Result post-processing method for FEA analysis

Abstract

The invention belongs to the technical field of finite element post-processing, and particularly relates to a result post-processing method for FEA analysis. Establishing a unit set of all finite element units in each structure in the finite element structure; the section direction of the sectioning body is recognized, and the three-dimensional sectioning body is mapped to visual information port coordinates through coordinate mapping; judging the direction of each composition surface patch of the three-dimensional sectioning body; internal circulation processing: in the volume rendering processing process, template test circulation processing is carried out on each cutting layer; performing multi-section volume editing pretreatment, volume rendering treatment and contour surface circulation treatment. The result post-processing method for FEA analysis is mainly used for further improving the efficiency of data preprocessing and finite element model data generation in the finite element analysis processing process, reducing the number of unnecessary data points located on the positive surface, further limiting the total data size in the finite element model post-processing process and improving the post-processing efficiency.

Description

Technical Field

[0001] The invention belongs to the technical field of finite element post-processing, and in particular relates to a result post-processing method for FEA analysis. Background Art

[0002] The post-processing of FEA analysis results mainly refers to the formation of visual three-dimensional data of key data in each vertex, facet, and configuration in the finite element model based on various finite element analysis schemes and volume rendering methods, etc., in order to improve the readability of the data, so that various spatial physical parameters and their energy and space-time relationships can be expressed in a simple and easy-to-understand form that is easy to analyze and process, so that it can achieve higher analysis and understanding efficiency in the process of scientific research and teaching. Its design content includes finite element model unit vertex analysis processing, unit model drawing, etc. Since different finite element analysis programs and model structures may use different data structure forms and processing schemes, most finite element analysis programs can often only perform corresponding post-processing analysis for specific fields, and the efficiency of post-processing and the accuracy of the results are greatly affected by changes in specific processing schemes. Summary of the invention

[0003] The purpose of the present invention is to provide a method for post-processing the results of FEA analysis, which is used to optimize the finite element data analysis process, improve the efficiency of finite element analysis data post-processing, reduce the total data capacity, and reduce the consumption of computing power and storage resources in the post-processing process.

[0004] To achieve the above purpose, the present invention adopts the following technical solution.

[0005] A method for post-processing results of FEA analysis, comprising the following steps:

[0006] Step 1, initialization processing, establishing a unit set of all finite element units in each structure in the finite element structure; defining a transformation function for controlling the color and transparency of the finite element units in the unit set based on the transformation function method; the unit set refers to a data structure table for expressing a finite element solid unit model, and in particular, in this embodiment, the unit set is composed of an array representing a unit name, a unit node number, a unit edge table, a unit face table, and a unit face node number;

[0007] Step 2: Identify the direction of the section of the section body, map the 3D section body to the coordinates of the visualization information port through coordinate mapping; determine the direction of each component face of the 3D section body; perform internal loop processing, and perform template test loop processing on each slice during the volume rendering process;

[0008] Step 3: Preprocessing of multi-section editing. Multi-section editing is only applicable to the case where the unit set of the finite element unit involves multiple sections. For the n sections involved, the pixels in the finite element unit set will be divided into z n There are two types of subsets, each of which is defined by a different transformation function. The subsets are divided into two categories. Category A is located inside the section body and is discarded during the carrier drawing process. Category B requires a corresponding transformation function for each section body to perform a volume drawing operation. During the drawing process, a section mark is established to mark the sectioning process of each vertex. If it is a vertex retained after sectioning, it is marked as 1, otherwise it is 0. For each unit, the unit set data structure table is queried to determine whether the mark value of each edge vertex is consistent. If not, it means that there is an intersection between the edge and the section plane, and the intersection parameters are calculated.

[0009] Step 4: Volume rendering processing, including:

[0010] 4a Node coordinate conversion specifically refers to converting the finite element unit node coordinates from the space coordinates of the finite element unit model to the visualization information port coordinates;

[0011] 4b Surface data extraction is used to store all external surface storage sequences. Each element in the external surface storage sequence stores the surface information of a certain external surface.

[0012] 4c Overlapping external surfaces screening: Get the vertex sequences of all external surfaces. For any two surfaces, to determine whether they overlap, compare the first sequence values ​​in the corresponding vertex sequences of the two surfaces. If they are different, they must not overlap; if the first sequence values ​​are the same, compare the second sequence values. If they are different, they must not overlap, and continue to compare the third sequence values... Repeat the above steps until it is determined whether the two faces overlap;

[0013] 4d active object processing: Establish a multi-level object storage table structure, the multi-level object includes a first-level edge storage table structure, a second-level face storage structure, and a third-level unit storage structure; the edge storage table structure stores the edge data of a section, the elements in the storage table are edge object linked lists, and the edges in each edge object linked list perform data storage twice, and the stored data are two vertex sequences of the edge object, and the two vertex sequences are filled in sequence according to their order in the vertex sequence of the finite element model; the face storage structure stores an outer surface linked list of a finite element unit, extracts the order of each outer surface in the surface sequence of the finite element model, and fills the sequence number into each outer surface linked list in sequence; the unit storage structure stores the unit data of the finite element model, and the elements in the storage table are finite element units;

[0014] 4e interactive object activity processing, including the cells, surfaces or edges that intersect with the currently analyzed object, specifically refers to: in each object analysis and processing process, analyzing the elements of all the next-level storage structures of the object in the multi-level object storage table structure, and judging the interactivity of the corresponding elements with the current object;

[0015] 4f surface drawing: extract the active surface determined in the previous step, establish an active surface data table consisting of the surface serial number, marking information, and the intersection data of the surface and the section, and determine the drawing method through the intersection information of adjacent sections and the active surface;

[0016] Step 5: Optimize the visualization isosurface. To improve the mixed expression effect of isosurfaces in the volume rendering image and optimize the interference between isosurfaces, the following method is used:

[0017] 5a. Extract the vertex data of the finite element model unit, establish the vertex gradient direction table, and set the buffer value of the depth test to the minimum value of the Z axis in the finite element mechanism;

[0018] 5b. Isosurface loop processing, the loop steps include: 1. Extracting unit section polygon parameters; 2. Pre-drawing section polygons, generating isosurface pixels based on the points that pass the test, and assigning the pixel values ​​to the template test buffer; using the vertex gradient direction table to perform lighting calculations to draw colors; 3. Using the template test to complete the volume rendering of the remaining pixels, and using the corresponding section polygon transformation function to determine the pixel value of each pixel.

[0019] As a further improvement or specific implementation method of the above-mentioned post-processing method for the results of FEA analysis, the direction of each component facet of the three-dimensional sectioned body is determined in step 2 based on the following method: generating a normal vector from the inside of the three-dimensional sectioned body to the outside on each component facet of the three-dimensional sectioned body; calculating the dot product of each normal vector and the unit vector of the coordinate axis. If the result is positive, it means that the direction of the facet is axially positive, otherwise it is axially negative.

[0020] Further improvement or specific implementation of the above-mentioned post-processing method for FEA analysis results, the template test loop processing in step 2 includes: first, clearing the content of the template test buffer and replacing the depth information with the current Z-axis coordinate; in the process of executing the depth test, shielding the color editing processing of the volume rendering image; performing a depth test and a template test that are incremented by one until the volume rendering parameter generation of all the rear surfaces of the sectioned polyhedron is completed; secondly, under the current configuration, performing a depth test and a template test that are decremented by one until the drawing parameter generation of all the front surfaces of the sectioned polyhedron is completed; finally, closing the depth test, opening the color editing processing of the volume rendering image, and executing volume rendering.

[0021] For further improvement or specific implementation of the above-mentioned post-processing method for FEA analysis results, in step 5, the vertex gradient direction table is determined based on the following method:

[0022] Establish a unit node list of the finite element model, wherein the first node element of the unit node list is connected to the remaining node elements through a unit variable;

[0023] Establish the relationship between node data value, three-axis coordinate difference and gradient direction: where v m ,v n are the data values ​​of nodes m and n respectively, i=x, y, z represent three coordinate axes, T i is the gradient value of the i-axis object, i m ,i n are the i-axis coordinate values ​​of nodes m and n respectively;

[0024] In order to solve the gradient of a node n in the unit node list, node n is connected to the remaining nodes in the unit node list to establish gradient direction relationships, and the gradient is solved based on the least squares method. The calculation method is as follows:

[0025]

[0026] Where i≠j and j=x, y, z represent three coordinate axes; o represents all other nodes in the unit node list except node n.

[0027] For further improvement or specific implementation of the above-mentioned post-processing method for FEA analysis results, the surface information in step 4 includes: the finite element unit affiliation of the outer surface, the face sequence of the outer surface in the finite element unit, and the vertex sequence of the outer surface; the finite element unit affiliation refers to which finite element unit the outer surface belongs to; the face sequence refers to the order in which the outer surface is located in all outer surface sequences of the finite element unit; the vertex sequence refers to a number of vertices that surround the outer surface and can determine the surface position, and these vertices are selected sequentially according to their order in the vertex sequence of the finite element model.

[0028] Further improvement or specific implementation of the above-mentioned post-processing method for FEA analysis results, the step 4f specifically includes: in the process of surface drawing for each unit, analyzing the outer surface list of each finite element unit, directly drawing the outer surface that is completely between two adjacent sections; extracting the vertex information of the newly added outer surface that has no intersection with the previous section. Determine the intersection of the outer surface and the current section by the active edge data, and determine its positional relationship with the current section in combination with the outer surface vertex information, draw the area before the current section, and draw the area after the current section as the outer surface to be processed by the next section; establish a vertex position mark of the finite element unit, the mark content is the relative position relationship between the vertex and the section, for the edge composed of any two vertices of the finite element unit, determine the mark attributes of the two vertices and the section, if the mark attributes are different, it means that the edge intersects with the section, generate the intersection data of the edge and the section, and generate all the intersection data of the finite element unit and the section in the order of vertices to obtain the section polygon.

[0029] Its beneficial effects are:

[0030] The post-processing method for FEA analysis results in this application is mainly used to further improve the efficiency of data preprocessing and finite element model data generation during the finite element analysis process, reduce the number of unnecessary data points located on the active surface, and thus limit the total data volume in the finite element model post-processing process, thereby improving the post-processing efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a cell set representation method for tetrahedral finite element units;

[0032] Figure 2 This is a schematic diagram of the basic principle of template testing. DETAILED DESCRIPTION

[0033] The present invention is described in detail below in conjunction with specific embodiments.

[0034] The present application relates to a post-processing method for the results of FEA analysis. The method is aimed at the post-processing process of basic finite element structural models based on points, edges, and surfaces. It is not limited to specific finite element programs or types of finite element models. It mainly further optimizes the vertices, edges, surfaces, sectioned bodies and other elements of the finite element model to cooperate with optimized surface sectioning, volume rendering and other steps to improve the efficiency of post-processing.

[0035] This method designs several continuous or independent preprocessing or optimization processing steps, which are based on independent implementation or combined with the current finite element analysis and post-processing process. Some of the basic concepts or contents of the finite element analysis processing involved can be obtained by querying the corresponding public algorithms or the corresponding program instructions, and will not be expanded in this application.

[0036] The following describes the main steps of the post-processing method for FEA analysis results:

[0037] Step 1, initialization processing, establishing a unit set of all finite element units in each structure in the finite element structure; defining a transformation function for controlling the color and transparency of the finite element units in the unit set based on the transformation function method; the unit set refers to a data structure table for expressing a finite element solid unit model, and in particular, in this embodiment, the unit set is composed of an array representing a unit name, a unit node number, a unit edge table, a unit face table, and a unit face node number;

[0038] In the present application, a data structure table is separately configured for optimizing the processing of vertices, edges and unit faces in the subsequent processing flow, which is similar to the multi-dimensional data expression of points, edges, faces and unit bodies in the traditional finite element model. The data structure table stores the index sequence of the corresponding units, nodes, edges and unit faces to facilitate the rapid establishment of their topological relationships to meet the needs of subsequent edge and face cutting.

[0039] like Figure 1 As shown in FIG. 1 , a unit set representation method for a common tetrahedral finite element unit is shown, where A, B, and C represent vertices, edges, and surfaces, respectively, and the inner surface is represented by a lead line.

[0040] 2. Identify the direction of the section of the section body, map the 3D section body to the coordinates of the visualization information port through coordinate mapping; determine the direction of each component face of the 3D section body; internal loop processing, perform template test loop processing on each slice during the volume rendering process;

[0041] As a preferred method, the direction of each component face of the three-dimensional section body is determined based on the following method: generating a normal vector from the inside of the three-dimensional section body to the outside on each component face of the three-dimensional section body; calculating the dot product of each normal vector and the unit vector of the coordinate axis. If the result is positive, it means that the direction of the face is axially positive, otherwise it is axially negative;

[0042] The template test loop processing means: first, clear the template test buffer content and replace the depth information with the current Z-axis coordinate; in the process of executing the depth test, shield the color editing processing of the volume rendering image; perform the depth test and template test of increasing by one successively until the volume rendering parameter generation of all the rear surfaces of the sectioned polyhedron is completed; secondly, perform the depth test and template test of decreasing by one successively under the current configuration until the rendering parameter generation of all the front surfaces of the sectioned polyhedron is completed; finally, turn off the depth test, open the color editing processing of the volume rendering image, and perform volume rendering;

[0043] 3. Preprocessing of multi-section body editing. Multi-section body editing is only for the case where the unit set of the finite element unit involves multiple sections. For the n sections involved, the pixels in the finite element unit set will be divided into z n There are two types of subsets, each of which is defined by a different transformation function. The A type is located inside the section body and is discarded during the carrier drawing process. The B type requires a transformation function to be used for each section body before volume drawing.

[0044] During the drawing process, a cutting mark is established to mark the cutting process of each vertex. If it is a vertex to be retained after cutting, it is marked as 1, otherwise it is marked as 0. For each unit, the unit set data structure table is queried to determine whether the marking value of each edge vertex is consistent. If it is inconsistent, it means that there is an intersection between the edge and the cutting surface, and the intersection parameters are calculated.

[0045] 4. Volume rendering processing:

[0046] 4a Node coordinate conversion specifically refers to converting the finite element unit node coordinates from the space coordinates of the finite element unit model to the visualization information port coordinates;

[0047] 4b Surface data extraction is constructed to store all external surface storage sequences. Each element in the external surface storage sequence stores the surface information of a certain external surface. The surface information includes: the finite element unit to which the external surface belongs, the face sequence of the external surface in the finite element unit, and the vertex sequence of the external surface. The finite element unit to which the external surface belongs refers to the finite element unit to which the external surface belongs; the face sequence refers to the order in which the external surface is located in all external surface sequences of the finite element unit; the vertex sequence refers to a number of vertices that surround the external surface and can determine the surface position, and these vertices are selected in sequence according to their order in the vertex sequence of the finite element model;

[0048] 4c Overlapping external surfaces screening: Get the vertex sequences of all external surfaces. For any two surfaces, to determine whether they overlap, compare the first sequence values ​​in the corresponding vertex sequences of the two surfaces. If they are different, they must not overlap; if the first sequence values ​​are the same, compare the second sequence values. If they are different, they must not overlap, and continue to compare the third sequence values... Repeat the above steps until it is determined whether the two faces overlap;

[0049] 4d active object processing: Establish a multi-level object storage table structure, the multi-level object includes a first-level edge storage table structure, a second-level face storage structure, and a third-level unit storage structure; the edge storage table structure stores the edge data of a section, the elements in the storage table are edge object linked lists, and the edges in each edge object linked list perform data storage twice, and the stored data are two vertex sequences of the edge object, and the two vertex sequences are filled in sequence according to their order in the vertex sequence of the finite element model; the face storage structure stores an outer surface linked list of a finite element unit, extracts the order of each outer surface in the surface sequence of the finite element model, and fills the sequence number into each outer surface linked list in sequence; the unit storage structure stores the unit data of the finite element model, and the elements in the storage table are finite element units;

[0050] 4e interactive object activity processing, including the cells, surfaces or edges that intersect with the currently analyzed object, specifically refers to: in each object analysis and processing process, analyzing the elements of all the next-level storage structures of the object in the multi-level object storage table structure, and judging the interactivity of the corresponding elements with the current object;

[0051] 4f surface drawing: extract the active surface determined in the previous step, establish an active surface data table consisting of the surface serial number, marking information, and the intersection data between the surface and the section, and determine the drawing method through the intersection information of adjacent sections and the active surface. Specifically: in the process of surface drawing for each unit, analyze the external surface list of each finite element unit, and directly draw the external surface that is completely between two adjacent sections; for the newly added external surface that has no intersection with the previous section, extract the vertex information of the external surface. The intersection of the outer surface and the current section is determined by the active edge data, and its positional relationship with the current section is determined in combination with the outer surface vertex information. The area before the current section is drawn, and the area after the current section is drawn as the outer surface to be processed by the next section; a vertex position mark of a finite element unit is established, and the mark content is the relative positional relationship between the vertex and the section surface. For an edge formed by any two vertices of the finite element unit, the mark attributes of the two vertices and the section surface are determined. If the mark attributes are different, it means that the edge is an active edge intersecting with the section surface, and the intersection data of the edge and the section surface are generated. All the intersection data of the finite element unit and the section surface are generated in sequence according to the vertex order to obtain the section polygon;

[0052] 5. Visualization of isosurface optimization processing

[0053] Isosurface is a visualization method of the three-dimensional data field of the finite element model, which is used to express the area or space with a specific value. In this application, in order to improve the mixed expression effect of isosurfaces in the volume rendering image and optimize the interference problem between isosurfaces, the following method is used for processing:

[0054] 5a. Vertex gradient analysis: extract vertex data of finite element model units, establish vertex gradient direction table, and set the buffer value of depth test to the minimum value of Z axis in finite element mechanism;

[0055] In particular, the vertex gradient direction table is determined based on the following method: 1. Establishing a unit node list of the finite element model, the first node element of the unit node list is connected to the remaining node elements through a unit variable; 2. Establishing the relationship between the node data value, the three-axis coordinate difference and the gradient direction: where v m ,v n are the data values ​​of nodes m and n respectively, i=x, y, z represent three coordinate axes, T i is the gradient value of the i-axis object, i m ,i n are the i-axis coordinate values ​​of nodes m and n respectively; 3. To solve the gradient of a node n in the unit node list, connect the remaining nodes in the unit node list with node n to establish gradient direction relationships, and solve the gradient based on the least squares method. The calculation method is as follows:

[0056]

[0057] Where i≠j and j=x, y, z represent three coordinate axes; o represents all other nodes in the unit node list except node n;

[0058] 5b. Isosurface loop processing, the loop steps include:

[0059] 1. Extract unit section polygon parameters;

[0060] 2. Pre-draw the slice polygon, generate isosurface pixels according to the points that pass the test, and assign the pixel values ​​to the template test buffer; use the vertex gradient direction table to perform lighting calculations to draw colors;

[0061] 3. Use template testing to complete the volume rendering of the remaining pixels, and use the corresponding sectioning polygon transformation function to determine the pixel value of each pixel. The template test may have different graphics APIs or rendering modes used by different finite element models, but they are all based on the same test principle. The basic principle of the template test is as follows: Figure 2 shown.

[0062] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention, rather than to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the essence and scope of the technical solution of the present invention.

Claims

1. A method for post-processing results of FEA analysis, characterized in that: The steps include: Step 1, initialization processing, establishing a unit set of all finite element units in each structure in the finite element structure; defining a transformation function for controlling the color and transparency of the finite element units in the unit set based on the transformation function method; the unit set refers to a data structure table for expressing a finite element solid unit model; Step 2: Identify the direction of the section of the section body, map the 3D section body to the coordinates of the visualization information port through coordinate mapping; determine the direction of each component face of the 3D section body; perform internal loop processing, and perform template test loop processing on each slice during the volume rendering process; Step 3: Preprocessing of multi-section editing. Multi-section editing is only applicable to the case where the unit set of the finite element unit involves multiple sections. For the n sections involved, the pixels in the finite element unit set will be divided into z n There are two types of subsets, each of which is defined by a different transformation function. The subsets are divided into two categories. Category A is located inside the section body and is discarded during the carrier drawing process. Category B requires a corresponding transformation function for each section body to perform a volume drawing operation. During the drawing process, a section mark is established to mark the sectioning process of each vertex. If it is a vertex retained after sectioning, it is marked as 1, otherwise it is 0. For each unit, the unit set data structure table is queried to determine whether the mark value of each edge vertex is consistent. If not, it means that there is an intersection between the edge and the section plane, and the intersection parameters are calculated. Step 4: Volume rendering processing, including: 4a Node coordinate conversion specifically refers to converting the finite element unit node coordinates from the space coordinates of the finite element unit model to the visualization information port coordinates; 4b Surface data extraction is used to store all external surface storage sequences. Each element in the external surface storage sequence stores the surface information of a certain external surface. 4c Overlapping external surfaces screening: Get the vertex sequences of all external surfaces. For any two surfaces, to determine whether they overlap, compare the first sequence values ​​in the corresponding vertex sequences of the two surfaces. If they are different, they must not overlap; if the first sequence values ​​are the same, compare the second sequence values. If they are different, they must not overlap, and continue to compare the third sequence values... Repeat the above steps until it is determined whether the two faces overlap; 4d active object processing: Establish a multi-level object storage table structure, the multi-level object includes a first-level edge storage table structure, a second-level face storage structure, and a third-level unit storage structure; the edge storage table structure stores the edge data of a section, the elements in the storage table are edge object linked lists, and the edges in each edge object linked list perform data storage twice, and the stored data are two vertex sequences of the edge object, and the two vertex sequences are filled in sequence according to their order in the vertex sequence of the finite element model; the face storage structure stores an outer surface linked list of a finite element unit, extracts the order of each outer surface in the surface sequence of the finite element model, and fills the sequence number into each outer surface linked list in sequence; the unit storage structure stores the unit data of the finite element model, and the elements in the storage table are finite element units; 4e interactive object activity processing, including the cells, surfaces or edges that intersect with the currently analyzed object, specifically refers to: in each object analysis and processing process, analyzing the elements of all the next-level storage structures of the object in the multi-level object storage table structure, and judging the interactivity of the corresponding elements with the current object; 4f surface drawing: extract the active surface determined in the previous step, establish an active surface data table consisting of the surface serial number, marking information, and the intersection data of the surface and the section, and determine the drawing method through the intersection information of adjacent sections and the active surface; Step 5: Optimize the visualization isosurface. To improve the mixed expression effect of isosurfaces in the volume rendering image and optimize the interference between isosurfaces, the following method is used: 5a. Extract the vertex data of the finite element model unit, establish the vertex gradient direction table, and set the buffer value of the depth test to the minimum value of the Z axis in the finite element mechanism; 5b. Isosurface loop processing, the loop steps include:

1. Extracting unit section polygon parameters; 2. Pre-drawing section polygons, generating isosurface pixels based on the points that pass the test, and assigning the pixel values ​​to the template test buffer; using the vertex gradient direction table to perform lighting calculations to draw colors; 3. Using the template test to complete the volume rendering of the remaining pixels, and using the corresponding section polygon transformation function to determine the pixel value of each pixel.

2. The method for post-processing results of FEA analysis according to claim 1, characterized in that: The direction of each component facet of the three-dimensional sectioned body is determined in step 2 based on the following method: generating a normal vector from the inside of the three-dimensional sectioned body to the outside on each component facet of the three-dimensional sectioned body; calculating the dot product of each normal vector and the unit vector of the coordinate axis. If the result is positive, it means that the direction of the facet is axially positive, otherwise it is axially negative.

3. The method for post-processing results of FEA analysis according to claim 1, characterized in that: The template test loop processing in step 2 includes: first, clearing the content of the template test buffer and replacing the depth information with the current Z-axis coordinate; in the process of executing the depth test, shielding the color editing processing of the volume rendering image; performing a depth test and a template test that are incremented by one, until the volume rendering parameter generation of all the rear surfaces of the sectioned polyhedron is completed; secondly, under the current configuration, performing a depth test and a template test that are decremented by one, until the rendering parameter generation of all the front surfaces of the sectioned polyhedron is completed; finally, closing the depth test, opening the color editing processing of the volume rendering image, and executing volume rendering.

4. The method for post-processing results of FEA analysis according to claim 1, characterized in that: In step 5, the vertex gradient direction table is determined based on the following method: Establish a unit node list of the finite element model, wherein the first node element of the unit node list is connected to the remaining node elements through a unit variable; Establish the relationship between node data value, three-axis coordinate difference and gradient direction: where v m ,v n are the data values ​​of nodes m and n respectively, i=x, y, z represent three coordinate axes, T i is the gradient value of the i-axis object, i m ,i n are the i-axis coordinate values ​​of nodes m and n respectively; In order to solve the gradient of a node n in the unit node list, node n is connected to the remaining nodes in the unit node list to establish gradient direction relationships, and the gradient is solved based on the least squares method. The calculation method is as follows: Where i≠j and j=x, y, z represent three coordinate axes; o represents all other nodes in the unit node list except node n.

5. The method for post-processing results of FEA analysis according to claim 1, characterized in that: The surface information in step 4 includes: the finite element unit to which the outer surface belongs, the face sequence of the outer surface in the finite element unit, and the vertex sequence of the outer surface; the finite element unit to which the outer surface belongs refers to which finite element unit the outer surface belongs to; the face sequence refers to the order in which the outer surface is located in all outer surface sequences of the finite element unit; the vertex sequence refers to a number of vertices that surround the outer surface and can determine the surface position, and these vertices are selected sequentially according to their order in the vertex sequence of the finite element model.

6. The method for post-processing results of FEA analysis according to claim 1, characterized in that: The step 4f specifically includes: in the process of surface drawing for each unit, analyzing the outer surface linked list of each finite element unit, and directly drawing the outer surface that is completely between two adjacent sections; for the newly added outer surface that has no intersection with the previous section, extracting the vertex information of the outer surface; determining the intersection of the outer surface and the current section by the active edge data, judging its positional relationship with the current section in combination with the outer surface vertex information, drawing the area before the current section, and drawing the area after the current section as the outer surface to be processed by the next section; establishing a vertex position mark for the finite element unit, the mark content is the relative positional relationship between the vertex and the section, for the edge formed by any two vertices of the finite element unit, judging the mark attributes of the two vertices and the section, if the mark attributes are different, it means that the edge is an active edge that intersects with the section, generating the intersection data of the edge and the section, and generating all the intersection data of the finite element unit and the section in sequence according to the vertex order to obtain the section polygon.

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