Method for calculating stress and deformation of roller carrier supporting thin-walled cylinder under action of dead weight

Abstract

The invention discloses a method for calculating stress and deformation of a roller carrier supporting thin-walled cylinder under the action of dead weight, which comprises the following specific steps of: S1, calculating the bending moment and deflection of a cylinder body in the longitudinal direction by adopting an overhanging beam model in the longitudinal direction, and determining the optimal position of the roller carrier in the longitudinal direction according to the maximum bending moment minimization and the maximum deflection minimization of a beam; s2, transversely utilizing symmetry to establish a semicircular curved beam model, and calculating bending moment and displacement in a transverse plane of the cylinder by adopting a Temosinke beam theory; s3, calculating the maximum stress in the cylindrical surface according to the in-surface bending moment, and determining the optimal half wrap angle required by the strength; and S4, calculating the ovality and root-mean-square roundness of the curved beam according to the displacement, and determining the optimal half wrap angle required by deformation. According to the method, the maximum stress and the deformation shape of the thin-walled cylinder are accurately predicted, and the optimal wrap angles of the roller carrier under the strength requirement and the deformation requirement can be determined to be 67.4 degrees and 90 degrees respectively, so that the optimal wrap angle is suggested to be between 67.4 degrees and 90 degrees in engineering.

Description

Technical Field

[0001] The invention belongs to the field of marine engineering, and in particular relates to a method for calculating stress and deformation of a thin-walled cylinder supported by a roller frame under the action of its own weight. Background Art

[0002] Large, thin-walled cylinders, crucial components of large-scale equipment and pressure vessels in the marine, chemical, and energy sectors, often require roller supports during manufacturing, transportation, and assembly. Rollers, a simple, compact, low-cost, and technologically mature auxiliary equipment for large-tonnage placement, facilitate the rotation, handling, and docking of cylinders, significantly improving construction efficiency. Due to the weight of the cylinder, changes in the roller's position and wrap angle can affect the cylinder's stress distribution and deformation.

[0003] If the angle of the roller frame is selected according to the standard JB / T9187-1999 "Welding Roller Frame", the angle range of the roller frame should be between 45° and 110°. However, there is currently no suitable verification and calculation method for the specific selection basis of the roller frame position and wrap angle. Therefore, analyzing the impact of different wrap angles on the cylinder is of great significance for the selection of the roller frame wrap angle. Summary of the Invention

[0004] The purpose of the present invention is to overcome the above shortcomings and provide a method for calculating the stress and deformation of a thin-walled cylinder supported by a roller frame under the action of its own weight.

[0005] The purpose of the present invention is achieved through the following technical solution: A method for calculating the stress and deformation of a thin-walled cylinder supported by a roller frame under the action of its own weight, the specific steps comprising:

[0006] S1. The longitudinal bending moment and deflection of the cylinder are calculated using the cantilever beam model. The optimal longitudinal position of the roller frame is determined by minimizing the maximum bending moment and maximum deflection of the beam.

[0007] S2. A semicircular curved beam model is established using symmetry in the transverse direction, and the bending moment and displacement in the transverse plane of the cylinder are calculated using the Timoshenko beam theory.

[0008] S3. Calculate the maximum stress in the cylinder surface based on the in-plane bending moment and determine the optimal half-wrapped angle required for strength;

[0009] S4. Calculate the ovality and RMS roundness of the curved beam based on the displacement and determine the optimal half-angle required for deformation.

[0010] A further improvement of the present invention is that step S1 specifically includes:

[0011] S11. Establish an outrigger beam model and calculate the longitudinal bending moment and deflection of the cylinder to determine the optimal position of the roller frame in the outrigger beam. The calculation formula is: (1); (2);

[0012] is the longitudinal length of the cylinder, The weight of the cylinder is distributed uniformly on the load. is the distance from the roller frame to the ends of the cylinder, is the bending moment of the extended beam, is the deflection of the cantilever beam;

[0013] S12. According to formula (1) and formula (2), the maximum positive bending moment occurs in the mid-span of the cantilever beam, and the bending moment is , the maximum negative bending moment occurs at the support point, and its value is , according to the minimum optimization requirement of maximum bending moment, when the maximum positive bending moment value is equal to the maximum negative bending moment value, that is , determine the optimal position of the support point under strength requirements as the distance from the end The maximum bending moment in the beam is , the longitudinal bending moment is minimized, the bending normal stress is minimized, and it is the best strength design position;

[0014] S13. According to the deflection calculation formula, the maximum deformation deflection occurs at the mid-span of the cantilever beam or at both ends of the cantilever beam, and the deflections are and , in order to ensure the optimization requirement of the maximum deflection, the values at the point where the maximum deflection occurs must be equal, that is, , determine the optimal position of the support point under the deflection requirement as the distance from the end The position where the deflection is the smallest is the best design position for deflection deformation.

[0015] The longitudinal model determines the optimal position of the support point under the requirements of strength and deformation, and the distance from the end is and The best range in the project is to between.

[0016] A further improvement of the present invention is that step S2 specifically includes:

[0017] S21. Based on the symmetry of the structure and load, the Timoshenko beam theory is used in the transverse direction of the cylinder to establish a half-semicircular curved beam model to calculate the in-plane bending moment and displacement of the cylinder.

[0018] The axial force, shear force and bending moment of the curved beam are: (3);

[0019] The various terms in the formula are the axial force, shear force and bending moment caused by gravity, support force, symmetrical pressure and symmetrical bending moment. The analytical expressions are: (4); (5); (6); (7);

[0020] in: 、 、 are the axial force, shear force, and bending moment caused by gravity within the cylinder surface; 、 、 are the axial force, shear force and bending moment caused by the support force in the cylinder surface; 、 、 are the axial force, shear force and bending moment caused by the symmetrical pressure in the cylinder surface; 、 、 are the axial force, shear force and bending moment caused by the symmetrical bending moment in the cylinder surface, is the angle corresponding to the desired deformation, t is the thickness of the steel plate of the cylinder section, R is the outer radius of the cylinder, is the specific gravity of steel, E is the elastic modulus of steel, is the cross-sectional area of the curved beam, is the moment of inertia, is the shear modulus;

[0021] S22. The curved beam structure is quadratically indeterminate. The boundary conditions determined by symmetry are: (8);

[0022] S23. Use the unit force method to calculate the symmetrical pressure and symmetrical bending moment , the calculation formula is as follows: (9); (10);

[0023] In formula (10), the expressions of the internal forces generated by the unit force and unit bending moment at the lower end are as follows: (11); (12);

[0024] in: 、 、 They represent the axial force, shear force and bending moment of the curved beam under the action of axial unit force respectively; 、 、 They represent the axial force, shear force and bending moment of the curved beam under unit bending moment respectively;

[0025] S24. Calculate the symmetrical pressure according to formula (9) and formula (10). and symmetrical bending moment The expression is as follows: (13) ; (14);

[0026] The symmetrical pressure and symmetrical bending moment Substitute the values into formulas (4), (5), (6), and (7), and then substitute the obtained values into formula (3) to solve the distribution of axial force, shear force, and bending moment of the cylinder in the surface.

[0027] A further improvement of the present invention is that step S3 specifically includes calculating an analytical formula for the bending normal stress at any position of the curved beam, and the calculation formula is: (15);

[0028] in: is the bending normal stress at any position of the curved beam, is the bending section modulus of the curved beam. The point where the cylinder’s in-plane bending moment is the largest is the contact point between the roller frame and the cylinder in formula (14). The maximum normal bending stress is also here. The half wrap angle of the roller frame is further optimized based on the strength requirement. Let , insert M and In, right Derivative, the calculation formula is as follows: (16);

[0029] According to formula (16), when the half angle When , the bending moment at the contact point between the cylinder and the roller frame is the smallest, that is, the hoop stress in the cylinder surface is the smallest under this half wrap angle.

[0030] A further improvement of the present invention is that step S4 includes applying a unit radial force at any position and calculating the radial displacement according to the force method, and the expression is as follows:

[0031] when When , the radial displacement equation is: (17);

[0032] when When , the radial displacement equation is: (18);

[0033] The internal force expression of the curved beam under the radial unit force is: (19);

[0034] in: is the angle corresponding to the internal force of the curved beam; according to the calculation formula (19), the radial displacement is calculated ;

[0035] The ellipticity and root mean square roundness of the curved beam at different half-wrapped angles are calculated based on the radial displacement. The calculation formula is: (20);

[0036] in: is the ellipticity of the curved beam at different half-wrapped angles; is the root mean square roundness of the curved beam at different half wrap angles; is the maximum deformation diameter of the curved beam; is the minimum deformation diameter of the curved beam;

[0037] According to the requirements of strength and deformation determined by the transverse model, the optimal angle range of the roller frame is within the range.

[0038] Compared with the prior art, the present invention has the following advantages:

[0039] The present invention uses an extended beam model to calculate the longitudinal bending moment and deflection of the cylinder, and determines the optimal longitudinal position of the roller frame based on minimizing the maximum bending moment and maximum deflection of the beam. Transversely, a semicircular curved beam model is established using symmetry, and the Timoshenko beam theory is used to calculate the bending moment and displacement within the transverse plane of the cylinder. The maximum stress within the cylinder surface is calculated based on the in-plane bending moment, and the optimal half-angle of support required for strength is determined. The ellipticity and root mean square roundness of the curved beam are calculated based on the displacement, and the optimal half-angle of support required for deformation is determined. The present invention accurately predicts the maximum stress and deformed shape of a thin-walled cylinder, and can determine that the optimal angle of support for the roller frame under strength and deformation requirements is 67.4° and 90°, respectively. Therefore, the optimal angle of support recommended in engineering is between 67.4° and 90°. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 These are longitudinal and transverse model diagrams of the thin-walled cylinder supported by a roller frame in the present invention.

[0041] Figure 2 This is a diagram of the transversely symmetrical semicircular curved beam model of the cylinder in the present invention.

[0042] Figure 3Schematic diagram of the variation of the in-plane bending moment of the thin-walled cylinder with different angles in the present invention.

[0043] Figure 4 The figures are the deformation diagrams of the cylinder before and after deformation at different half-wrapped angles obtained by the method of the present invention and Ansys simulation.

[0044] Figure 5 Schematic diagram of the variation of the ovality and RMS roundness of the cylinder with the half wrap angle of the present invention. DETAILED DESCRIPTION

[0045] In order to deepen the understanding of the present invention, the present invention will be further described in detail below with reference to embodiments and drawings. The embodiments are only used to explain the present invention and do not constitute a limitation on the scope of protection of the present invention.

[0046] The calculation method of stress and deformation of thin-walled cylinder supported by roller frame under the action of deadweight includes the following steps:

[0047] S1. The longitudinal bending moment and deflection of the cylinder are calculated using the cantilever beam model. The optimal longitudinal position of the roller frame is determined by minimizing the maximum bending moment and maximum deflection of the beam.

[0048] S2. A semicircular curved beam model is established using symmetry in the transverse direction, and the bending moment and displacement in the transverse plane of the cylinder are calculated using the Timoshenko beam theory.

[0049] S3. Calculate the maximum stress in the cylinder surface based on the in-plane bending moment and determine the optimal half-wrapped angle required for strength;

[0050] S4. Calculate the ellipticity and root mean square roundness of the curved beam based on the displacement and determine the optimal half-angle required for deformation.

[0051] The step S1 specifically includes:

[0052] S11. Build an outrigger beam model, such as Figure 1 As shown, the longitudinal bending moment and deflection of the cylinder are calculated to determine the optimal position of the roller frame in the outrigger beam. The calculation formula is: (1); (2);

[0053] is the longitudinal length of the cylinder, The weight of the cylinder is distributed uniformly on the load. is the distance from the roller frame to the ends of the cylinder, is the bending moment of the extended beam, is the deflection of the cantilever beam;

[0054] S12. According to formula (1) and formula (2), the maximum positive bending moment occurs in the span of the cantilever beam, and the bending moment is , the maximum negative bending moment occurs at the support point (A / B section), and the value is , according to the minimum optimization requirement of maximum bending moment, when the maximum positive bending moment value is equal to the maximum negative bending moment value, that is , determine the optimal position of the support point under strength requirements as the distance from the end The maximum bending moment in the beam is , the longitudinal bending moment is minimized, the bending normal stress is minimized, and it is the best strength design position;

[0055] S13. According to the deflection calculation formula, the maximum deformation deflection occurs at the mid-span of the cantilever beam or at both ends of the cantilever beam (C and D), and the deflections are and , in order to ensure the optimization requirement of the maximum deflection, the values at the point where the maximum deflection occurs must be equal, that is, , determine the optimal position of the support point under the deflection requirement as the distance from the end The position where the deflection is the smallest is the best design position for deflection deformation.

[0056] The longitudinal model determines the optimal position of the support point under the requirements of strength and deformation, and the distance from the end is and The best range in the project is to between.

[0057] The step S2 specifically includes:

[0058] S21, based on the symmetry of structure and load, e.g. Figure 2 As shown, the Timoshenko beam theory is used in the transverse direction of the cylinder to establish a curved beam model in the shape of half a semicircle to calculate the in-plane bending moment and displacement of the cylinder;

[0059] The axial force, shear force and bending moment of the curved beam are: (3);

[0060] The various terms in the formula are the axial force, shear force and bending moment caused by gravity, support force, symmetrical pressure and symmetrical bending moment. The analytical expressions are: (4); (5); (6); (7);

[0061] in: 、 、 are the axial force, shear force, and bending moment caused by gravity within the cylinder surface; 、 、 are the axial force, shear force and bending moment caused by the support force in the cylinder surface; 、 、 are the axial force, shear force and bending moment caused by the symmetrical pressure in the cylinder surface; 、 、 are the axial force, shear force and bending moment caused by the symmetrical bending moment in the cylinder surface, is the angle corresponding to the desired deformation, t is the thickness of the steel plate of the cylinder section, R is the outer radius of the cylinder, is the specific gravity of steel, E is the elastic modulus of steel, is the cross-sectional area of the curved beam, is the moment of inertia, is the shear modulus;

[0062] S22. The curved beam structure is quadratically indeterminate. The boundary conditions determined by symmetry are: (8);

[0063] S23. Use the unit force method to calculate the symmetrical pressure and symmetrical bending moment , calculated as follows: (9); (10);

[0064] In formula (10), the expressions of the internal forces generated by the unit force and unit bending moment at the lower end are as follows: (11); (12);

[0065] in: 、 、 They represent the axial force, shear force and bending moment of the curved beam under the action of axial unit force respectively; 、 、 They represent the axial force, shear force and bending moment of the curved beam under unit bending moment respectively;

[0066] S24, calculate the symmetrical pressure according to formula (9) and formula (10) and symmetrical bending moment The expression is as follows: (13) ; (14);

[0067] The symmetrical pressure and symmetrical bending moment Substitute the values into formulas (4), (5), (6), and (7), and then substitute the obtained values into formula (3) to solve the distribution of axial force, shear force, and bending moment of the cylinder in the surface.

[0068] Step S3 specifically includes calculating the analytical formula of the bending normal stress at any position of the curved beam, and the calculation formula is: (15);

[0069] in: is the bending normal stress at any position of the curved beam, is the bending section modulus of the curved beam. The point where the cylinder’s in-plane bending moment is the largest is the contact point between the roller frame and the cylinder in formula (14). The maximum normal bending stress is also here. The half wrap angle of the roller frame is further optimized based on the strength requirement. Let , insert M and In, right Derivative, the calculation formula is as follows: (16);

[0070] According to formula (16), when the half angle When , the bending moment at the contact point between the cylinder and the roller frame is the smallest, that is, the hoop stress in the cylinder surface is the smallest under this half wrap angle.

[0071] The step S4 includes applying a unit radial force at any position and calculating the radial displacement according to the force method. The expression is as follows:

[0072] when When , the radial displacement equation is: (17);

[0073] when When , the radial displacement equation is: (18);

[0074] The internal force expression of the curved beam under the radial unit force is: (19);

[0075] in: is the angle corresponding to the internal force of the curved beam; according to the calculation formula (19), the radial displacement is calculated ;

[0076] The ellipticity and root mean square roundness of the curved beam at different half-wrapped angles are calculated based on the radial displacement. The calculation formula is: (20);

[0077] in: is the ellipticity of the curved beam at different half-wrapped angles; is the root mean square roundness of the curved beam at different half wrap angles; is the maximum deformation diameter of the curved beam; is the minimum deformation diameter of the curved beam;

[0078] In summary, the longitudinal model determines the optimal positions of the support points under the requirements of strength and deformation, respectively, the distance from the end is and Therefore, the best range recommended in the project is to Through the transverse embodiment, it is shown that this method can accurately predict the maximum stress and deformation shape of the thin-walled cylinder. It can be determined that the optimal wrap angle of the roller frame under the strength and deformation requirements is 67.4° and 90° respectively. Therefore, the optimal wrap angle recommended in engineering is between 67.4° and 90°.

[0079] Now analyze as Figure 1 The stress and deformation of the thin-walled cylinder shown in the figure are supported by a roller frame. Geometric parameters of the thin-walled cylinder: , , ;Material parameters: , , ; Gravitational acceleration is taken , the shear coefficient of the Timoshenko beam is .

[0080] The optimal position of the roller frame on the cylinder under the requirements of strength and deformation is determined according to the symmetrical cantilever beam model. The optimal position of the roller frame to the cylinder end under the requirements of strength and deformation is calculated as follows: and .

[0081] First, according to the bending moment equation (3-14), the position of the maximum bending moment (dangerous section) is determined to be the support point, and compared with the finite element results to avoid the influence of contact stress. The circumferential stress of the inner wall of the cylinder support point is calculated according to the bending normal stress formula (15). This point is in a unidirectional stress state, and its value is equal to the Mise stress. Then, according to the radial displacement formula (17-18), the radial deformation displacement of each point of the thin-walled cylinder is calculated, and the ovality and root mean square roundness are further calculated. Table 1 shows the Mise stress (close to the maximum Mise stress of the structure) and the ovality and root mean square roundness of the inner wall of the support point of the cylinder calculated by theory and simulation at different half-wrapped angles. As can be seen from the table, the Mise stress and ovality given by the theoretical solution and the simulation results are very consistent, verifying the accuracy of the method of the present invention.

[0082] Table 1 Maximum mise stress and deformation of the cylinder under different roller frame half angles ;

[0083] According to the principle of strength optimization, the maximum bending moment is minimized and the optimal half wrap angle is determined using formula (16): For half angle 、 and Three situations, Figure 3 The in-plane bending moment of the thin-walled cylinder with different angles is given. It can be seen that the bending moment at the support point is the maximum bending moment of the cylinder, and The maximum bending moment is the smallest, which verifies the optimal half-wrapped angle under the strength requirement determined by formula (16).

[0084] Figure 4 The deformation diagrams of the cylinder before and after deformation at different half-wrapped angles obtained by the method of the present invention and Ansys simulation are given. Comparative analysis shows that the theoretical deformation and the simulated deformation are highly consistent, further verifying the correctness of the method of the present invention. As the half-wrapped angle increases, the shape of the thin-walled cylinder after deformation gradually changes from a flat ellipse to an inverted pear. In order to further analyze the influence of the half-wrapped angle on the deformation of the cylinder, Figure 5 The variation of cylinder ellipticity and root mean square roundness with half wrap angle is given. Starting from 20°, the roundness and RMS roundness decrease slowly. When the half-wrapped angle reaches 45°, the roundness and RMS roundness increase rapidly. When the half-wrapped angle is equal to 45°, the ellipticity and RMS roundness are both minimum, the ellipticity is close to 0, and the RMS roundness is 8.167mm. At this time, the deformed shape is as follows Figure 3 In the inverted pear shape (d), it can be seen that the root mean square roundness is a better measure of its deformation than the ellipticity. It can be seen that under the principle of giving priority to deformation optimization, the half-wrapped angle is selected to be 45° (that is, when the wrap angle is 90°), the deformation of the cylinder is the smallest. Taking comprehensive considerations, combined with the optimization of the longitudinal strength and deflection of the cylinder, the optimal range of the distance between the roller support point and the end is to In combination with the optimization of the cylinder's transverse strength and deformation, the cylinder's wrap angle should be selected between 67.4° and 90°.

[0085] Those skilled in the art will appreciate that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. The calculation method of stress and deformation of thin-walled cylinder supported by roller frame under the action of deadweight is characterized by: The specific steps include: S1. The longitudinal bending moment and deflection of the cylinder are calculated using the cantilever beam model. The optimal longitudinal position of the roller frame is determined by minimizing the maximum bending moment and maximum deflection of the beam. S2. A semicircular curved beam model is established using symmetry in the transverse direction, and the bending moment and displacement in the transverse plane of the cylinder are calculated using the Timoshenko beam theory. S3. Calculate the maximum stress in the cylinder surface based on the in-plane bending moment and determine the optimal half-wrapped angle required for strength; S4. Calculate the ellipticity and root mean square roundness of the curved beam based on the displacement and determine the optimal half-angle required for deformation.

2. The method for calculating stress and deformation of a thin-walled cylinder supported by a roller frame under its own weight according to claim 1, characterized in that: The step S1 specifically includes: S11. Establish an outrigger beam model and calculate the longitudinal bending moment and deflection of the cylinder to determine the optimal position of the roller frame in the outrigger beam. The calculation formula is: （1）； （2）； is the longitudinal length of the cylinder, The weight of the cylinder is distributed uniformly on the load. is the distance from the roller frame to the ends of the cylinder, is the bending moment of the extended beam, is the deflection of the cantilever beam; S12. According to formula (1) and formula (2), the maximum positive bending moment occurs in the span of the cantilever beam, and the bending moment is , the maximum negative bending moment occurs at the support point, and its value is , according to the minimum optimization requirement of maximum bending moment, when the maximum positive bending moment value is equal to the maximum negative bending moment value, that is , determine the optimal position of the support point under strength requirements as the distance from the end The maximum bending moment in the beam is , the longitudinal bending moment is minimized, the bending normal stress is minimized, and it is the best strength design position; S13. According to the deflection calculation formula, the maximum deformation deflection occurs at the mid-span of the cantilever beam or at both ends of the cantilever beam, and the deflections are and , in order to ensure the optimization requirement of the maximum deflection, the values at the point where the maximum deflection occurs must be equal, that is, , determine the optimal position of the support point under the deflection requirement as the distance from the end The position where the deflection is the smallest is the best design position for deflection deformation. The longitudinal model determines the optimal position of the support point under the requirements of strength and deformation, and the distance from the end is and The best range in the project is to between.

3. The method for calculating the stress and deformation of a thin-walled cylinder supported by a roller frame under its own weight according to claim 1 is characterized by: The step S2 specifically includes: S21. Based on the symmetry of the structure and load, the Timoshenko beam theory is used in the transverse direction of the cylinder to establish a half-semicircular curved beam model to calculate the in-plane bending moment and displacement of the cylinder. The axial force, shear force and bending moment of the curved beam are: （3）； The various terms in the formula are the axial force, shear force and bending moment caused by gravity, support force, symmetrical pressure and symmetrical bending moment. The analytical expressions are: （4）； （5）； （6）； （7）； in: 、 、 are the axial force, shear force, and bending moment caused by gravity within the cylinder surface; 、 、 are the axial force, shear force and bending moment caused by the support force in the cylinder surface; 、 、 are the axial force, shear force and bending moment caused by the symmetrical pressure in the cylinder surface; 、 、 are the axial force, shear force and bending moment caused by the symmetrical bending moment in the cylinder surface, is the angle corresponding to the desired deformation, t is the thickness of the steel plate of the cylinder section, R is the outer radius of the cylinder, is the specific gravity of steel, E is the elastic modulus of steel, is the cross-sectional area of the curved beam, is the moment of inertia, is the shear modulus; S22. The curved beam structure is quadratically indeterminate. The boundary conditions determined by symmetry are: （8）； S23, using the unit force method, apply axial unit force and axial unit bending moment Acting on the lower end of the statically determinate curved beam, calculate the symmetrical pressure and symmetrical bending moment , the calculation formula is as follows: （9）； （10）； In formula (10), the expressions of the internal forces generated by the unit force and unit bending moment at the lower end are as follows: （11）； （12）； in: 、 、 They represent the axial force, shear force and bending moment of the curved beam under the action of axial unit force respectively; 、 、 They represent the axial force, shear force and bending moment of the curved beam under unit bending moment respectively; S24. Calculate the symmetrical pressure according to formula (9) and formula (10). and symmetrical bending moment The expression is as follows: （13） ； （14）； The symmetrical pressure and symmetrical bending moment Substitute the values into formulas (4), (5), (6), and (7), and then substitute the obtained values into formula (3) to solve the distribution of axial force, shear force, and bending moment of the cylinder in the surface.

4. The method for calculating stress and deformation of a thin-walled cylinder supported by a roller frame under its own weight according to claim 1 is characterized by: The step S3 specifically includes calculating an analytical formula for the bending normal stress at any position of the curved beam, and the calculation formula is: （15）； in: is the bending normal stress at any position of the curved beam, is the bending section modulus of the curved beam. The point where the cylinder’s in-plane bending moment is the largest in formula (14) is the contact point between the roller frame and the cylinder. The maximum normal bending stress is also here. The half wrap angle of the roller frame is further optimized based on the strength requirement. Let , insert M and In, yes Derivative, the calculation formula is as follows: （16）； According to formula (16), when the half angle When , the bending moment at the contact point between the cylinder and the roller frame is the smallest, that is, the hoop stress in the cylinder surface is the smallest under this half wrap angle.

5. The method for calculating stress and deformation of a thin-walled cylinder supported by a roller frame under its own weight according to claim 1 is characterized by: The step S4 includes applying a unit radial force at any position and calculating the radial displacement according to the force method. The expression is as follows: when When , the radial displacement equation is: （17）； when When , the radial displacement equation is: （18）； （19）； in: is the angle corresponding to the internal force of the curved beam; according to the calculation formula (19), the radial displacement is calculated ; The ellipticity and root mean square roundness of the curved beam at different half-wrapped angles are calculated based on the radial displacement. The calculation formula is: （20）； in: is the ellipticity of the curved beam at different half-wrapped angles; is the root mean square roundness of the curved beam at different half wrap angles; is the maximum deformation diameter of the curved beam; is the minimum deformation diameter of the curved beam; According to the requirements of strength and deformation determined by the transverse model, the optimal angle range of the roller frame is within the range.

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