Geometric method-based beamless steel branch pipe design method controlled by waist line break angle

Abstract

A beamless steel bifurcated pipe design method controlled by a waist line break angle based on a geometric method comprises the following steps that firstly, a taper pipe bus of a beamless steel bifurcated pipe is generated through the geometric method with the waist line break angle as a control condition; 2, generating a projection line of the intersecting line of the beamless steel branch pipe through a geometric method; 3, establishing a three-dimensional model of the beamless steel branch pipe by using the taper pipe generatrix in the step 1 and the horizontal projection of the intersecting line in the step 2; and 4, performing finite element analysis based on the three-dimensional model in the step 3, and rechecking and determining waist line reduction and pipe wall thickness. The geometric method is adopted, the steel bifurcated pipe body shape is designed with the waist line break angle as the control condition, and the design efficiency of the water conservancy project can be improved.

Description

Technical Field

[0001] This invention relates to the field of computer-aided design technology for water conservancy and hydropower projects, and in particular to a design method for beamless steel branch pipes based on geometric methods and controlled by waistline angle. Background Technology

[0002] The beamless steel branch pipe uses a smooth connection between tapered pipe and spherical shell to branch, completely eliminating the need for reinforcing components. It bears the load through a smoothly connected spatial shell structure. There are two common structural forms of beamless steel branch pipes in engineering: one is that the main pipe is symmetrically divided into two branch pipes, and the other is that the main pipe is symmetrically divided into three branch pipes.

[0003] Taking a structure where the main pipe is symmetrically divided into two branches as an example, such as... Figure 1 As shown, the main conical pipe 2, upper branch conical pipe 4, and lower branch conical pipe 6 of the beamless steel branch pipe are tangent to the same common tangent sphere. Since the beamless steel branch pipe is a spatial shell structure, its design and calculation are quite challenging. Challenge 1: The shape of the beamless steel branch pipe is determined by multiple parameters, requiring adjustments to obtain a reasonable shape design, which is inefficient. Challenge 2: The beamless steel branch pipe is a combination of conical and spherical surfaces, making the creation of a 3D model complex. 3D modeling typically involves Boolean operations between surfaces to segment spatial surfaces such as conical and spherical shells. However, Boolean operations between surfaces have high requirements for geometry, spatial relationships, accuracy, and normal direction, often leading to Boolean operation failures. Challenge 3: There is a lack of theoretical or empirical calculation formulas for beamless steel branch pipes, and the preprocessing is complex when using finite element analysis.

[0004] Therefore, it is essential to find suitable body shape design and calculation methods. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a design method for beamless steel branch pipe based on geometric method and controlled by waistline angle. The method uses geometric method and waistline angle as control condition for steel branch pipe body design, which can improve the design efficiency of water conservancy projects.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] The geometric method for designing beamless steel branch pipes controlled by waistline bend angle includes the following steps:

[0008] Step 1: Using the waistline bend angle as the control condition, generate the tapered tube busbar of the beamless steel branch pipe through geometric method;

[0009] Step 2: Generate the projection line of the intersection line of the beamless steel branch pipe using a geometric method;

[0010] Step 3: Using the horizontal projection of the tapered tube busbar from Step 1 and the intersection line from Step 2, establish a three-dimensional model of the beamless steel branch pipe.

[0011] Step 4: Perform finite element analysis based on the 3D model from Step 3 to verify and determine the waistline reduction and pipe wall thickness.

[0012] Furthermore, step one specifically includes:

[0013] Step 1.1: Based on the common tangent sphere radius R0, the main pipe inner sphere radius R1, the branch pipe inner sphere radius R2, the bifurcation angle β, and the preset waistline bend angles α1, α2, and θ of the obtuse angle region, satisfying α1+α2+θ=β / 2, determine the sphere centers O1, O2, and O3 of the inner spheres of the main pipe, upper branch pipe, and lower branch pipe through geometric relationships; wherein, the common tangent sphere radius R0 is 1.0 to 1.2 times R1, and O2 is obtained by mirroring O3;

[0014] In the process of determining the center of the ball O1, center of the ball O2 and center of the ball O3, two initial generatrices are obtained: the main tapered tube generatrice AC and the lower branch tapered tube generatrice DE, where AC is the common tangent of the main tube and the common tangent ball, and DE is the common tangent of the lower branch tube and the common tangent ball.

[0015] 1.2: Generate the remaining tapered tube busbar:

[0016] The common tangent line A1C1 between the inner ball and the common tangent ball in the main pipe, the common tangent lines G1F1 and GF between the inner ball and the common tangent ball in the upper branch pipe, and the common tangent line D1E1 between the inner ball and the common tangent ball in the lower branch pipe are the bus lines, thus obtaining the remaining 4 bus lines A1C1, G1F1, GF and D1E1.

[0017] The intersection of A1C1 and G1F1 is determined as the intersection of their common tangents, B1; the intersection of D1E1 and GF is determined as the intersection of their common tangents, H.

[0018] Furthermore, step two specifically includes:

[0019] Step 2.1: Connect the lines CC1, DD1, and FF1 formed by the endpoints of the tapered tube in Step 1 to obtain the intersection points K, J, and L. The common area enclosed by the focal lines KJ, JL, and LK forms the common tangent spherical shell region.

[0020] Step 2.2: Determine the horizontal projection of the intersection line: Based on the intersection points B1 and H of the common tangents determined in Step 1.2, connect B1L as the projection of the intersection line between the main cone pipe and the upper branch cone pipe, BJ as the projection of the intersection line between the main cone pipe and the lower branch cone pipe, and HK as the projection of the intersection line between the branch cone pipe and the lower branch cone pipe.

[0021] Furthermore, step three specifically includes:

[0022] Step 3.1: Generate a sketch in the 3D modeling software, rotate the conical tube generatrix from Step 1 around the axis to obtain the main conical tube, upper branch conical tube, lower branch conical tube, main tube and branch tube, and establish a common tangent spherical shell to form the basic surface;

[0023] Step 3.2: Based on the horizontal projections KJ, JL, LK, B1L, BJ, and HK of the 6 intersection lines obtained in Step 2, establish 6 dividing planes perpendicular to the sketch plane, and trim the basic surface to form a 3D model of the spatial surface.

[0024] Step 3.3: In CATIA, use parametric modeling to extract the waistline bend angle (α1, α2, θ) and the inscribed sphere radius (R1, R2) as feature parameters to generate a standard template and establish a standard template for the steel branch pipe; for branch pipes of different sizes, the 3D model can be automatically updated simply by modifying the feature parameters.

[0025] Furthermore, step four specifically includes:

[0026] Step 4.1: Import the 3D model into the finite element software, use shell elements to simulate and perform stress analysis;

[0027] Step 4.2: Adjust the waistline bend angle (α1, α2, θ) and pipe wall thickness parameters to ensure that the shape and stress performance of the branch pipe meet the requirements of the hydraulic engineering design specifications, and complete the design of the beamless steel branch pipe.

[0028] Furthermore, the intersection line mentioned in step two is an ellipse or circular curve in space, and is reflected as a straight line on the horizontal projection diagram. When each cone tube is tangent to the same common tangent sphere, the intersection line is a planar curve.

[0029] Furthermore, the 3D modeling software is CATIA.

[0030] Furthermore, the finite element software mentioned in step four is ANSYS.

[0031] Compared with the prior art, the present invention, employing the above technical solution, has the following advantages:

[0032] (1) There is no need to derive the calculation formula of the intersection line. The horizontal projection of the intersection line and the body shape of the beamless steel branch pipe can be obtained directly by geometric method, which is simple and clear;

[0033] (2) The stress characteristics of the branch pipe are mainly determined by the three waistline bends. The three waistline bends are used as control conditions. The control conditions are intuitive and convenient for adjusting the shape of the beamless steel branch pipe to find a reasonable shape.

[0034] (3) Three-dimensional modeling of branch pipes generally involves dividing spatial surfaces such as conical surfaces and spherical shell surfaces by performing Boolean operations between surfaces. Boolean operations between surfaces have high requirements for the geometric shape, spatial relationship, accuracy, and normal direction of the surfaces, which often leads to calculation failure. This invention finds six main intersection lines based on the geometric method, establishes six cutting planes on the six intersection lines, and uses the six cutting planes to divide the conical surface and the spherical shell surface. The operation is simple and the steps are clear.

[0035] (4) By adopting this technical solution, parametric modeling can be used in CATIA to establish a standard template for steel branch pipes. Only by adjusting the relevant parameter values ​​of the branch pipes can a three-dimensional drawing be automatically generated.

[0036] (5) By adopting this technical solution, it is convenient to use the APDL language of ANSYS software to parameterize and establish three-dimensional modeling and perform finite element analysis, thus organically combining body design with finite element calculation.

[0037] (6) This method is applicable to the design of crescent-ribbed branch pipes, beam-type branch pipes, and other branch pipes. Attached Figure Description

[0038] Figure 1 This is a three-dimensional spatial view of the beamless steel branch pipe of the present invention;

[0039] Figure 2 This is a geometric diagram of the beamless steel branch pipe of the present invention;

[0040] Figure 3 for Figure 2 Enlarged view of section I;

[0041] Figure 4 This is a planar projection of the intersection line of the beamless steel branch pipe of the present invention;

[0042] Figure 5 This represents the state in which the three main parts of the beamless steel branch pipe of the present invention have not undergone intersection calculation;

[0043] Figure 6 for Figure 4 A breakdown diagram of the intersection lines of the main conical tube, upper conical tube, lower conical tube, and the male tangent sphere;

[0044] Figure 7 This is an unfolded view of the main cone pipe, upper cone pipe, and lower cone pipe of the beamless steel branch pipe of the present invention.

[0045] The reference numerals in the figure are described below:

[0046] 1—Main pipe; 2—Main tapered pipe; 3—Upper branch pipe; 4—Upper branch tapered pipe; 5—Lower branch pipe; 6—Lower branch tapered pipe; 7—Male spherical shell; 8—Main pipe busbar; 9—Lower branch pipe busbar

[0047] R0—Radius of the common tangent sphere; O—Center of the common tangent sphere; R1—Radius of the sphere inside the main pipe; O1—Center of the sphere inside the main pipe; R2—Radius of the spheres inside the upper and lower branches; O2—Center of the sphere inside the upper branch; O3—Center of the sphere inside the lower branch; α1—Angle of the waistline of the main conical pipe; α2—Angle of the waistline of the upper and lower conical pipes; θ—Angle of the waistline in the obtuse angle region; β—Bifurcation angle;

[0048] Among them, the spherical shell that is tangent to the main cone tube, the upper branch cone tube and the lower branch cone tube at the same time is called the common tangent sphere;

[0049] The waistline bends α1 and α2 of the tapered tube are defined as the angles between the generatrix of the tapered tube and the axis of rotation.

[0050] The waistline bend angle θ in the obtuse angle region is defined as the angle between the generatrix of the main tapered tube and the generatrix of the branch tapered tube;

[0051] The bifurcation angle β is defined as the angle between the axes of the two branch pipes. Since the branch pipes are arranged symmetrically, the angle between the axes of the upper and lower branch pipes and the horizontal line is β / 2. The main busbar 8 is horizontal, and the axis of the same pipe is parallel to the busbar. Therefore, the angle between the lower branch pipe busbar 9 and the main busbar 8 is also β / 2, α1 + α2 + θ = β / 2. Figure 3 As shown. Detailed Implementation

[0052] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the scope of protection is not limited to the description.

[0053] Please see Figure 1-7 This invention provides a geometric method for designing beamless steel branch pipes controlled by waistline angles. Known conditions: radius R0 of the common tangent sphere, radius R1 of the main pipe's inner sphere, radius R2 of the inner spheres of the upper and lower branch pipes, bifurcation angle β, where R0 is 1.0 to 1.2 times R1. The specific steps are as follows:

[0054] Step 1: Using the waistline bend angle as the control condition, generate the tapered busbar of the beamless steel branch pipe using a geometric method.

[0055] Step 1.1: Determine the center of the ball O1 inside the main pipe 1, the center of the ball O2 inside the upper branch pipe 3, and the center of the ball O3 inside the lower branch pipe 5 by using the waistline bend angle.

[0056] Assume the waistline bend angle α1 of the main conical tube 2, the waistline bend angle α2 between the upper conical tube 4 and the lower conical tube 6, and the waistline bend angle θ in the obtuse angle region. From geometric relationships, we know that α1 + α2 + θ = β / 2.

[0057] like Figure 2Draw point O as the center of the common tangent sphere. With O as the center and the radius R0 of the common tangent sphere as the circle, draw a horizontal line OO4 and symmetrical lines OO5 and OO6 along the horizontal line. The angle between OO5 and OO6 is β. OO4, OO5, and OO6 are the axes of main pipe 1, upper branch pipe 3, and lower branch pipe 5, respectively. Draw the generatrices of main pipe 1, upper branch pipe 3, and lower branch pipe 5 based on R1 and R2.

[0058] Draw a line through the center O of the circle, making an angle α1 with the vertical line. The intersection of this line and the circumference is C. Draw a perpendicular line from C to OC, intersecting the main pipe generatrix 9 at point A. Draw a line parallel to AC, with a perpendicular distance R1 between the two parallel lines. The intersection of this parallel line and OO4 is O1. This determines the center O1 of the sphere inscribed in the main pipe 1. AC is the common tangent line between the common sphere and the sphere inscribed in the main pipe 1, and it is also the generatrix of the main cone tube 2. Geometrically, the angle between AC and the main pipe generatrix 8 is α1, which is the waistline bend angle of the main cone tube 2. Figure 2 and Figure 3 .

[0059] Draw a line through the center O of the circle, making an angle of α1+θ with the vertical line. The intersection of this line and the circumference is D. Draw a perpendicular line from D to OD, intersecting the lower branch pipe generatrix 9 at E. Draw a line parallel to DE, with a perpendicular distance of R2 between the two parallel lines. The intersection of this parallel line and OO6 is O3. This determines the center O3 of the sphere inscribed in the lower branch pipe 5. DE is the common tangent of the common sphere and the sphere inscribed in the lower branch pipe 5, and is also the generatrix of the lower branch conical pipe 6. The angle between DE and the lower branch pipe generatrix 9 is α2, which is the waistline bend angle α2 of the lower branch conical pipe 6. The lower branch pipe generatrix 9 is parallel to OO6 and makes an angle of β / 2 with the horizontal line. From geometric relationships, we know that the angle between AC and DE is θ, which is the waistline bend angle in the obtuse angle region. Since the angle between the lower branch pipe generatrix 9 and the main pipe generatrix 8 is β / 2, then α1+α2+θ=β / 2. Figure 2 and Figure 3 The intersection of AC and DE is point B.

[0060] O2 is determined using the same method, or by mirroring O3 along the horizontal line. Through the above steps, the center of the ball in the main pipe 1 (O1), the center of the ball in the upper branch pipe 3 (O2), and the center of the ball in the lower branch pipe 5 (O3) are determined.

[0061] Step 1.2: Generate the remaining four busbars of the tapered pipe of the beamless steel branch pipe using the geometric method.

[0062] like Figure 2As shown, draw the common tangent A1C1 between the inner ball and the common tangent ball of the main pipe 1. Draw the common tangents G1F1 and GF between the inner ball and the common tangent ball of the upper branch pipe 3, and the intersection point B1 of A1C1 and G1F1. Draw the common tangent D1E1 between the inner ball and the common tangent ball of the lower branch pipe 5, and the intersection point H of D1E1 and GF. The common tangents drawn in step 1.2 are the generatrices of the tapered pipe, and the four generatrices are A1C1, G1F1, GF, and D1E1. In the process of determining the center of the sphere O1, O2, and O3 in step 1.1, two generatrices AC and DE were obtained. Thus, six generatrices were obtained: AC, DE, A1C1, G1F1, GF, and D1E1.

[0063] Step 2: Generate the projection line of the intersection line of the beamless steel branch pipes using a geometric method.

[0064] According to the principles of spatial geometry, when each conical tube is tangent to the same common tangent sphere, their intersection line is a planar curve, which is an ellipse or circular curve in space and a straight line on a plane diagram.

[0065] exist Figure 2 In the middle, connect CC1, connect DD1, connect FF1. The three lines intersect each other in pairs, obtaining intersection points K, J, and L. The common area enclosed by KJ, JL, and LK is the projection of the common tangent spherical shell 7, as shown below. Figure 4 As shown.

[0066] like Figure 4 Connect B1L, BJ, and HK. These three lines are the horizontal projections of the intersection lines of the main cone tube 2, the upper branch cone tube 4, and the lower branch cone tube 6. This yields six intersection lines: KJ, JL, LK, B1L, BJ, and HK.

[0067] To facilitate understanding of the geometric relationships between them, Figure 4 Divide into three shapes, as follows: Figure 5 , Figure 6 As shown. Figure 5 The left side shows the projection line after the main pipe, the main tapered tube, and the male tangent ball intersect. AA1 is the projection of the intersection line between the main pipe and the main tapered tube. CC1 is the projection of the intersection line between the main tapered tube and the male tangent ball. AA1CC1 is the main tapered tube. Figure 5 The upper right side shows the projection line after the intersection of the upper branch pipe, the upper branch tapered pipe, and the common tangent ball. GG1 is the projection of the intersection line between the upper branch pipe and the upper branch tapered pipe, FF1 is the projection of the intersection line between the main tapered pipe and the common tangent ball, and GG1FF1 is the upper branch tapered pipe. Figure 5The lower right side shows the projection line after the lower branch pipe intersects with the lower branch tapered pipe and the common tangent sphere. EE1 is the projection of the intersection line between the upper branch pipe and the upper branch tapered pipe. DD1 is the projection of the intersection line between the main tapered pipe and the common tangent sphere. EE1DD1 is the lower branch tapered pipe. The three lines CC1, DD1, and FF1 intersect each other to obtain intersection points K, J, and L. The common area enclosed by KJ, JL, and LK is the projection of the common tangent sphere shell 7. KJ, JL, and LK are parts of three circular curves in space, as shown in the figure. Figure 6 As shown.

[0068] The projection of the intersection line between the main tapered tube AA1CC1 and the upper branch tapered tube GG1FF1 is B1L; the projection of the intersection line between the main tapered tube AA1CC1 and the lower branch tapered tube EE1DD1 is BJ; and the projection of the intersection line between the upper branch tapered tube GG1FF1 and the lower branch tapered tube EE1DD1 is HK. B1L, BJ, and HK are each part of three elliptic curves in space, as shown below. Figure 6 As shown.

[0069] like Figure 6 As shown, A1B1LJBA, G1B1LKHG, and E1HKJBE are the main cone pipe 2, upper branch cone pipe 4, and lower branch cone pipe 6 of the beamless branch pipe, respectively. The common area enclosed by KJ, JL, and LK is the projection of the common spherical shell 7, which together form the core part of the beamless steel branch pipe.

[0070] Step 3: In CATIA, generate a 3D model of the spatial surface based on the generatrix of the beamless steel branch tapered pipe.

[0071] (1) Generate a draft in CATIA according to the methods in steps one and two. Figure 4 .

[0072] (2) Output the characteristic line, rotate the generatrix around the axis to obtain the tapered tube, main tube and branch tube, and establish the common tangent spherical shell.

[0073] (3) Based on the horizontal projections of the six intersection lines KJ, JL, LK, B1L, BJ, and HK, establish six cutting planes. These six cutting planes are perpendicular to the plane containing the sketch. Use these six cutting planes to trim redundant surfaces to generate a three-dimensional model of the spatial surface, such as... Figure 1 As shown.

[0074] (4) In CATIA, parametric modeling is used to establish a standard template for steel branch pipes. Only by adjusting the relevant parameter values ​​of the branch pipes can a three-dimensional drawing that meets the shape design requirements be automatically generated.

[0075] (5) Unfold into an engineering drawing, such as Figure 7 Then, dimensioning is performed.

[0076] Step 4: Perform finite element analysis to verify and determine the waistline reduction and pipe wall thickness.

[0077] The 3D model is imported into finite element software, and shell element simulation is used for finite element analysis. Alternatively, this technique can be used to directly create a 3D model in ANSYS software using the APDL language for parametric modeling and then perform finite element analysis. By adjusting the values ​​of α1, α2, and θ, as well as the pipe wall thickness, the shape and stress distribution are made to meet the specifications, thus completing the design of the beamless steel branch pipe.

[0078] This invention uses the waistline angle as a control condition and optimizes the body shape design by adjusting three waistline angles, which is simple and intuitive. This invention uses a geometric method to establish six intersecting lines, and establishes six cutting planes based on the six intersecting lines. The six cutting planes are used to cut the spatial curved surface, which overcomes the shortcoming that Boolean operations between spatial curved surfaces are prone to failure.

[0079] The embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details of the above embodiments. Within the scope of the inventive concept, any changes or substitutions to the technical solutions of the present invention should be easily included within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the scope of the claims.

Claims

1. A geometrically based design method for beamless steel branch pipes controlled by waistline angle, characterized in that, Includes the following steps: Step 1: Using the waistline bend angle as the control condition, generate the tapered tube busbar of the beamless steel branch pipe through geometric method; Step 2: Generate the projection line of the intersection line of the beamless steel branch pipe using a geometric method; Step 3: Using the horizontal projection of the tapered tube busbar from Step 1 and the intersection line from Step 2, establish a three-dimensional model of the beamless steel branch pipe. Step 4: Perform finite element analysis based on the 3D model from Step 3 to verify and determine the waistline reduction and pipe wall thickness.

2. The design method according to claim 1, characterized in that, Step one specifically includes: Step 1.1: Based on the common tangent sphere radius R0, the main pipe inner sphere radius R1, the branch pipe inner sphere radius R2, the bifurcation angle β, and the preset waistline bend angles α1, α2, and θ of the obtuse angle region, satisfying α1+α2+θ=β / 2, determine the sphere centers O1, O2, and O3 of the inner spheres of the main pipe, upper branch pipe, and lower branch pipe through geometric relationships; wherein, the common tangent sphere radius R0 is 1.0 to 1.2 times R1, and O2 is obtained by mirroring O3; In the process of determining the center of the ball O1, center of the ball O2 and center of the ball O3, two initial generatrices are obtained: the main tapered tube generatrice AC and the lower branch tapered tube generatrice DE, where AC is the common tangent of the main tube and the common tangent ball, and DE is the common tangent of the lower branch tube and the common tangent ball. Step 1.2: Generate the remaining tapered tube busbar: The common tangent line A1C1 between the inner ball and the common tangent ball in the main pipe, the common tangent lines G1F1 and GF between the inner ball and the common tangent ball in the upper branch pipe, and the common tangent line D1E1 between the inner ball and the common tangent ball in the lower branch pipe are the bus lines, thus obtaining the remaining 4 bus lines A1C1, G1F1, GF and D1E1. The intersection of A1C1 and G1F1 is determined as the intersection of their common tangents, B1; the intersection of D1E1 and GF is determined as the intersection of their common tangents, H.

3. The design method according to claim 2, characterized in that, Step two specifically includes: Step 2.1: Connect the lines CC1, DD1, and FF1 formed by the endpoints of the tapered tube in Step 1 to obtain the intersection points K, J, and L. The common area enclosed by the focal lines KJ, JL, and LK forms the region of the common tangent spherical shell. Step 2.2: Determine the horizontal projection of the intersection line: Based on the intersection points B1 and H of the common tangents determined in Step 1.2, connect B1L as the projection of the intersection line between the main cone pipe and the upper branch cone pipe, BJ as the projection of the intersection line between the main cone pipe and the lower branch cone pipe, and HK as the projection of the intersection line between the branch cone pipe and the lower branch cone pipe.

4. The design method according to claim 1, characterized in that, Step three specifically includes: Step 3.1: Generate a sketch in the 3D modeling software, rotate the conical tube generatrix from Step 1 around the axis to obtain the main conical tube, upper branch conical tube, lower branch conical tube, main tube and branch tube, and establish a common tangent spherical shell to form the basic surface; Step 3.2: Based on the horizontal projections KJ, JL, LK, B1L, BJ, and HK of the 6 intersection lines obtained in Step 2, establish 6 dividing planes perpendicular to the sketch plane, and trim the basic surface to form a 3D model of the spatial surface. Step 3.3: In CATIA, use parametric modeling to extract the waistline bend angle (α1, α2, θ) and the inscribed sphere radius (R1, R2) as feature parameters to generate a standard template and establish a standard template for the steel branch pipe; for branch pipes of different sizes, the 3D model can be automatically updated simply by modifying the feature parameters.

5. The design method according to claim 1, characterized in that, Step four specifically includes: Step 4.1: Import the 3D model into the finite element software, use shell elements to simulate and perform stress analysis; Step 4.2: Adjust the waistline bend angle (α1, α2, θ) and pipe wall thickness parameters to ensure that the shape and stress performance of the branch pipe meet the requirements of the hydraulic engineering design specifications, and complete the design of the beamless steel branch pipe.

6. The design method according to claim 1, characterized in that, The intersection line mentioned in step two is an ellipse or circular curve in space, and is reflected as a straight line on the horizontal projection diagram. When each cone tube is tangent to the same common tangent sphere, the intersection line is a planar curve.

7. The design method according to claim 4, characterized in that, The 3D modeling software used is CATIA.

8. The design method according to claim 5, characterized in that, The finite element software mentioned in step four is ANSYS.

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