain the type of each stress zone; S3: Determine the crack propagation direction of each stress zone based on the stress zone type; Draw an initial rectangular plate with the crack initiation point as the origin, the crack propagation direction as the initial direction, and the four intersection points of the four orthogonal directions with the outer boundary of the wheel structure as edge points; S4: Transform the Cartesian coordinate system of the wheel into a polar coordinate system with the crack initiation point as the origin and the crack propagation direction as the positive direction. Divide the initial rectangular plate into four sectors along the four angular rays and obtain the polar radius of the intersection point of the ray of each sector with the boundary of the wheel structure. The shortest distance from the origin to the boundary of the disk within the sector is taken as the width of the rectangular plate in the main direction of each sector. The rectangular plate is drawn according to the width of the rectangular plate in the main direction of each sector to obtain the fracture mechanics rectangular plate. S5: Take samples at equal intervals along the crack propagation direction of the rectangular plate used for fracture mechanics analysis. Extract the crack-free stress of the rectangular plate.

2. The method for generating a disk-shaped rectangular plate with a structured mesh suitable for fracture mechanics analysis according to claim 1, characterized in that, Step S1: The partitioning information of the finite element model of the wheel includes the partitioning stress, temperature, number of elements, volume, center x-coordinate, center y-coordinate, partitioning type, and x-coordinate and y-coordinate of the stress maximum point on all stress partitions on the principal stress orthogonal plane of the wheel.

3. The method for generating a disk-shaped rectangular plate with a structured mesh suitable for fracture mechanics analysis according to claim 1, characterized in that, Step S3 specifically includes: S31. Based on the stress zone type, determine the crack propagation direction of each stress zone; The stress partitioning types include internal stress partitioning, surface stress partitioning, and corner element stress partitioning; S32. Using the crack initiation point as the origin, and the crack propagation direction as the origin. D i As the initial direction, construct a Cartesian coordinate system. x ' Oy '; Get+ x - x + y - y The four intersection points of the four orthogonal directions with the outer boundary of the wheel structure are represented as points in the Cartesian coordinate system. x + , 0), point ( x - , 0), point (0, y + ) and point (0, y - ); S33, in Cartesian coordinate system x ' Oy 'the point below' As the initial geometric center, with ( x + - x - ) as the initial length, with ( y + - y - Draw a rectangle with the initial width to obtain the initial rectangular plate.

4. The method for generating a disk-shaped rectangular plate with a structured mesh suitable for fracture mechanics analysis according to claim 3, characterized in that, Step 31 includes the following specific steps: S311, Selecting stress zones i A group of points formed by several points of maximum stress in the inner front S max, i The point group formed by the first few stress minimum points S min, i The average coordinates of each are taken as the center of the stress maximum point group and the stress minimum point group; Optionally, the stress of each node within the stress partition is known. The node sequence is sorted according to the stress value, and the node indexed by the maximum stress value is the point of maximum stress, and the node indexed by the minimum stress value is the point of minimum stress. S312, the vector pointing from the center of the stress minimum point group to the center of the stress minimum point group. G i As stress zone i The stress gradient direction serves as the crack propagation direction for internal stress zones; S313, When stress partitioning i When a stress zone is identified, the surface boundary segment closest to the geometric center within that stress zone is located, and the corresponding normal vector is used as the stress zone. i Crack propagation direction S ⊥, i ; S314, When stress partitioning i When a stress partition is defined as a corner element, the normal of the boundary segment connecting the corner node and its two surrounding surface nodes within the stress partition is taken as the partition line. i Crack propagation direction C ⊥, i .

5. The method for generating a disk-shaped rectangular plate with a structured mesh suitable for fracture mechanics analysis according to claim 1, characterized in that, The crack initiation point can be the point of maximum stress or the geometric center of the zone.

6. The method for generating a disk-shaped rectangular plate with a structured mesh suitable for fracture mechanics analysis according to claim 1, characterized in that, The specific steps of step S4 include: Cartesian coordinate system x ' Oy Transform it into a polar coordinate system with the crack initiation point as the origin and the crack propagation direction as the positive direction. r , θ ), r Polar radius, θ Polar angle; With the origin of the polar coordinate system O Starting from the initial point, draw rays to the four vertices of the initial rectangular plate. OE ,ray OF ,ray OG and rays OH The finite element model of the roulette wheel is divided into sectors. HOE sector EOF sector FOG and sectors GOH Their principal directions are the Cartesian coordinate system. x ' Oy 'of+ x Direction, + y direction,- x Direction and - y direction; Within each sector, by sector HOE For example, find the rays respectively OH Intersection with the outer boundary of the wheel structure H '( r H’ , θ H’ Record the corresponding polar radius of the intersection point. r H’ Find the ray OE Intersection with the outer boundary of the wheel structure E ' ( r E’ , θ E’ Record the corresponding polar radius of the intersection point. r E’ ; In sector HOE Within, iterate through all the roulette wheel boundary segments to obtain the boundary segments and points of each roulette wheel. O The distance between the points and the polar radius of the intersection. r H’ and the polar radius of the intersection point r E’ Merge the values ​​and take the minimum value as the sector. HOE Width of the rectangular plate in the main direction d +x ; Similarly, sectors can be obtained. EOF Corresponding rectangular plate width d +y , FOG Corresponding rectangular plate width d -x and GOH Corresponding rectangular plate width d -y ; In the Cartesian coordinate system x ' Oy 'Next, determine the geometric center as The length of the rectangular plate is ( d +x + d -x The width of the rectangular plate is ( d +y + d -y A rectangular plate for fracture mechanics analysis is obtained according to the stated geometric center, length, and width.

7. The method for generating a disk-shaped rectangular plate with a structured mesh suitable for fracture mechanics analysis according to claim 1, characterized in that, The specific steps of step S5 include: Equally spaced samples are taken along the crack propagation direction of the rectangular plate used for fracture mechanics analysis. For each sampling point, the stress value in the crack-free state is extracted from the finite element analysis results or stress field interpolation, that is, the stress at that point is not considered when a crack exists. The stress values ​​in the crack-free state are derived from the elastic or elastoplastic stress analysis of the wheel under rated operating conditions, reflecting the stress distribution along the crack propagation direction near the crack initiation point. Pair the sampling point locations with the corresponding stress values ​​in the crack-free state to plot a stress-location curve. This curve can be used to calculate the stress intensity factor at the crack tip using the weighted function method.

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