Method to assist in building a finite element analysis model for hot spot stress of offshore engineering pipe nodes

Abstract

The present invention relates to the technical field of fatigue strength assessment of marine engineering structures, and in particular to a method for assisting in modeling a finite element analysis model of hot spot stress at a pipe node in a marine engineering project, comprising the following steps: S1: establishing a parameter equation of an intersection line between a pipe node strut and a chord rod based on the intersection form of a cylindrical surface of a chord rod and a cylindrical surface of a strut rod; S2: establishing a local coordinate system at any position of the intersection line; S3: obtaining the coordinates of a hot spot stress interpolation reference point on the chord rod surface at a certain distance from the intersection line; S4: performing finite element modeling based on the coordinates of the reference point. The present invention establishes a parameter equation of an intersection line between a strut and a chord rod, sets analysis points at intervals on the intersection line, establishes a local coordinate system, and determines the distances from the analysis points to the local coordinate system. r 1 and r 2. Interpolate the coordinates of the hot spot stress reference point, perform finite element modeling and analysis based on the coordinates, read the stress results of the reference point, determine the hot spot stress at different analysis points, and obtain the distribution of the hot spot stress.

Description

Technical Field

[0001] The invention relates to the technical field of fatigue strength assessment of marine engineering structures, and in particular to a method for assisting in modeling a finite element analysis model of hot spot stress of a marine engineering pipe node. Background Art

[0002] A pipe node is a connection point between two or more pipes, and is one of the typical structural forms on an offshore jacket platform. Due to geometric discontinuity, pipe nodes are stress concentration locations, and fatigue cracks are prone to initiation and expansion under marine environmental loads, threatening the structural safety of the entire platform. Therefore, fatigue strength assessment of pipe nodes is required.

[0003] The hot spot stress method is the main method for evaluating the fatigue strength of offshore engineering pipe joints. The calculation of hot spot stress of pipe joints is the key to fatigue strength evaluation. Generally, the simplified formula method and the finite element method can be used. The simplified formula is obtained by fitting a large number of finite element analysis results. Among them, the most widely used is the Efthymiou formula, which is adopted by multiple specifications. It should be pointed out that the simplified formula method has restrictions on the form, geometric parameters and load type of pipe joints. It cannot predict the hot spot stress of all positions along the weld toe of the pipe joint, which has certain limitations. The finite element method is applicable to more general situations and can more accurately determine the hot spot stress at various positions along the weld. However, the finite element model for hot spot stress analysis of pipe joints is complex and needs to be established by experienced engineers or researchers. The basic process of finite element analysis of hot spot stress of pipe joints mainly includes modeling and post-processing. Modeling is the basis of the entire finite element analysis. According to the definition of hot spot stress, the hot spot stress at the weld toe of the pipe joint generally needs to be obtained by interpolating the stress at two surface reference points at a certain distance from the weld toe, which means that the finite element analysis must be able to obtain the stress results at the surface reference points. The simplest method is to set a node at the reference point and directly read the stress of the node after the finite element analysis is completed. However, since the weld toe of the tube node is a three-dimensional curve and the surface of the tube node is also a spatial curved surface, the coordinates of the reference point at a certain distance from the weld toe and on the surface of the tube node are difficult to determine, which brings difficulties to the establishment of the finite element model for hot spot stress analysis of the tube node.

[0004] The Chinese invention patent application with publication number CN115730492A discloses an interpolation point extraction method and system and a hot spot stress calculation method and system, comprising: marking at least two interpolation lines parallel to the weld toe line on the surface of the base material of the three-dimensional model of the weld joint; performing grid discretization processing on the three-dimensional model of the weld joint to determine all hot spot nodes on the weld toe line and all interpolation surface nodes between two of the interpolation lines; selecting interpolation points corresponding to each of the hot spot nodes from all the interpolation surface nodes according to the relative position relationship between the interpolation surface nodes and the hot spot nodes, and automatically and quickly extracting interpolation points corresponding to a large number of hot spot nodes in batches, thereby improving the extraction efficiency of hot spot stress. However, the disclosed solution does not solve the difficulty of establishing a finite element model for hot spot stress analysis of pipe nodes. Summary of the invention

[0005] Technical purpose: In order to overcome the deficiencies in the prior art, the present invention provides a method for assisting in modeling a finite element analysis model of hot spot stress of marine engineering pipe nodes.

[0006] Technical solution: To achieve the above purpose, the method disclosed in the present invention for assisting the modeling of a finite element analysis model for hot spot stress of a marine engineering pipe node comprises the following steps:

[0007] S1: Based on the intersection of the outer cylindrical surface of the chord and the outer cylindrical surface of the strut, the parametric equation of the intersection line between the tube node strut and the chord is established;

[0008] S2: Establish a local coordinate system at any position of the intersection line;

[0009] S3: Get the coordinates of the hot spot stress interpolation reference point on the chord surface far away from the intersection line;

[0010] S4: Perform finite element modeling based on the reference point coordinates.

[0011] Furthermore, the outer cylindrical surface of the chord is defined as the lower cylindrical surface, and its axis is Axis, define the outer cylinder of the support rod as the upper cylindrical surface, and its axis is Axis, Axis and The intersection point of the axes is the origin In step S1, when the outer cylindrical surface of the chord rod is orthogonal to the outer cylindrical surface of the strut rod, the method for establishing the parameter equation of the intersection line of the tube node strut rod and the chord rod is as follows:

[0012] Establishing an orthogonal coordinate system , the Cartesian equations of the intersection line when the upper cylindrical surface is orthogonal to the lower cylindrical surface are:

[0013] ,

[0014] in, is the radius of the upper cylindrical surface, is the radius of the lower cylindrical surface, , , is the coordinate value of the point on the cylindrical surface;

[0015] The parametric equation of the intersection line when the upper cylindrical surface and the lower cylindrical surface are orthogonal is obtained from the Cartesian equations of the intersection line when the upper cylindrical surface and the lower cylindrical surface are orthogonal:

[0016] ,

[0017] in, The intersection line is projected on Any point on the circle formed by the plane is relative to the circle and Plane intersection angle.

[0018] Furthermore, when the outer cylindrical surface of the chord and the outer cylindrical surface of the strut are oblique in step S1, the coordinate system Around Axis rotation Angle, is the inclination angle of the upper cylindrical surface relative to the orthogonal situation; after rotation, the coordinate system is , in this coordinate system, the equation of the upper cylindrical surface is:

[0019] ,

[0020] In the formula,

[0021] ,

[0022] ,

[0023] in, , To rotate the coordinate system The coordinates of the points on the upper cylindrical surface after the axis rotates;

[0024] Thus, the upper cylindrical surface is Equations in coordinate system:

[0025] ,

[0026] Therefore, by combining the equations of the two cylindrical surfaces, we can obtain the Cartesian equations of the intersection line when the intersection is oblique:

[0027] ,

[0028] The parametric equation of the oblique intersection line is obtained from the Cartesian equations of the oblique intersection line:

[0029] ,

[0030] in,

[0031] .

[0032] Furthermore, the steps of establishing the local coordinate system in step S2 are as follows:

[0033] S101: Parametric equations Take the derivative and get the tangent vector at any point on the intersection line ;

[0034] S102: Normal vector perpendicular to the lower cylindrical surface at any point on the intersection line The calculation formula is as follows:

[0035] ;

[0036] S103: Based on the tangent vector and the normal vector Calculate the vector , the local coordinate system of any point on the intersection line can be determined. The vector Both perpendicular to the tangent vector And perpendicular to the normal vector , the vector The calculation formula is:

[0037] .

[0038] Furthermore, the tangent vector in step S101 The calculation formula in orthogonality is as follows:

[0039] ;

[0040] Tangent Vector The calculation formula for oblique intersection is as follows:

[0041] .

[0042] Furthermore, the specific steps of step S3 are as follows:

[0043] S201: When orthogonal, define the point on the lower cylindrical surface far from the intersection line as point C, and define point D as a point on the intersection line of the two cylinders. The coordinates of point D are , its corresponding for , the tangent vector is , the plane equation with the tangent as the normal vector at point D is:

[0044] ;

[0045] S202: The plane equation of step S201 is combined with the equation of the lower cylindrical surface to obtain a space curve located on the lower cylindrical surface. The space curve is perpendicular to the intersection line, and point C is located on it. The arc length distance between point C and point D is ;

[0046] The parametric equation of the lower cylindrical surface is:

[0047] , ,

[0048] in, The space curve is projected on Any point on the circle formed by the plane is relative to the circle and The angle of the plane intersection point B;

[0049] By combining the plane equation and the parametric equation of the lower cylinder, we can get the complete parametric equation formula of the space curve:

[0050] ,

[0051] The complete parameterized equation formula of the space curve gives the differential of the arc length as:

[0052] ;

[0053] S203: Determine the coordinates of point C by numerical method, the specific steps are as follows:

[0054] (A1) First find the initial value corresponding to point D , assuming a small increment , we can obtain the corresponding ;

[0055] (A2) Update value, calculate the next Corresponding , the calculation is repeated, and finally the arc length is accumulated to of Substituting the value into the parameterized equation of the space curve, the coordinates of point C can be obtained.

[0056] Furthermore, the steps of step S4 are as follows:

[0057] S301: According to the hot spot stress analysis specification of pipe nodes, determine two hot spot stress interpolation reference points C and E. The arc length distance between point C and point E and point D is and , according to step S3, determine the coordinates of two reference points corresponding to different weld toe positions of the pipe node;

[0058] S302: points, lines and surfaces are established according to the coordinates of the reference points, the geometric model of the pipe node is divided, and the finite element mesh division is controlled to ensure that there are nodes at the reference points, so as to facilitate the subsequent reference point stress extraction.

[0059] The beneficial effects of the present invention are:

[0060] The present invention establishes the parameter equation of the intersection line of the brace and the chord through the geometric parameters of the brace and the chord; Set the analysis points and establish the local coordinate system; determine the distances from the analysis points. r 1 and r 2. The coordinates of the hot spot stress interpolation reference point; perform finite element modeling and analysis based on these coordinates, read the stress results of the reference point, determine the hot spot stress at different analysis points, and obtain the distribution of the hot spot stress. In addition, the method of the present invention is scalable and can be used for different forms of pipe nodes. It can be modified to determine the coordinates of the reference point on the strut, which is helpful to accurately calculate the hot spot stress of the pipe node and evaluate the fatigue strength, thereby improving the safety and reliability of the marine engineering structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 is a flow chart of the overall method of the present invention;

[0062] Figure 2 Schematic diagram of the pipe node coordinate system when orthogonal and oblique in the present invention;

[0063] Figure 3 It is a geometrical schematic diagram of the T-type tube node in the present invention;

[0064] Figure 4 It is the finite element model of the T-type tube node in the present invention. DETAILED DESCRIPTION

[0065] The following is combined with Figure 1 To Attachment Figure 4 The principles and features of the present invention are described, and the examples given are only used to explain the present invention, rather than to limit the scope of the present invention.

[0066] A method to assist in modeling the finite element analysis model of hot spot stress in offshore engineering pipe nodes is designed to obtain the coordinates of the hot spot stress interpolation reference point corresponding to any position of the pipe node weld toe. Based on these coordinates, the geometric model can be divided, the mesh can be divided, and the stress results of the reference point can be extracted more effectively. This method is applied to the determination of the coordinates of the hot spot stress interpolation reference point on the chord. With slight modifications on the basis of this method, it can also be used to determine the coordinates of the hot spot stress interpolation reference point on the strut. The application scope of this method covers the finite element solid unit model and the shell unit model of the pipe node. This method helps to accurately calculate the hot spot stress of the pipe node and evaluate the fatigue strength, thereby improving the safety and reliability of offshore engineering structures, such as Figure 1 — Figure 2 As shown, the following steps are included:

[0067] S1: Based on the intersection of the outer cylindrical surface of the chord and the outer cylindrical surface of the strut, the parametric equation of the intersection line between the tube node strut and the chord is established;

[0068] S2: Establish a local coordinate system at any position of the intersection line;

[0069] S3: Get the coordinates of the hot spot stress interpolation reference point on the chord surface far away from the intersection line;

[0070] S4: Perform finite element modeling based on the reference point coordinates.

[0071] The intersection of two cylindrical surfaces can be divided into three basic situations: orthogonal, oblique and eccentric. The present invention mainly discusses the two situations of orthogonal and oblique.

[0072] Furthermore, the outer cylindrical surface of the chord is defined as the lower cylindrical surface, and its axis is Axis, define the outer cylinder of the support rod as the upper cylindrical surface, and its axis is Axis, Axis and The intersection point of the axes is the origin In step S1, when the outer cylindrical surface of the chord rod is orthogonal to the outer cylindrical surface of the strut rod, the method for establishing the parameter equation of the intersection line of the tube node strut rod and the chord rod is as follows:

[0073] Establishing an orthogonal coordinate system , the Cartesian equations of the intersection line when the upper cylindrical surface is orthogonal to the lower cylindrical surface are:

[0074] ,

[0075] in, is the radius of the upper cylindrical surface, is the radius of the lower cylindrical surface, , , is the coordinate value of the point on the cylindrical surface; the above two formulas represent the equations of the upper and lower cylindrical surfaces respectively.

[0076] The parametric equation of the intersection line when the upper cylindrical surface and the lower cylindrical surface are orthogonal is obtained from the Cartesian equations of the intersection line when they are orthogonal:

[0077] ,

[0078] in, The intersection line is projected on Any point on the circle formed by the plane is relative to the circle and Plane intersection The angle can be used to describe the position of any point on the intersection line.

[0079] Furthermore, when the outer cylindrical surface of the chord and the outer cylindrical surface of the strut are oblique in step S1, the coordinate system Around Axis rotation angle, is the inclination angle of the upper cylindrical surface relative to the orthogonal situation; after rotation, the coordinate system is , in this coordinate system, the equation of the upper cylindrical surface is:

[0080] ,

[0081] In the formula,

[0082] ,

[0083] ,

[0084] in, , To rotate the coordinate system The coordinates of the points on the upper cylindrical surface after the axis rotates;

[0085] Thus, the upper cylindrical surface is Equations in coordinate system:

[0086] ,

[0087] Therefore, by combining the equations of the two cylindrical surfaces, we can obtain the Cartesian equations of the intersection line when the intersection is oblique:

[0088] ,

[0089] The parametric equation of the oblique intersection line is obtained from the Cartesian equations of the oblique intersection line:

[0090] ,

[0091] in,

[0092] .

[0093] Furthermore, the steps for establishing the local coordinate system in step S2 are as follows:

[0094] S101: Parametric equations Take the derivative and get the tangent vector at any point on the intersection line ;

[0095] Furthermore, the tangent vector in step S101 The calculation formula in orthogonality is as follows:

[0096] ;

[0097] Tangent Vector The calculation formula for oblique intersection is as follows:

[0098] .

[0099] S102: Normal vector perpendicular to the lower cylindrical surface at any point on the intersection line The calculation formula is as follows:

[0100] ;

[0101] S103: Based on the tangent vector and the normal vector Calculate the vector , the local coordinate system of any point on the intersection line can be determined, and the vector Both perpendicular to the tangent vector And perpendicular to the normal vector ,vector The calculation formula is:

[0102] .

[0103] Furthermore, in step S3, the coordinates of the hot spot stress interpolation reference point on the chord surface at a certain distance from the intersection line are obtained. Taking the orthogonal case as an example, the specific steps are as follows:

[0104] S201: When orthogonal, define the point on the lower cylindrical surface far from the intersection line as point C, and define point D as a point on the intersection line of the two cylinders. The coordinates of point D are , its corresponding for , the tangent vector is , the plane equation with the tangent as the normal vector at point D is:

[0105] ;

[0106] S202: The plane equation of step S201 is combined with the equation of the lower cylindrical surface to obtain a space curve located on the lower cylindrical surface. The space curve is perpendicular to the intersection line, and the point C is located on it. The arc length distance between point C and point D is ;

[0107] The parametric equation of the lower cylindrical surface is:

[0108] , ,

[0109] in, The space curve is projected on Any point on the circle formed by the plane is relative to the circle and The angle of the plane intersection point B;

[0110] By combining the plane equation and the parametric equation of the lower cylinder, we can get the complete parametric equation formula of the space curve:

[0111] ,

[0112] The above formula combined with the parametric equation of the lower cylinder gives the complete parametric equation of the space curve. The differential of the arc length can be obtained from the complete parametric equation of the space curve:

[0113] ;

[0114] S203: Determine the coordinates of point C by numerical method, the specific steps are as follows:

[0115] (A1) First find the initial value corresponding to point D , assuming a small increment , we can obtain the corresponding ;

[0116] (A2) Update value, calculate the next Corresponding , the calculation is repeated, and finally the arc length is accumulated to of Substituting the value into the parameterized equation of the space curve, the coordinates of point C can be obtained.

[0117] Furthermore, the steps of step S4 are as follows:

[0118] S301: According to the hot spot stress analysis specification of pipe nodes, determine two hot spot stress interpolation reference points C and E. The arc length distance between point C and point E and point D is and , according to step S3, determine the coordinates of two reference points corresponding to different weld toe positions of the pipe node;

[0119] S302: points, lines and surfaces are established according to the coordinates of the reference points, the geometric model of the pipe node is divided, and the finite element mesh division is controlled to ensure that there are nodes at the reference points, so as to facilitate the subsequent reference point stress extraction.

[0120] like Figure 3 As shown, in this embodiment, taking a typical T-type tube node as an example, its geometric model is mainly determined by four dimensionless geometric parameters α, β, γ, and τ. The diameter D and the diameter d represent the outer wall diameters of the chord and the strut respectively; T and t represent the wall thickness of the chord and the strut respectively; and L represents the length of the chord. Finite element modeling is performed using the large-scale general finite element analysis software ANSYS. The hot spot stress analysis finite element model uses three-dimensional solid elements and ignores the local weld shape. According to the provisions of the International Welding Association Welded Joint Fatigue Strength Assessment Guide, the distance between the hot spot stress interpolation reference point and the weld toe is 0.4T and T, and T is the thickness of the chord.

[0121] First, the brace and chord are established, and the geometric model of the intersection of the brace and chord is obtained through geometric operations. The entire structure is divided into three different areas: the fine mesh area near the intersection line, the coarse mesh area at both ends of the brace and chord, and the transition mesh area connecting the two areas. This division can not only easily control the quality of the mesh, but also control the number of meshes, reduce calculation time, and avoid singular units.

[0122] According to the method provided by the present invention, the calculation of different weld toe positions (intervals ) corresponding to the reference point coordinates. Since the reference point coordinates obtained by the present invention are approximate values ​​obtained by numerical methods, if the coordinates of the reference points are directly used to establish key points, the key points will be at a certain distance from the chord surface (generally the distance is very small, representing a numerical error). To this end, the y coordinates of all reference points with a distance of 0.4T from the weld toe are added and subtracted by 1.5T, respectively, to obtain two sets of key point coordinates, one set is all located above the outer surface of the chord, and the other set is all located inside the chord. The two sets of key points can form a curved surface that intersects with the outer surface of the chord, and the intersection line is the approximate position of the hot spot stress interpolation reference point on the chord surface. The curved surface is used to cut the chord geometry model to obtain the first reference point connection line. The same treatment is performed on the reference point with a distance of T from the weld toe to obtain a curved surface, and the chord geometry model is also cut to obtain the second reference point connection line. On the cut geometric model, meshing is performed by controlling the number of meshes on the edge. The constructed finite element model of the T-tube is shown as follows. Figure 4 The above modeling results prove that the present invention can effectively assist in the modeling of the finite element analysis model of hot spot stress of marine engineering pipe nodes, which is helpful to accurately calculate the hot spot stress of pipe nodes and evaluate the fatigue strength, thereby improving the safety and reliability of marine engineering structures.

[0123] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for assisting the modeling of a finite element analysis model for hot spot stress of a marine engineering pipe node, characterized in that: The following steps are involved: S1: Based on the intersection of the outer cylindrical surface of the chord and the outer cylindrical surface of the strut, the parametric equation of the intersection line between the tube node strut and the chord is established; Define the outer cylindrical surface of the chord as the lower cylindrical surface, and its axis is Axis, define the outer cylinder of the support rod as the upper cylindrical surface, and its axis is Axis, Axis and The intersection point of the axes is the origin , the method for establishing the parametric equation of the intersection line between the tube node brace and the chord is as follows: When the cylindrical surface of the chord is orthogonal to the cylindrical surface of the strut, an orthogonal coordinate system is established. , obtaining a Cartesian equation group of the intersection line when the upper cylindrical surface and the lower cylindrical surface are orthogonal, and obtaining a parametric equation of the intersection line when the upper cylindrical surface and the lower cylindrical surface are orthogonal through the Cartesian equation group; Or, when the cylindrical surface of the chord and the cylindrical surface of the strut are oblique, the coordinate system Around Axis rotation Angle, is the inclination angle of the upper cylindrical surface relative to the orthogonal situation. After rotation, the coordinate system is , the Cartesian equations of the intersection line when the intersection is skewed are calculated, and the parametric equations of the intersection line when the intersection is skewed are obtained from the Cartesian equations of the intersection line when the intersection is skewed; S2: Establish a local coordinate system at any position of the intersection line; S3: Get the coordinates of the hot spot stress interpolation reference point on the chord surface far away from the intersection line. The specific steps are as follows: S201: When orthogonal, define the point on the lower cylindrical surface far from the intersection line as point C, and define point D as a point on the intersection line of the two cylinders. The coordinates of point D are , its corresponding for , the tangent vector is , obtain the plane equation with the tangent line as the normal vector at the point D; S202: The plane equation of step S201 is combined with the equation of the lower cylindrical surface to obtain a space curve located on the lower cylindrical surface. The space curve is perpendicular to the intersection line, and point C is located on it. The arc length distance between point C and point D is , the plane equation and the lower cylindrical surface parametric equation are combined to obtain a complete parametric equation of the space curve, and the differential of the arc length can be obtained from the complete parametric equation formula of the space curve; S203: Determine the coordinates of point C by numerical method; S4: Perform finite element modeling based on the reference point coordinates.

2. The method for assisting the finite element analysis modeling of hot spot stress of marine engineering pipe nodes according to claim 1 is characterized in that: When the outer cylindrical surface of the chord rod and the outer cylindrical surface of the strut rod are orthogonal in step S1, the Cartesian equations of the intersection line when the upper cylindrical surface and the lower cylindrical surface are orthogonal are: ， in, is the radius of the upper cylindrical surface, is the radius of the lower cylindrical surface, , , z is the coordinate value of the point on the cylindrical surface; The parametric equation of the intersection line when the upper cylindrical surface and the lower cylindrical surface are orthogonal is obtained from the Cartesian equations of the intersection line when the upper cylindrical surface and the lower cylindrical surface are orthogonal: ， in, The intersection line is projected on Any point on the circle formed by the plane is relative to the circle and Plane intersection angle.

3. The method for assisting the finite element analysis modeling of hot spot stress of marine engineering pipe nodes according to claim 2 is characterized in that: In step S1, when the outer cylindrical surface of the chord bar and the outer cylindrical surface of the strut bar are obliquely intersected, In the coordinate system, the equation of the upper cylindrical surface is: ， In the formula, ， ， Among them, x', z' are the coordinate values ​​of the points on the upper cylindrical surface after the coordinate system is rotated around the z axis; Thus, the upper cylindrical surface is Equations in coordinate system: ， Therefore, by combining the equations of the two cylindrical surfaces, we can obtain the Cartesian equations of the intersection line when the intersection is oblique: ， The parametric equation of the oblique intersection line is obtained from the Cartesian equations of the oblique intersection line: ， in, 。 4. The method for assisting the finite element analysis modeling of hot spot stress of marine engineering pipe nodes according to claim 3 is characterized in that: The steps for establishing the local coordinate system in step S2 are as follows: S101: Parametric equations Take the derivative and get the tangent vector at any point on the intersection line ; S102: Normal vector perpendicular to the lower cylindrical surface at any point on the intersection line The calculation formula is as follows: ； S103: Based on the tangent vector and the normal vector Calculate the vector , the local coordinate system of any point on the intersection line can be determined. The vector Both perpendicular to the tangent vector And perpendicular to the normal vector , the vector The calculation formula is: 。 5. The method for assisting the finite element analysis modeling of hot spot stress of marine engineering pipe nodes according to claim 4 is characterized in that: The tangent vector in step S101 The calculation formula in orthogonality is as follows: ； Tangent Vector The calculation formula for oblique intersection is as follows: 。 6. The method for assisting the finite element analysis modeling of hot spot stress of marine engineering pipe nodes according to claim 5 is characterized in that: The plane equation in step S201 is: ； The parameterized equation of the lower cylindrical surface in step S202 is: ， ， in, The space curve is projected on Any point on the circle formed by the plane is relative to the circle and The angle of the plane intersection point B; The complete parameterized equation formula of the space curve is: ， The differential of the arc length is: ； The step S203 determines the coordinates of point C by a numerical method, and the specific steps are as follows: (A1) First find the initial value corresponding to point D , assuming a small increment , we can obtain the corresponding ; (A2) Update value, calculate the next Corresponding , the calculation is repeated, and finally the arc length is accumulated to of Substituting the value into the parameterized equation of the space curve, the coordinates of point C can be obtained.

7. The method for assisting the finite element analysis modeling of hot spot stress of marine engineering pipe nodes according to claim 6 is characterized in that: The steps of step S4 are as follows: S301: According to the hot spot stress analysis specification of pipe nodes, determine two hot spot stress interpolation reference points C and E. The arc length distance between point C and point E and point D is r 1 and r 2. Determine the coordinates of two reference points corresponding to different weld toe positions of the pipe node according to step S3; S302: points, lines and surfaces are established according to the coordinates of the reference points, the geometric model of the pipe node is divided, and the finite element mesh division is controlled to ensure that there are nodes at the reference points, so as to facilitate the subsequent reference point stress extraction.

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