Model processing method for two-dimensional finite element analysis of cylindrical member and storage medium

Abstract

A model processing method for two-dimensional finite element analysis of a cylindrical member and a storage medium, which contribute to improvement of the accuracy of two-dimensional finite element analysis of a cylindrical member. In the model processing method for two-dimensional finite element analysis of a cylindrical member of the present invention, a plurality of pairs of polygons located in a plane of a cross section of a cylinder are used as equivalent cross sections of a circular cross section of the cylindrical member, the pairs of polygons are respectively axially symmetrical about a first axis passing through a center of the circular cross section, and each polygon is axially symmetrical about a second axis passing through the center and perpendicular to the first axis, on each side of the first axis, a plurality of polygons are adjacently arranged from the first axis in a direction away from the first axis, the more away from the first axis, the shorter the intersection line between the adjacent polygons, and the size of each polygon is determined in a manner satisfying a condition that the total area of the plurality of pairs of polygons is equal to the total area of the circular cross section and a condition that the total moment of inertia of the plurality of pairs of polygons is equal to the moment of inertia of the circular cross section.

Description

Technical Field

[0001] This invention relates to a model processing method and storage medium for two-dimensional finite element analysis of cylindrical components. Background Technology

[0002] In mechanical equipment across various fields such as aerospace, ground-based gas turbines, and construction machinery, different parts are often connected via bolts. Bolts play a crucial role in transferring loads and maintaining connections; their failure can compromise the stability of these connections, potentially leading to catastrophic accidents such as increased vibration and parts detachment. Therefore, in the finite element analysis phase of mechanical design, it is essential to perform detailed modeling of bolts to improve analysis accuracy and support component design. A screw is a cylindrical section of a bolt or screw with a certain length and helical grooves on its outer surface. When used in conjunction with a nut, it generates a preload and bears tensile / bending loads, thus securing the connected components. Therefore, the equivalent method of its finite element model is crucial for the accuracy of structural analysis.

[0003] In domestic research on two-dimensional structural stress analysis in various fields such as aerospace, ground-based gas turbines, and construction machinery, the main approach to screw equivalence is through mass equivalence, using plane stress elements of uniform thickness to simulate the screw. For example, ... Figure 4 As shown, if the screw radius is r, then the existing mass equivalence method sets the equivalent component of the screw as follows: Figure 5 The column shown has a rectangular cross-section with thickness t = πr / 2 and height h = 2r. Therefore, the moment of inertia of the equivalent component's cross-section is I = (1 / 3)πr. 4 (Representing bending stiffness), and the theoretical moment of inertia of the screw I=(1 / 4)πr 4 Inconsistency, i.e., differences in bending stiffness, will affect the analysis results. Summary of the Invention

[0004] The present invention was made in view of the above-mentioned problems, and its purpose is to provide a model processing method and storage medium for two-dimensional finite element analysis of cylindrical components, which helps to improve the accuracy of two-dimensional finite element analysis of cylindrical components.

[0005] To achieve the above objectives, the present invention provides a model processing method for two-dimensional finite element analysis of cylindrical components. This method uses multiple pairs of polygons located in the plane of the cylindrical cross-section as equivalent sections of the circular cross-section of the cylindrical component (different thickness parameters are set for the finite element elements of the cylindrical component). The multiple pairs of polygons are axisymmetric about a first axis passing through the center of the circular cross-section, and each polygon is axisymmetric about a second axis passing through the center and perpendicular to the first axis. On each side of the first axis, multiple polygons are arranged adjacently from the first axis in a direction away from it, and the further away from the first axis, the shorter the intersection line between adjacent polygons. The dimensions of each polygon are determined in a manner that satisfies a first condition and a second condition. The first condition is that the total area of ​​the multiple pairs of polygons is equal to the area of ​​the circular cross-section (mass equivalence), and the second condition is that the total moment of inertia of the multiple pairs of polygons is equal to the moment of inertia of the circular cross-section (stiffness equivalence).

[0006] According to the model processing method for two-dimensional finite element analysis of cylindrical components of the present invention, multiple pairs of polygons located in the plane of the cylindrical cross-section are set as the equivalent cross-section of the circular cross-section of the cylindrical component. The multiple pairs of polygons are axially symmetric about a first axis passing through the center of the circular cross-section, and each polygon is axially symmetric about a second axis passing through the center and perpendicular to the first axis. On each side of the first axis, multiple polygons are arranged adjacently from the first axis in a direction away from the first axis. The further away from the first axis, the shorter the intersection line between adjacent polygons. Therefore, the obtained equivalent cross-section is closer to a circle as a whole. When the cylindrical component forms a coupling relationship with the surrounding components, the finite element analysis result is closer to the real situation. Furthermore, the size of each polygon is determined in a way that satisfies the first and second conditions. The first condition is that the total area of ​​the multiple pairs of polygons is equal to the area of ​​the circular cross-section. The second condition is that the total moment of inertia of the multiple pairs of polygons is equal to the moment of inertia of the circular cross-section. That is, while ensuring that the mass of the finite element model and the real cylindrical component are consistent, the bending stiffness of the two is also consistent. Therefore, it helps to improve the accuracy of two-dimensional finite element analysis of cylindrical components.

[0007] Furthermore, in the model processing method for two-dimensional finite element analysis of cylindrical components of the present invention, the polygon is preferably a rectangle.

[0008] According to the model processing method for two-dimensional finite element analysis of cylindrical components of the present invention, the polygons are rectangles, thus further simplifying the calculation of the dimensions of multiple pairs of polygons.

[0009] Furthermore, in the model processing method for two-dimensional finite element analysis of cylindrical components of the present invention, it is preferable that on each side of the first axis, the dimension of each rectangle in the direction parallel to the first axis is b. iLet the dimension of each rectangle in the direction parallel to the second axis be r. i Where i is a natural number from 1 to n, and the larger i is, the further the rectangle is from the first axis, satisfying r1 to r n Given that the sum of the values ​​is equal to the radius of the circular cross-section, by pre-specifying r1 to r n The values ​​of b1 to b n The values ​​of n-2 in the set are used to determine b1 to b2 based on the first and second conditions. n The remaining two values ​​in the table.

[0010] According to the model processing method for two-dimensional finite element analysis of cylindrical components of the present invention, on each side of the first axis, the dimension of each rectangle in the direction parallel to the first axis is set to be b. i Let the dimension of each rectangle in the direction parallel to the second axis be r. i Where i is a natural number from 1 to n, and the larger i is, the further the rectangle is from the first axis, satisfying r1 to r n Given that the sum of the values ​​is equal to the radius of the circular cross-section, by pre-specifying r1 to r n The values ​​of b1 to b n The values ​​of n-2 in the set are used to determine b1 to b2 based on the first and second conditions. n The values ​​of the remaining two in the equation can be used to further simplify the calculation of the dimensions of multiple pairs of polygons.

[0011] Furthermore, in the model processing method for two-dimensional finite element analysis of cylindrical components of the present invention, it is preferable to use r1 to r n The value of each is set to one-nth of the radius of the circular cross-section.

[0012] According to the model processing method for two-dimensional finite element analysis of cylindrical components of the present invention, r1 to r n The values ​​are all set to one-nth of the radius of the circular cross section, which further simplifies the calculation of the dimensions of multiple pairs of polygons.

[0013] Furthermore, in the model processing method for two-dimensional finite element analysis of cylindrical components of the present invention, n is preferably 4 or more. If the straight line containing the side of the i-th rectangle closest to the first axis is defined as the i-th straight line, then the distance between the two intersection points of the first straight line to the (n-2)-th straight line and the edge of the circular cross-section is defined as b1 to b... n-2 The value of .

[0014] According to the model processing method for two-dimensional finite element analysis of cylindrical components of the present invention, when n is 4 or more, if the straight line containing the edge of the i-th rectangle closest to the first axis is defined as the i-th straight line, then the distances between the two intersection points of the first straight line to the (n-2)-th straight line and the edge of the circular cross-section are respectively defined as b1 to b... n-2 The value of can thus further simplify the calculation of the dimensions of multiple pairs of polygons.

[0015] Furthermore, in the model processing method for two-dimensional finite element analysis of cylindrical components of the present invention, it is preferable that the intersection line between adjacent polygons is parallel to the first axis.

[0016] According to the model processing method for two-dimensional finite element analysis of cylindrical components of the present invention, the intersection line between adjacent polygons is parallel to the first axis, thus further simplifying the calculation of the dimensions of multiple pairs of polygons.

[0017] Furthermore, in the model processing method for two-dimensional finite element analysis of cylindrical components of the present invention, the cylindrical component is preferably a screw.

[0018] Here, cylindrical components, for example, are connected to their surrounding components to form an assembly.

[0019] Furthermore, in order to achieve the above objectives, the present invention provides a storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the model processing method for two-dimensional finite element analysis of cylindrical components as described in any of the preceding claims.

[0020] (Invention Effects)

[0021] According to the present invention, multiple pairs of polygons located in the plane of the cylindrical cross-section are set as the equivalent cross-section of the circular cross-section of the cylindrical component. The multiple pairs of polygons are axially symmetric about a first axis passing through the center of the circular cross-section, and each polygon is axially symmetric about a second axis passing through the center and perpendicular to the first axis. On each side of the first axis, the multiple polygons are arranged adjacently from the first axis in a direction away from the first axis. The further away from the first axis, the shorter the intersection line between adjacent polygons. Therefore, the obtained equivalent cross-section is easy to approximate a circle as a whole. When the cylindrical component forms a coupling relationship with the surrounding components, the finite element analysis results are closer to the real situation. Furthermore, the size of each polygon is determined in a way that satisfies the first condition and the second condition. The first condition is that the total area of ​​the multiple pairs of polygons is equal to the area of ​​the circular cross-section. The second condition is that the total moment of inertia of the multiple pairs of polygons is equal to the moment of inertia of the circular cross-section. That is, while ensuring that the mass of the finite element model and the real cylindrical component are consistent, the bending stiffness of the two is also consistent. Therefore, it helps to improve the accuracy of the two-dimensional finite element analysis of the cylindrical component. Attached Figure Description

[0022] Figure 1 This is a schematic diagram showing the circular cross-section of a cylindrical component that is obtained through the model processing method of two-dimensional finite element analysis of cylindrical components according to the embodiments of the present invention.

[0023] Figure 2 This is a schematic diagram illustrating an example of the equivalent cross-section of a circular section of a cylindrical component obtained by the model processing method for two-dimensional finite element analysis of a cylindrical component according to an embodiment of the present invention.

[0024] Figure 3 This is another schematic diagram illustrating an example of the equivalent cross-section of a circular cross-section of a cylindrical component obtained by the model processing method for two-dimensional finite element analysis of a cylindrical component according to an embodiment of the present invention.

[0025] Figure 4 It is a three-dimensional diagram illustrating the screw.

[0026] Figure 5 It is a three-dimensional diagram schematically representing the equivalent model of the screw obtained through existing mass equivalence methods. Detailed Implementation

[0027] Below, in conjunction with Figures 1 to 3 The model processing method for two-dimensional finite element analysis of cylindrical components according to embodiments of the present invention will be described, wherein, Figure 1 This is a schematic diagram illustrating the circular cross-section of a cylindrical component to be obtained through the model processing method of two-dimensional finite element analysis of cylindrical components according to the embodiments of the present invention. Figure 2 This is a schematic diagram illustrating an example of the equivalent cross-section of a circular section of a cylindrical component obtained by the model processing method for two-dimensional finite element analysis of a cylindrical component according to an embodiment of the present invention. Figure 3 This is another schematic diagram illustrating an example of the equivalent cross-section of a circular cross-section of a cylindrical component obtained by the model processing method for two-dimensional finite element analysis of a cylindrical component according to an embodiment of the present invention.

[0028] First, a coordinate system is established for the finite element analysis model of the cylindrical component.

[0029] Here, as Figure 1 As shown, an XY coordinate system is established in the plane containing the cross-section of the cylindrical component. The intersection point O of the X-axis and Y-axis (i.e., the origin of the coordinate system) is located on the axis of the cylindrical component. The direction of the X-axis (also called the radial direction of the two-dimensional finite element analysis model of the cylindrical component) is perpendicular to the direction of the Y-axis (also called the normal direction of the two-dimensional finite element analysis model of the cylindrical component). The plane formed by the X-axis and Y-axis is coplanar with the circular cross-section (i.e., the cross section) of the cylindrical component.

[0030] Next, for the finite element analysis model of the cylindrical component, multiple pairs of polygons are defined.

[0031] Here, as Figure 2 As shown, within the plane containing the circular cross-section of the cylindrical component, n pairs of rectangles are formed as multiple pairs of polygons with the Y-axis as the axis of symmetry. Each rectangle is axially symmetric about the X-axis, meaning that on the positive side of the X-axis (closer to the intersection point O)... Figure 2 The upper middle side) and the negative side (closer to intersection O) Figure 2 On the lower side of the middle, n rectangles are formed respectively. The n rectangles on the positive side of the X-axis and the n rectangles on the negative side of the X-axis are symmetrical about the Y-axis, and these 2n rectangles are also symmetrical about the X-axis. Furthermore, on each side of the Y-axis (closer to the Y-axis...), ... Figure 2 (On one side above or below the center), n rectangles are arranged adjacently from the Y-axis in a direction away from the Y-axis. The further away from the Y-axis the rectangles are, the shorter the line of intersection parallel to the Y-axis between adjacent rectangles (i.e., the overlapping boundary lines of adjacent rectangles). Furthermore, one pair of opposite sides of each rectangle is parallel to the Y-axis. And let the width of each rectangle (its dimension along the Y-axis) be b. i Let the height (dimension along the X-axis) of each rectangle be r. i , where i is a natural number of 1, 2, ..., n, and the larger i is, the further away the rectangle is from the Y-axis.

[0032] Then, the dimensions of each of the n rectangles are determined in a manner that satisfies the first and second conditions, wherein the first condition is that the total area of ​​the aforementioned pairs of polygons is equal to the area of ​​the circular cross-section of the cylindrical component, and the second condition is that the total moment of inertia of the aforementioned pairs of polygons is equal to the moment of inertia of the circular cross-section of the cylindrical component.

[0033] Here, the dimensions of each of the n rectangles are determined in a manner that satisfies the following formulas (1) and (2).

[0034] πr 2 =2(r1b1+r2b2+…+r) n b n ) Formula (1)

[0035] (1 / 4)πr 4 =(1 / 12)b n (2r) 3 +(1 / 12)(b n-1 -b n )×(2r1+2r2+…2r n－1 ) 3 +…+(1 / 12)(b1-b n (2r1) 3 Formula (2)

[0036] Formula (1) above corresponds to the first condition above, and formula (2) above corresponds to the second condition above.

[0037] Then, satisfying r1 to r n Given that the sum is equal to the radius r of the circular cross-section of the cylindrical component, by pre-specifying r1 to r n The values ​​of b1 to b n The values ​​of n-2 in the formula are determined according to the above formulas (1) and (2). n The remaining two values ​​in the table.

[0038] Here, r1 to r n The values ​​are all set to r / n, and, as Figure 3 As shown, as b1 to b n The value of n-2 in the equation is defined as the distance between the two intersection points i1 and i2 of the straight line containing the side of the i-th rectangle closest to the Y-axis and the edge of the circular cross-section of the cylindrical component, denoted as b. i The value (i.e., the length of line segment i1i2 is b) i The value of (b). In this way, formulas (1) and (2) become formulas with two unknowns (the thickness b of the two different rectangles). i Solving this system of two equations yields the width values ​​of all rectangles, thus determining the thickness parameters of the plane stress elements at different radial positions in the two-dimensional finite element analysis model of the cylindrical component.

[0039] (Main technical effects of this embodiment)

[0040] According to the model processing method for two-dimensional finite element analysis of cylindrical components in this embodiment, as the equivalent section of the circular cross-section of the cylindrical component, multiple pairs of polygons are constructed or formed in the plane where the circular cross-section is located. These multiple pairs of polygons are axially symmetric about the Y-axis passing through the center of the circular cross-section of the cylindrical component, and each polygon is axially symmetric about the X-axis passing through the center and perpendicular to the Y-axis. On each side of the Y-axis, multiple polygons are arranged adjacently from the Y-axis in a direction away from the Y-axis. Furthermore, the further away from the Y-axis, the shorter the intersection line between adjacent polygons. Therefore, the obtained equivalent section is... The shape is closer to a circle, and when the cylindrical component is coupled with the surrounding components, the finite element analysis results are closer to the reality. Furthermore, the dimensions of each polygon are determined in a way that satisfies the first and second conditions. The first condition is that the total area of ​​multiple pairs of polygons is equal to the area of ​​the circular cross-section, and the second condition is that the total moment of inertia of multiple pairs of polygons is equal to the moment of inertia of the circular cross-section of the cylindrical component. That is, while ensuring that the mass of the finite element model and the real cylindrical component are consistent, the bending stiffness of the two is also consistent. Therefore, it helps to improve the accuracy of the two-dimensional finite element analysis of the cylindrical component.

[0041] Furthermore, according to the model processing method for two-dimensional finite element analysis of cylindrical components in this embodiment, the multiple polygons used as the equivalent cross-section of the circular cross-section of the cylindrical component are rectangles, thus further simplifying the calculation of the dimensions of multiple pairs of polygons.

[0042] Furthermore, according to the model processing method for two-dimensional finite element analysis of cylindrical components in this embodiment, r1 to r n The values ​​are all set to one-nth of the radius of the circular cross-section of the cylindrical component, thus further simplifying the calculation of the dimensions of multiple pairs of polygons.

[0043] Furthermore, according to the model processing method for two-dimensional finite element analysis of cylindrical components in this embodiment, the distance between the two intersection points i1 and i2 of the straight line containing the side of the i-th rectangle closest to the Y-axis and the edge of the circular cross-section of the cylindrical component is set as b. i The value of can thus further simplify the calculation of the dimensions of multiple pairs of polygons.

[0044] The present invention has been described above by way of example with reference to the accompanying drawings. Obviously, the specific implementation of the present invention is not limited to the above embodiments.

[0045] For example, in the above embodiment, the equivalent cross section of the circular cross section of the cylindrical component forms 4 pairs of rectangles with the Y-axis as the axis of symmetry. However, it is not limited to this. Only 2 pairs of rectangles can be formed, or more than 3 pairs of rectangles can be formed. The more pairs of rectangles formed, the easier it is for the analysis results to approach the real situation.

[0046] Furthermore, in the above embodiments, the polygons used for the equivalent cross-section of the circular cross-section of the cylindrical component are a set of rectangles with opposite sides parallel to the Y-axis, but are not limited to this. For example, isosceles trapezoids with the upper and lower bases parallel to the Y-axis and the longer of the upper and lower bases closer to the Y-axis can also be used as multiple polygons. Alternatively, rectangles and isosceles trapezoids can be used simultaneously, and the polygon furthest from the Y-axis can also be a triangle.

[0047] Furthermore, in the above embodiments, the heights of each rectangle used for the equivalent cross-section of the circular cross-section of the cylindrical component, i.e., r1 to r... n The values ​​are all set to one-nth of the radius of the circular cross-section of the cylindrical component, but are not limited to this; the heights of each rectangle can also be set to be different from each other.

[0048] Furthermore, the two-dimensional finite element analysis model processing method for cylindrical components described above is applicable to establishing the equivalent cross section of a two-dimensional finite element analysis model for a screw that forms a threaded connection structure with surrounding components.

[0049] Furthermore, a computer program can be stored in the storage medium, wherein the computer program, when executed by a processor, implements the two-dimensional finite element analysis model processing method for cylindrical components described in the above embodiments. For example, by running the computer program, the cylindrical component in the finite element analysis model can be automatically converted into a component with a cross-section composed of the aforementioned multiple pairs of polygons. In this case, for example, the value of n in the above embodiments can be set by default, and r1 to r in the above embodiments can be set... n The value of is set to r / n, or the value of n can be set before running the computer program as needed.

[0050] In addition, an electronic device may be formed comprising: a processor; and a memory for storing executable instructions of the processor, wherein the processor is configured to execute the model processing method for two-dimensional finite element analysis of cylindrical components according to the above embodiments by executing the executable instructions.

Claims

1. A model processing method for two-dimensional finite element analysis of cylindrical components, characterized in that, For the finite element analysis model of the cylindrical component, a coordinate system is established. This coordinate system has a first axis and a second axis. The first axis passes through the center of the circular cross-section of the cylindrical component, and the second axis passes through the center of the circle and is perpendicular to the first axis. For the finite element analysis model of a cylindrical component, multiple pairs of polygons are defined as the equivalent cross-section of the cylindrical component's circular section, located within the plane of the cylindrical cross-section. The plurality of pairs of polygons are respectively axially symmetric about the first axis, and each of the polygons is axially symmetric about the second axis. On each side of the first axis, a plurality of polygons are arranged adjacently from the first axis in a direction away from the first axis, and the further away from the first axis, the shorter the intersection line between adjacent polygons. The dimensions of each polygon are determined in a manner that satisfies a first condition and a second condition, wherein the total area of ​​the multiple pairs of polygons is equal to the area of ​​the circular cross-section, and the second condition is that the total moment of inertia of the multiple pairs of polygons is equal to the moment of inertia of the circular cross-section. The polygon is a rectangle. On each side of the first axis, the dimension of each of the rectangles in a direction parallel to the first axis is b i On each side of the second axis, the dimension of each of the rectangles in a direction parallel to the second axis is r i where i is a natural number from 1 to n, and the greater i is, the farther the rectangle is from the first axis, When satisfying r1 to r n Given that the sum of the values ​​is equal to the radius of the circular cross-section, by pre-specifying r1 to r n The values ​​of b1 to b n The values ​​of n-2 in the set are used to determine b1 to b2 based on the first and second conditions. n The remaining two values ​​in the table.

2. The model processing method for two-dimensional finite element analysis of cylindrical components as described in claim 1, characterized in that, r1 to r n The value of each is set to one-nth of the radius of the circular cross-section.

3. The model processing method for two-dimensional finite element analysis of cylindrical components as described in claim 2, characterized in that, When n is 4 or higher If the straight line containing the edge of the i-th rectangle closest to the first axis is designated as the i-th straight line, then the distances between the two intersection points of the first straight line to the (n-2)-th straight line and the edge of the circular cross-section are respectively designated as b1 to b... n-2 The value of .

4. The model processing method for two-dimensional finite element analysis of cylindrical components as described in claim 1, characterized in that, The intersection line between adjacent polygons is parallel to the first axis.

5. The model processing method for two-dimensional finite element analysis of cylindrical components as described in any one of claims 1 to 4, characterized in that, The cylindrical component is a screw.

6. A storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the model processing method for two-dimensional finite element analysis of cylindrical components as described in any one of claims 1 to 5.

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