Composite material pipeline analysis method under complex load

Abstract

The invention provides a two-stage analytical model based on a three-dimensional elastic theory. The two-stage analytical model is used for analyzing a failure behavior of a thick-wall composite material pipeline under a complex load condition. Through a stress superposition method, the stress state of the pipeline under the combination of axial pressure, torsional load and bending load is accurately determined. The parameterization research reveals the influence of the winding angle, the lamination sequence and the load on the failure behavior, and provides an important insight about the failure mode. A powerful tool is provided for design and optimization of the composite material pipeline, and application of the composite material pipeline in the oil and gas industry is promoted.

Description

Technical Field

[0001] The present invention belongs to the technical field of failure analysis of composite material pipelines under complex load conditions, and in particular relates to an analytical method for processing the behavior of composite material pipelines under complex axisymmetric and non-axisymmetric combined loads. Background Art

[0002] Composite pipes are currently widely used in the oil and gas industry to manufacture equipment such as submarine pipelines, drill pipes and storage tanks. These structures need to withstand various load conditions including bending, internal and external pressures, high temperatures, and axial and torsional loads. Existing technologies mainly focus on the analysis of the behavior of composite pipes under single load conditions, such as internal pressure, external pressure, cyclic internal pressure, and cyclic temperature loads. However, in practical applications, composite pipes are often subjected to a combination of axial pressure, torsional loads, and bending loads at the same time. This complex load interaction has a significant impact on the stress state and failure mechanism of the pipe. At present, there is a lack of comprehensive analytical models for the failure behavior of composite pipes under combined loads. Summary of the invention

[0003] The present invention aims to solve the deficiencies in the prior art in analyzing the failure behavior of composite pipes under combined loads, and develop a two-level analytical model based on three-dimensional elastic theory to accurately predict the failure behavior of thick-walled composite pipes under a combination of axial load, pressure, torsional load and bending load, thereby providing a reliable tool for the design and optimization of composite pipes.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0005] A method for analyzing composite material pipelines under complex loads adopts a two-stage calculation model to analyze composite material pipelines under complex loads, including:

[0006] The first stage model performs stress analysis for axisymmetric loads, which include pressure, axial loads, and torsional loads;

[0007] The second stage model performs stress analysis for non-axisymmetric bending loads, combines Lekhnitskii's stress function with the three-dimensional elastic solution, and uses the stress superposition method to determine the stress state of the pipeline under the combination of axisymmetric loads and non-axisymmetric bending loads;

[0008] The stress state of the composite pipe under axisymmetric and non-axisymmetric loads is obtained through a two-stage calculation model. The two-stage stress components are converted from the cylindrical coordinate system to the fiber principal direction coordinate system, and the failure coefficient is obtained by substituting the failure criterion to predict the failure behavior of the composite pipe under the combination of axisymmetric loads and non-axisymmetric bending loads.

[0009] Furthermore, the calculation method of the first stage model is:

[0010] S11, obtaining the displacement field of the pipeline in the cylindrical coordinate system, and calculating the strain-displacement relationship of the pipeline;

[0011] S12, calculating the stress-strain relationship of the pipeline according to the orthotropic parameters of any layer of the pipeline material;

[0012] S13. Calculate the pipeline equilibrium equation under axisymmetric load;

[0013] S14, substituting the strain-displacement relationship and the stress-strain relationship into the equilibrium equation to obtain a second-order differential equation of radial displacement, and solving the second-order differential equation to obtain a displacement field solution;

[0014] S15, substituting the displacement field solution into the strain-displacement relationship to obtain the strain, and then substituting it into the stress-strain relationship to obtain the stress distribution of the pipeline under the axisymmetric load;

[0015] S16. Add boundary conditions and continuity conditions to the stress distribution of the pipeline under the axisymmetric load, and calculate the stress state of the pipeline under the axisymmetric load.

[0016] Furthermore, the boundary conditions and continuity conditions are:

[0017] σ r (r in )=-P,σ r (r out )=0;

[0018]

[0019] P is the internal pressure, which acts directly on the inner wall of the pipe; A is the axial load, which is the integral of the axial stress in the radial direction; T is the torsional load, which is the integral of the product of the shear stress and the radius in the radial direction; r in is the inner diameter, r out is the outer diameter, σ r is the radial stress, σ z is the axial stress, τ θz is the in-plane shear stress; r, θ, z represent the radial, annular, and axial coordinates, respectively.

[0020] Furthermore, the calculation method of the second stage model is:

[0021] S21. In the cylindrical coordinate system, the stress functions (F(r,θ)) and (Ψ(r,θ)) defined by Lekhnitskii are analyzed;

[0022] S22, calculating the stress-strain relationship of the pipeline according to the orthotropic parameters of any layer of the pipeline material;

[0023] S23, expressing the stress function as (F = κf(r) sinθ) and (Ψ = κψ(r) sinθ), and calculating the bending stress function of the pipeline using the separation of variables method;

[0024] S24, obtaining the stress distribution of the pipeline under the non-axisymmetric load through the stress function;

[0025] S25. Add boundary conditions to the stress distribution of the pipeline under the non-axisymmetric load and calculate the stress state of the pipeline under the non-axisymmetric load.

[0026] Furthermore, the boundary condition added in S25 is an axial boundary condition, which is specifically expressed as:

[0027]

[0028] M z is the global bending load, which is the double integral of the product of the axial stress and the square of the radius in the radial and annular directions.

[0029] Furthermore, the failure criterion is calculated as follows:

[0030] S31. Calculate the failure rule of fiber tension based on the tensile strength in the fiber direction and the normal stress in the fiber direction, as well as the shear stress and shear strength;

[0031] S32, calculating the failure rule of fiber compression based on the compressive strength in the fiber direction and the normal stress in the fiber direction;

[0032] S33. Based on the normal stress in the matrix direction, the tensile strength in the matrix direction, the shear stress and the shear strength corresponding to the shear stress; calculate the matrix tension failure rule and the matrix compression failure rule.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] The analytical model proposed in the present invention is superior to the finite element model in terms of accuracy and efficiency, especially in dealing with complex stress conditions. Compared with the finite element model, the calculation speed is improved by three orders of magnitude. The model can then be used for parametric studies, revealing the effects of winding angle, stacking sequence and load size on failure behavior, providing important insights into failure modes and their locations. In addition, by using this model, the superiority of winding angle combinations in anti-failure performance can be revealed. The present invention significantly promotes the application of composite pipe technology in the oil and gas industry, and helps to design safer, more reliable and lower-cost pipeline systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic diagram of the three-dimensional composite pipeline model of the present invention;

[0036] Figure 2 It is the verification result diagram of the finite element model and the stress distribution diagram in different thickness directions of the pipeline;

[0037] Figure 3 It is the distribution diagram of Hashin failure coefficient. DETAILED DESCRIPTION

[0038] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] The thick-walled composite pipe used in this implementation is composed of four layers of AS4 / APC-2 carbon / PEEK material, with an inner diameter of 53.5mm and a thickness of 2.5mm per layer. The pipe size complies with the API 5D standard. It is assumed that the pipe is subjected to an internal pressure of P = 51.7MPa, an axial compression force of A = 133.5kN, and a torque and bending moment of T = 40.7kNm. The specific parameters of the material are:

[0040] The orthotropic parameters of AS4 / APC-2 carbon / PEEK materials are as follows:

[0041]

[0042]

[0043] To ensure the authenticity of the examples, the data are taken from industry and related literature.

[0044] like Figure 1-Figure 3 As shown, the technical solution adopted by the present invention is as follows: a method for analyzing composite material pipelines under complex loads, using a two-stage calculation model to analyze composite material pipelines under complex loads, including:

[0045] The first stage model performs stress analysis for axisymmetric loads such as pressure, axial force and torsion.

[0046] The calculation method of the first stage model is:

[0047] S11. Obtain the displacement field of the pipeline in the cylindrical coordinate system and calculate the strain-displacement relationship of the pipeline. In the cylindrical coordinate system, the displacement field can be expressed as:

[0048] u r =u r (r),u θ =uθ (r,θ),u z =u z (z);

[0049] The strain-displacement relationship is:

[0050]

[0051] where u r 、u θ 、u z Represent radial, annular and axial displacements respectively, and r, β, z represent radial, annular and axial coordinates respectively.

[0052] S12. Calculate the stress-strain relationship of the pipeline for the orthotropic parameters of any layer of the pipeline material. For the orthotropic material of the kth layer, the stress-strain relationship is:

[0053]

[0054] C ij is the stiffness coefficient; σ r , σ θ , σ z Represent radial, annular, and axial stress components respectively; τ θz , τ rz , τ rθ is the shear stress component; correspondingly, ∈ is the strain component.

[0055] S13. Calculate the pipeline equilibrium equation under axisymmetric loading. Under axisymmetric loading, the equilibrium equation is simplified to:

[0056]

[0057] S14. Substitute the strain-displacement relationship and the stress-strain relationship into the equilibrium equation to obtain the second-order differential equation of radial displacement, and solve the second-order differential equation to obtain the displacement field solution. The second-order differential equation of radial displacement is:

[0058]

[0059] The solution is:

[0060] u r =Γr β +Ωr -β +α1∈0r+α2γ0r 2 ;

[0061] in, is a constant determined by boundary conditions and continuity conditions.

[0062] S15. Substitute the displacement field solution into the strain-displacement relationship to obtain the strain, and then substitute it into the stress-strain relationship to obtain the stress distribution of the pipeline under the axisymmetric load. The specific formula is:

[0063]

[0064] S16. Add boundary conditions and continuity conditions to the stress distribution of the pipeline under the axisymmetric load, and calculate the stress state of the pipeline under the axisymmetric load.

[0065] Under boundary conditions, the radial stress on the inner wall (σ r ) is equal to the internal pressure P, the radial stress on the outer wall is zero, the axial stress is integrated to obtain the axial force, and the torsional stress is integrated to obtain the torque. The continuity condition includes the continuity of displacement and stress between layers. The boundary conditions and continuity conditions are:

[0066] σ r (r in )=-P,σ r (r out )=0;

[0067]

[0068]

[0069] P is the internal pressure, which acts directly on the inner wall of the pipe; A is the axial load, which is the integral of the axial stress in the radial direction; T is the torsional load, which is the integral of the product of the shear stress and the radius in the radial direction; r in is the inner diameter, r out is the outer diameter, σ r is the radial stress, σ z is the axial stress, τ θz is the in-plane shear stress; r, θ, z represent the radial, annular, and axial coordinates, respectively.

[0070] The first stage model performs stress analysis for axisymmetric loads such as pressure, axial force and torsion. Based on three-dimensional elastic theory, it takes into account the anisotropic properties of the composite material and the cylindrical geometry of the pipe. The calculation results are more consistent with the actual values, with high accuracy and high data credibility.

[0071] The second stage model performs stress analysis on non-axisymmetric bending loads, combines Lekhnitskii's stress function and three-dimensional elastic solution, and uses the stress superposition method to determine the stress state of the pipeline under the combined load.

[0072] The calculation method of the second stage model is:

[0073] S21. In the cylindrical coordinate system, the stress functions (F(r,θ)) and (Ψ(r,θ)) defined by Lekhnitskii are analyzed. The specific formula is:

[0074]

[0075]

[0076]

[0077]

[0078]

[0079] S22. Calculate the stress-strain relationship of the pipeline based on the orthotropic parameters of any layer of the pipeline material:

[0080]

[0081] S ij is the flexibility coefficient.

[0082] S23. The stress function is expressed as (F = κf(r) sinθ) and (Ψ = κψ(r) sinθ), and the bending stress function of the pipeline is calculated using the separation of variables method. The stress function of the pipeline is:

[0083]

[0084]

[0085] Among them, (α i ) and (g i ) is a constant to be determined, (χ i ) is the characteristic root and is related to the boundary conditions; (μ1) and (μ2) are constants and are related to the material parameters.

[0086] S24. The stress distribution of the pipeline under non-axisymmetric load is obtained through the stress function:

[0087]

[0088]

[0089] where (κ) is the curvature of the pipe, which is related to the boundary conditions.

[0090] S25. Add boundary conditions to the stress distribution of the pipeline under non-axisymmetric loads and calculate the stress state of the pipeline under non-axisymmetric loads. The stress of the pipeline is not only related to the r axis, but also to the θ axis. The boundary condition is an axial boundary condition, which is specifically expressed as:

[0091]

[0092] M z is the global bending load, which is the double integral of the product of the axial stress and the square of the radius in the radial and annular directions.

[0093] The second stage model performs stress analysis on non-axisymmetric bending loads, combines Lekhnitskii's stress function and three-dimensional elastic solution, and uses the stress superposition method to determine the stress state of the pipeline under the combined load.

[0094] By combining the results of the first-stage model and the second-stage model, a comprehensive description of the stress state and deformation of the pipeline under the combined load is obtained.

[0095] The stress state of the composite pipe under combined axisymmetric and non-axisymmetric loads is obtained through a two-stage calculation model. The two-stage stress components are converted from the cylindrical coordinate system to the fiber principal direction coordinate system, and the failure coefficient is obtained by substituting the failure criterion to predict the failure behavior of the composite pipe under the combination of axial load, pressure, torsional load and bending load.

[0096] The failure criterion is calculated as:

[0097] S31. Calculate the failure rule of fiber tension based on the tensile strength in the fiber direction and the normal stress in the fiber direction, as well as the shear stress and shear strength.

[0098] When calculating the failure rule of fiber tension, the normal stress in the fiber direction is greater than 0, and the fiber tension failure mode is calculated as follows:

[0099] or

[0100] Where σ1 is the normal stress in the fiber direction, is the tensile strength in the fiber direction, τ 12 and τ 13 is the shear stress, is the corresponding shear strength.

[0101] S32. Calculate the failure rule of fiber compression based on the compressive strength in the fiber direction and the normal stress in the fiber direction.

[0102] When calculating the failure rule of fiber compression, the normal stress in the fiber direction is less than 0, and the fiber compression failure mode is calculated as follows:

[0103]

[0104] in is the compressive strength in the fiber direction.

[0105] S33. Based on the normal stress in the matrix direction, the tensile strength in the matrix direction, the shear stress and the shear strength corresponding to the shear stress; calculate the matrix tension failure rule and the matrix compression failure rule.

[0106] When calculating the matrix tensile failure rule, the normal stress in the matrix direction is greater than 0. The specific calculation formula for the matrix tensile failure mode is:

[0107]

[0108] Among them, σ2 and σ3 are the normal stresses in the matrix direction, is the tensile strength in the matrix direction, τ 23 , τ 12 and τ 13 is the shear stress, and is the corresponding shear strength.

[0109] When calculating the matrix compression failure rule, the normal stress in the matrix direction is less than 0. The specific calculation formula for the matrix compression failure mode is:

[0110]

[0111] By applying the above-mentioned Hashin failure criterion, the failure risk of composite pipes under complex loading conditions can be accurately assessed, thereby optimizing the design and improving the safety and reliability of the pipes.

[0112] Through the calculation of the primary and secondary models, we obtained the stress distribution of the composite pipe with a stacking order of [±45°]2 under the rated combined load, and the calculation time was less than 1 second. Figure 2 As shown in Figure 2, the verification results show that the calculated stress distribution (TLM) is highly consistent with the finite element model (FEM) results, confirming the reliability and accuracy of the model. Figure 3 As shown in Figure 2, based on the converted stress components and the Hashin failure criterion, we predict the failure coefficient distribution of the composite material. This not only provides a reference for the optimal design of composite pipes under combined axisymmetric and non-axisymmetric loads, but also provides technical support for the prediction of the ultimate load of the pipe.

[0113] In order to explore the influence of stacking and winding angle on the optimization design, we take five composite pipes with different stacking ([±45° / ±15°], [±15° / ±45°], [±45°], [±75° / ±45°], [±45° / ±75°]) as examples, and analyze them by using the technical solution provided by the present invention under the action of internal pressure of P=51.7MPa, axial compression force of A=133.5kN, torque of T=40.7kNm and bending moments of 15kNm and 30kNm. The results show that when the bending moment load is 15kNm, the 45° composite layer is more suitable to be placed in the outer layer to resist the shear stress caused by the torque, while the 75° composite layer is suitable to be placed in the inner layer to resist the circumferential stress of the pipeline. When the bending moment load increases to 30kNm, the failure coefficient of the [±45° / ±75°] composite pipe increases significantly, mainly due to the weak lateral strength of the 75° composite layer. In contrast, the failure coefficients of the [±15° / ±45°] and [±45° / ±15°] composite pipes did not increase much, indicating that the low-angle composite layer is more suitable for resisting larger axial stresses. In summary, under this combined load condition, the low-angle composite layer can be used to resist bending moment and axial loads, the medium-angle composite layer is suitable for resisting torsional loads, and the high-angle composite layer is suitable for resisting internal pressure loads. Considering the complexity of multi-load coupling, the mathematical model established by the present invention improves the calculation efficiency, provides an efficient tool for composite pipe design, and can be used for subsequent computer-aided, combined with algorithms for fiber winding angle and stacking optimization projects.

[0114] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A composite material pipeline analysis method under complex loads, characterized in that: A two-stage computational model is used to analyze composite pipes under complex loads, including: The first stage model performs stress analysis for axisymmetric loads, which include pressure, axial loads, and torsional loads; The second stage model performs stress analysis for non-axisymmetric bending loads, combines Lekhnitskii's stress function with the three-dimensional elastic solution, and uses the stress superposition method to determine the stress state of the pipeline under the combination of axisymmetric loads and non-axisymmetric bending loads; The stress state of the composite pipe under axisymmetric and non-axisymmetric loads is obtained through a two-stage calculation model. The two-stage stress components are converted from the cylindrical coordinate system to the fiber principal direction coordinate system, and the failure coefficient is obtained by substituting the failure criterion to predict the failure behavior of the composite pipe under the combination of axisymmetric loads and non-axisymmetric bending loads.

2. The method for analyzing composite material pipelines under complex loads according to claim 1, characterized in that: The calculation method of the first stage model is: S11, obtaining the displacement field of the pipeline in the cylindrical coordinate system, and calculating the strain-displacement relationship of the pipeline; S12, calculating the stress-strain relationship of the pipeline according to the orthotropic parameters of any layer of the pipeline material; S13. Calculate the pipeline equilibrium equation under axisymmetric load; S14, substituting the strain-displacement relationship and the stress-strain relationship into the equilibrium equation to obtain a second-order differential equation of radial displacement, and solving the second-order differential equation to obtain a displacement field solution; S15, substituting the displacement field solution into the strain-displacement relationship to obtain the strain, and then substituting it into the stress-strain relationship to obtain the stress distribution of the pipeline under the axisymmetric load; S16. Add boundary conditions and continuity conditions to the stress distribution of the pipeline under the axisymmetric load, and calculate the stress state of the pipeline under the axisymmetric load.

3. The method for analyzing composite material pipelines under complex loads according to claim 2 is characterized in that: The boundary conditions and continuity conditions are: s r (r in )=-P,σ r (r out )=0; P is the internal pressure, which acts directly on the inner wall of the pipe; A is the axial load, which is the integral of the axial stress in the radial direction; T is the torsional load, which is the integral of the product of the shear stress and the radius in the radial direction; r in is the inner diameter, r out is the outer diameter, σ r is the radial stress, σ z is the axial stress, τ θz is the in-plane shear stress; r, θ, z represent the radial, annular, and axial coordinates, respectively.

4. The method for analyzing composite material pipelines under complex loads according to claim 1, characterized in that: The calculation method of the second stage model is: S21. In the cylindrical coordinate system, the stress functions (F(r,θ)) and (Ψ(r,θ)) defined by Lekhnitskii are analyzed; S22, calculating the stress-strain relationship of the pipeline according to the orthotropic parameters of any layer of the pipeline material; S23, expressing the stress function as (F = κf(r) sinθ) and (Ψ = κψ(r) sinθ), and calculating the bending stress function of the pipeline using the separation of variables method; S24, obtaining the stress distribution of the pipeline under the non-axisymmetric load through the stress function; S25. Add boundary conditions to the stress distribution of the pipeline under the non-axisymmetric load and calculate the stress state of the pipeline under the non-axisymmetric load.

5. The method for analyzing composite material pipelines under complex loads according to claim 4 is characterized in that: The boundary condition added in S25 is an axial boundary condition, which is specifically expressed as: M z is the global bending load, which is the double integral of the product of the axial stress and the square of the radius in the radial and annular directions.

6. The method for analyzing composite material pipelines under complex loads according to claim 1, characterized in that: The failure criterion is calculated as: S31, tensile strength based on the fiber direction and normal stress in the fiber direction, as well as shear stress and shear strength; Calculate failure rules for fiber tension; S32, calculating the failure rule of fiber compression based on the compressive strength in the fiber direction and the normal stress in the fiber direction; S33. Based on the normal stress in the matrix direction, the tensile strength in the matrix direction, the shear stress and the shear strength corresponding to the shear stress; calculate the matrix tension failure rule and the matrix compression failure rule.

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