Method for calculating bending stiffness and bending stress of marine fiber reinforced thermoplastic composite pipe

Abstract

The present application relates to a kind of marine fiber reinforced thermoplastic composite pipe bending stiffness and bending stress calculation method, comprising, S1, input the relevant parameters of composite pipe;S2, the constitutive relation of each layer material of composite pipe is established;S3, the normal stress and shear stress of each layer material are calculated from the constitutive relation of each layer material and the strain generated by the axial stress of each layer;S4, based on functional principle, establish the equilibrium equation of composite pipe under bending load, derive the theoretical model for calculating the bending stiffness of composite pipe;S5, the theoretical model obtained from S4 is combined with geometric relationship and statics relationship, and the axial strain at any position in the cross section of pipe is deduced;S6, the axial strain obtained in S5 is substituted into the stress expression in S3, and the stress value at any position in the cross section of composite pipe is obtained.The present application has the characteristics of high efficiency and strong applicability, and helps to improve the technical level of composite pipe in design, analysis and installation, etc., and has high practical engineering application value.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of ocean oil and gas engineering technology, especially a kind of ocean fiber reinforced thermoplastic composite pipe bending stiffness and bending stress analysis calculation method. BACKGROUND

[0002] The development of oil and gas resources plays an important role in social and economic development. The design, production and installation of oil and gas pipelines are very important deepwater key technologies. In the process of oil and gas resource development, pipelines have the advantages of fast transportation speed, low cost and high safety, which cannot be replaced by other transportation tools.

[0003] Ocean fiber reinforced thermoplastic composite pipe is an important tool for the development of ocean oil and gas resources, with the characteristics of fast transportation speed, low cost, good safety and high reliability.

[0004] Currently, in the engineering field, metal pipes and non-bonded composite flexible pipes are two types of pipes that are more commonly used. Especially in marine engineering, metal pipes are easily corroded by seawater, causing oil and gas leakage, which may eventually lead to serious production accidents and ecological disasters. There is friction between the layers of non-bonded composite flexible pipes. During long-term in-situ operation, interlayer wear leads to interlayer separation and functional layer failure, which reduces the compression and fatigue resistance of the pipe.

[0005] Ocean fiber reinforced thermoplastic composite pipe is a new type of bonded composite pipe. Compared with traditional metal pipes, this type of pipe has good corrosion resistance and compression resistance, good thermal conductivity, high stiffness-to-mass ratio, and is easy to install and maintain. The pipe is a composite structure composed of an inner liner, a fiber reinforced layer and an outer sheath layer, as shown in the accompanying Figure 6 The inner liner and the outer sheath layer are made of isotropic materials such as high-density polyethylene; the middle layer is a fiber reinforced layer made of anisotropic materials such as glass fiber tape or carbon fiber tape wound at a certain angle, which is the main load-bearing layer. The inner liner is used to prevent the transported liquid from eroding the fiber reinforced layer, and the outer sheath layer is used to prevent the fiber reinforced layer from being corroded by the external environment.

[0006] During coiling, installation and service in seawater, the mechanical properties of ocean fiber reinforced thermoplastic composite pipe need to be analyzed, especially in complex marine environments, as the pipe is affected by waves and currents, so the overall response of ocean fiber reinforced thermoplastic composite pipe needs to be analyzed. In the overall analysis, the bending stiffness and bending stress of ocean fiber reinforced thermoplastic composite pipe are very important parameters. For ocean fiber reinforced thermoplastic composite pipe, which is a complex pipe made of multiple materials, multiple layers of winding and multiple winding angles, it brings great challenges to the solution of the bending stiffness and bending stress of ocean fiber reinforced thermoplastic composite pipe.

[0007] For the solution of bending stiffness and bending stress of composite pipe with anisotropy, Jolicoeur and Cardou proposed a theoretical model for calculating the bending stiffness and bending stress of composite pipe based on the differential stress function in the elastic theory of anisotropic body and the continuity condition between layers, which is widely used (Jolicoeur C, Cardou A. Analytical solution for bending of coaxial orthotropic cylinders[J]. Journal of engineering mechanics, 1994, 120(12): 2556-2574). When the model is applied, the Cauchy-Euler equation needs to be solved, and the calculation process is complex. In particular, when solving the bending stiffness and bending stress of a marine fiber-reinforced thermoplastic composite pipe with n layers, the theoretical model proposed by Jolicoeur and Cardou contains 14n unknowns. To solve the above unknowns, a 4n×4n order flexibility matrix needs to be calculated, which will cause the calculation process to be complex and the calculation amount to be too large, resulting in low calculation efficiency. At the same time, since the model does not consider the special cases of fiber winding angles of 0° and 90°, it cannot solve the bending stiffness and bending stress of pipes containing the above winding angles.

[0008] When calculating the bending stiffness and bending stress of marine fiber-reinforced thermoplastic composite pipes by experimental method, the main problems are that the test scheme design and test piece production are greatly restricted by test equipment, the economic cost and time cost are high, and it is difficult to obtain the stress results of the fiber reinforced layer under bending conditions.

[0009] When solving the bending stiffness and bending stress of marine fiber-reinforced thermoplastic composite pipes by numerical method, a separate finite element model needs to be established for each model, which has high time cost and high demand for computer hardware equipment, and it is difficult to directly obtain the relationship between the material parameters, geometric parameters and bending stiffness of the fiber-reinforced thermoplastic composite pipe from the finite element model.

[0010] In view of the limitations of the existing theoretical method, experimental method and numerical method, the economic cost is high, and the time period is long. The theoretical model for solving the bending stiffness and bending stress of marine fiber-reinforced thermoplastic composite pipe is developed, which has higher calculation efficiency, less limitation and better universality, which provides an important reference for the section design, overall analysis and engineering practical application of the pipe. SUMMARY

[0011] The application aims to overcome the shortcomings of the prior art and provide a method for calculating bending stiffness and bending stress of an ocean fiber-reinforced thermoplastic composite pipe.

[0012] To achieve the above object, the application adopts the following technical scheme:

[0013] The method for calculating bending stiffness and bending stress of the ocean fiber-reinforced thermoplastic composite pipe comprises the following steps:

[0014] S1, inputting cross-sectional geometric parameters and material parameters of the ocean fiber-reinforced thermoplastic composite pipe;

[0015] S2, establishing a constitutive relation of each layer material of the ocean fiber-reinforced thermoplastic composite pipe;

[0016] S3, calculating normal stress of the i-th layer material and shear stress of the i-th layer material based on the constitutive relation of each layer material and axial stress of each layer material on the cross section of the ocean fiber-reinforced thermoplastic composite pipe and strain generated by the axial stress and the shear stress, respectively, to obtain expressions corresponding to and , wherein i represents the i-th layer, and the value range of i is an integer greater than or equal to 1; S4, based on the functional principle, establishing an equilibrium equation of the ocean fiber-reinforced thermoplastic composite pipe under bending load by equating work done by the bending moment to total strain energy increased by the ocean fiber-reinforced thermoplastic composite pipe, and combining the expressions of the stresses of each layer material

[0017] and obtained in step S3 with the above equilibrium equation and deriving a theoretical expression for calculating the bending stiffness of the ocean fiber-reinforced thermoplastic composite pipe by summation; S5, combining the geometric relation expression, the statics relation expression and the theoretical expression for calculating the bending stiffness of the ocean fiber-reinforced thermoplastic composite pipe obtained in step S4, and deriving an axial strain

[0018] at any position in the i-th layer material of the ocean fiber-reinforced thermoplastic composite pipe under the bending moment M;

[0019] S6, substituting obtained in step S5 into each stress expression in step S3, and deriving a theoretical expression of stress at any position in the i-th layer material of the cross section of the ocean fiber-reinforced thermoplastic composite pipe under the bending moment M.

[0020] The application has the following beneficial effects:

[0021] The present application provides a theoretical model for solving the bending stiffness and bending stress of the marine fiber-reinforced thermoplastic composite pipe, compared with the existing theoretical method (the theoretical method proposed by Jolicoeur and Cardou), the test method and the numerical method, the bending stiffness and bending stress calculation formula derived by the two-dimensional constitutive model based on the function conservation principle has the characteristics of simple form and good universality for different media, different winding angles and different diameter thickness ratios.

[0022] In the theoretical model proposed by the present application, since the flexibility matrix and stiffness matrix involved in the constitutive relation is a 3*3 matrix, in the process of calculating the bending stiffness and bending stress of an n-layer marine fiber-reinforced thermoplastic composite pipe, the complex stress function can be effectively avoided, the analysis and calculation process is greatly simplified, the disadvantages of high time cost and inability to solve special winding angles are solved, the applicability of the calculation method is improved, so that the bending stiffness and bending stress of the marine fiber-reinforced thermoplastic composite pipe can be accurately analyzed and calculated.

[0023] Meanwhile, the present application has high practical engineering application value, provides necessary parameters for the overall design and analysis of the marine fiber-reinforced thermoplastic composite pipe, is beneficial to improve the safety of engineering structure, is helpful to improve the technical level of the marine fiber-reinforced thermoplastic composite pipe in design, analysis and installation, has great practical value for the linear optimization design and overall fatigue life evaluation of the pipeline.

[0024] Based on the two-dimensional constitutive model of the composite material, the function conservation principle is combined to meet the bending moment work equal to the total strain energy increase. The work of the bending moment on the marine fiber-reinforced thermoplastic composite pipe and the strain energy increase of the marine fiber-reinforced thermoplastic composite pipe are respectively obtained, and the balance equation is established, and the analytical formula of the bending stiffness and bending stress of the marine fiber-reinforced thermoplastic composite pipe is derived. The present application has the following advantages:

[0025] (1) In terms of accuracy: the present application uses the function conservation principle to establish the balance equation of the marine fiber-reinforced thermoplastic composite pipe under the bending load, so that the bending moment work is equal to the total strain energy increase of the marine fiber-reinforced thermoplastic composite pipe, and the complex stress function is effectively avoided;

[0026] (2) In terms of applicability: compared with the existing theoretical calculation method (the theoretical method proposed by Jolicoeur and Cardou), the present application can solve the bending stiffness and bending stress of the pipeline under different diameter thickness ratios, various winding angles and different laying materials (isotropic material and anisotropic material), and overcome the problem that special winding angles (0° and 90°) cannot be solved;

[0027] (3) In the cost consumption: when solving the bending stiffness and stress by using the existing theoretical method (the theoretical method proposed by Jolicoeur and Cardou and the improved method proposed by Zhang and Hoa), the solution of a matrix with very large order is involved, while the stiffness matrix and the flexibility matrix involved in the theoretical model established in the application is a 3*3 order matrix, so a lot of calculation time can be saved in the solving process. At the same time, compared with the numerical method and the test method, the application can greatly reduce the economic cost and time cost;

[0028] (4) In the actual engineering application value: the application provides necessary parameters for the overall design and analysis of the marine fiber-reinforced thermoplastic composite pipe, which is beneficial to improve the safety of the engineering structure, and is helpful to improve the technical level of the marine fiber-reinforced thermoplastic composite pipe in design, analysis and installation, and has great practical value for the linear optimization design and dynamic response analysis of the pipeline. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 It is a schematic diagram of the principal coordinate system of single-layer fiber-reinforced material;

[0030] Figure 2 It is a schematic diagram of the coordinate conversion relationship of single-layer fiber-reinforced material;

[0031] Figure 3 It is a schematic diagram of the bending stress of the marine fiber-reinforced thermoplastic composite pipe;

[0032] Figure 4 It is a schematic diagram of the cross-section stress of the marine fiber-reinforced thermoplastic composite pipe under the bending working condition;

[0033] Figure 5 It is a flow chart of the bending stiffness and bending stress analysis and calculation method of the marine fiber-reinforced thermoplastic composite pipe according to the application;

[0034] Figure 6 It is a schematic diagram of the structure composition form of the marine fiber-reinforced thermoplastic composite pipe;

[0035] Figure 7 It is a schematic diagram of the verification model;

[0036] Figure 8 It is a cross-section geometric description diagram of the marine fiber-reinforced thermoplastic composite pipe;

[0037] Figure 9 It is a schematic diagram of the stress output path along the hoop direction in the finite element model;

[0038] Figure 10The comparison chart of the theoretical calculation stress result and the numerical model calculation stress result for the present application. Among them, A is the comparison result of the inner lining layer, B is the comparison result of the first layer of the fiber reinforced layer, C is the comparison result of the second layer of the fiber reinforced layer, D is the comparison result of the fourth layer of the fiber reinforced layer, E is the comparison result of the sixth layer of the fiber reinforced layer, and F is the comparison result of the outer sheath layer. DETAILED DESCRIPTION

[0039] The present application is further illustrated below in conjunction with the drawings and examples.

[0040] The structure, proportion, size, etc. shown in the drawings of the present specification are only used to cooperate with the content disclosed in the specification for understanding and reading by those skilled in the art, and are not used to define the limiting conditions for the implementation of the present application, so they do not have substantial technical significance. Any modification of the structure, change of the proportional relationship or adjustment of the size, without affecting the effects and purposes that can be achieved by the present application, should still fall within the scope of the technical content disclosed by the present application. At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" used in the present specification are only for the convenience of clear description, and are not used to limit the scope of the implementation of the present application. The change or adjustment of the relative relationship, without substantially changing the technical content, is also considered as the implementation scope of the present application.

[0041] As shown in Figures 1-7 , the bending stiffness and bending stress calculation method of the marine fiber-reinforced thermoplastic composite pipe, comprising the following steps:

[0042] S1, input the cross-sectional geometric parameters and material parameters of the marine fiber-reinforced thermoplastic composite pipe.

[0043] The cross-sectional geometric parameters include: the inner radius a, the outer radius b, the thickness of the inner lining layer, the thickness of the fiber reinforced layer, the thickness of the outer sheath layer, the number of layers of the fiber reinforced layer and the winding angle of the fiber in each layer of the fiber reinforced layer of the marine fiber-reinforced thermoplastic composite pipe, see Figure 8 ;

[0044] The material parameters include: the elastic modulus and Poisson's ratio of the inner lining layer and the outer sheath layer, the two elastic moduli E1 and E2 of the fiber reinforced layer, the Poisson's ratio v 21 of the fiber reinforced layer, and the shear modulus G 12 of the fiber reinforced layer.

[0045] S2, establish the constitutive relationship of the materials of each layer of the marine fiber-reinforced thermoplastic composite pipe.

[0046] According to the constitutive relation of each layer of the fiber reinforced layer in the marine fiber reinforced thermoplastic composite pipe in the material principal coordinate system, the constitutive relation of each layer of the fiber reinforced layer in the marine fiber reinforced thermoplastic composite pipe in the Cartesian coordinate system is constructed. Specifically, the constitutive relation of each layer of the fiber reinforced layer in the marine fiber reinforced thermoplastic composite pipe in the material principal coordinate system is in the form of stress representing strain:

[0047]

[0048] In the above formula, 1 represents the direction of the fiber in the material principal coordinate system; 2 represents the direction perpendicular to the fiber direction in the material principal coordinate system; the 1-2 plane is the plane formed by the material principal coordinate axes 1 and 2; σ1 is the normal stress of the material in the 1 direction; σ2 is the normal stress of the material in the 2 direction; τ 12 is the shear stress of the material in the 1-2 plane; ε1 is the axial strain of the material in the 1 direction, and ε2 is the axial strain of the material in the 2 direction; γ 12 is the shear strain of the material in the 1-2 plane; is the compliance matrix in the material principal coordinate system, and each element S in the compliance matrix is called a compliance coefficient, which can be calculated by the following independent elastic constants:

[0049]

[0050] In the above formula, E1 and E2 are the elastic moduli in the 1 direction and the 2 direction in the material principal coordinate system, respectively, v 12 and v 21 are the Poisson's ratios in the 1-2 plane in the material principal coordinate system, and G 12 is the shear modulus in the 1-2 plane. According to the reciprocal law of Betti, the Poisson's ratios v 12 and v 21 have the following relationship:

[0051]

[0052] The inverse operation of the compliance matrix in the material principal coordinate system can obtain the stiffness matrix Therefore, the above constitutive relation formula of stress representing strain can be written as the constitutive relation formula of strain representing stress:

[0053]

[0054] is the stiffness matrix in the material principal coordinate system, and each element Q in the stiffness matrix is called a stiffness coefficient, which can be calculated by the following independent elastic constants:

[0055]

[0056] Especially, for the isotropic material of the inner liner and the outer jacket, it has infinite symmetry planes with respect to any point, and is generally considered to have a laying angle of 0°, and thus can also be processed according to the above constitutive relationship.

[0057] The constitutive relationship of the material in the principal coordinate system is converted into the constitutive relationship in the Cartesian coordinate system through matrix operation. Define x as the axial direction of the marine fiber-reinforced thermoplastic composite pipe; y as the circumferential direction of the marine fiber-reinforced thermoplastic composite pipe; is the normal stress of the i-th layer of the marine fiber-reinforced thermoplastic composite pipe in the axial direction of the pipe; is the normal stress of the i-th layer of the marine fiber-reinforced thermoplastic composite pipe perpendicular to the pipe direction, that is, the stress along the pipe circumferential direction; is the shear stress of the i-th layer of the marine fiber-reinforced thermoplastic composite pipe in the plane, that is, the shear stress along the pipe axial direction; θ (i) is the included angle between the axial direction of the marine fiber-reinforced thermoplastic composite pipe and the fiber winding direction of the i-th layer of the marine fiber-reinforced thermoplastic composite pipe, i is an integer greater than or equal to 1. The stiffness matrix of each layer of material in the principal coordinate system is Matrix operation is performed to obtain the stiffness matrix of each layer of material in the Cartesian coordinate system The matrix calculation formula is as follows:

[0058]

[0059] In the formula, is the stiffness matrix of the i-th layer of material in the Cartesian coordinate system, T (i) is the stiffness matrix coordinate conversion matrix, which is represented by the following formula:

[0060]

[0061] According to the conversion relationship, the constitutive relationship of the i-th layer of material of the marine fiber-reinforced thermoplastic composite pipe in the Cartesian coordinate system is as follows:

[0062]

[0063] In the above formula, Each element in the formula can be expressed as:

[0064]

[0065] It should be pointed out that the above transformation relationship is also applicable to the inner liner and the outer jacket made of isotropic material. Since the isotropic material has many symmetry planes at any point, when using the transformation relationship, the winding angle can be assumed to be 0°.

[0066] S3, the constitutive relation of each layer of material and the axial stress of each layer of material on the cross section of the marine fiber-reinforced thermoplastic composite pipe the axial strain generated the hoop strain and the shear strain the hoop normal stress of the i-th layer of material is calculated and the shear stress of the i-th layer of material

[0067] The analysis of the composite micro-unit under bending load is carried out, the axial direction of the marine fiber-reinforced thermoplastic composite pipe is x direction, the hoop direction of the pipe is y direction, the axial normal stress of the i-th layer of material is The following strains will be generated:

[0068]

[0069] In the above formula, represents the strain of the i-th layer of material in the x direction (axial strain), represents the strain of the i-th layer of material in the y direction (hoop strain), represents the shear strain on the x-y plane, represents the elastic modulus of the i-th layer of material. represents the Poisson's ratio of the i-th layer of material, and the negative ratio of The shear coupling coefficient represents and the ratio of and are in the following form:

[0070]

[0071] In the above formula, S is the compliance coefficient of the material in the Cartesian coordinate system.

[0072] According to the constitutive relation of the i-th layer of material of the marine fiber-reinforced thermoplastic composite pipe in the Cartesian coordinate system in S2 and the expression of the axial normal stress generated by the i-th layer of material, the axial normal stress of the i-th layer of material of the marine fiber-reinforced thermoplastic composite pipe can be obtained the hoop normal stress the shear stress can be represented by the following formula:

[0073]

[0074] S4, based on the principle of conservation of function, the bending moment does work equal to the total strain energy of the pipe, the equilibrium equation of the marine fiber-reinforced thermoplastic composite pipe under bending load is established, and the equilibrium equation is combined with the stresses of each layer obtained in step S3 and​ The expressions are solved simultaneously and summed up to derive a theoretical expression for calculating the bending stiffness of the marine fiber-reinforced thermoplastic composite pipe.

[0075] In combination with the geometric relationship and the statics relationship, the work W done by the external bending moment on the marine fiber-reinforced thermoplastic composite pipe per unit length under the bending load working condition is obtained as follows:

[0076]

[0077] In the above formula, M is the bending moment acting on the marine fiber-reinforced thermoplastic composite pipe, is the central angle of the marine fiber-reinforced thermoplastic composite pipe per unit length after bending, ρ is the radius of curvature of the marine fiber-reinforced thermoplastic composite pipe, E x is the axial overall elastic modulus of the marine fiber-reinforced thermoplastic composite pipe, I z is the moment of inertia of the cross section of the marine fiber-reinforced thermoplastic composite pipe. As shown in the accompanying drawings, the following can be obtained according to the geometric relationship: Figure 3 According to the statics relationship, the following can be obtained: M = E x I z / ρ.

[0078] The total strain energy of the marine fiber-reinforced thermoplastic composite pipe under the bending load working condition is calculated. First, the strain energy of the single-layer material is calculated, and the strain energy U i of the single-layer material can be expressed as follows:

[0079]

[0080] The stress expression obtained in step S3 is substituted into the above formula, and the strain energy of the single-layer material under the bending working condition can be calculated. Finally, the strain energy of the single-layer material is expressed as:

[0081]

[0082] In the above formula, V i is the micro-volume unit of the i-th layer material in the marine fiber-reinforced thermoplastic composite pipe; r i is the radius of the i-th layer of the marine fiber-reinforced thermoplastic composite pipe, and r is the radius of the marine fiber-reinforced thermoplastic composite pipe;

[0083] The total strain energy U of the marine fiber-reinforced thermoplastic composite pipe per unit length is as follows:

[0084]

[0085] Wherein, the value range of n is n≥1, and n is an integer;

[0086] ​According to the principle of energy conservation, the work done by the external bending moment M on the marine fiber-reinforced thermoplastic composite pipe is equal to the increase of the strain energy inside the marine fiber-reinforced thermoplastic composite pipe, and thus the following balance equation is established:

[0087] U = W

[0088] According to the work W done by the external bending moment on the marine fiber-reinforced thermoplastic composite pipe and the increase of the strain energy U inside the marine fiber-reinforced thermoplastic composite pipe obtained above, the above formula can be written as:

[0089]

[0090] The bending stiffness calculation expression of the marine fiber-reinforced thermoplastic composite pipe can be obtained by transforming the above formula:

[0091]

[0092] S5, the geometric relationship expression, the statics relationship expression and the theoretical expression of the bending stiffness of the marine fiber-reinforced thermoplastic composite pipe obtained in step S4 are associated to deduce the axial strain of the marine fiber-reinforced thermoplastic composite pipe at any position in the i-th layer material under the bending moment M:

[0093] As shown in the accompanying Figure 3 , the axial strain can be obtained according to the geometric relationship:

[0094]

[0095] In the above formula, y (i) is the distance from any point in the i-th layer material on the cross section of the marine fiber-reinforced thermoplastic composite pipe to the neutral axis of the marine fiber-reinforced thermoplastic composite pipe, and y (i) can be expressed as rsinα according to the accompanying Figure 4 . According to the statics relationship, the curvature radius p can be expressed by the following formula:

[0096]

[0097] The corresponding axial strain of the marine fiber-reinforced thermoplastic composite pipe at any position in the i-th layer material on the cross section when the applied bending moment load is M can be obtained from the above expression as:

[0098]

[0099] S6, the expression of deduced in step S5 is substituted into each stress expression in step S3 to deduce the stress value of the marine fiber-reinforced thermoplastic composite pipe at any position in the i-th layer material on the cross section when the applied bending moment load is M.​

[0100] Specifically, the result obtained in step S5 Substituting these values ​​into the stress expressions in step S3, we obtain the expression for the stress at any position in the i-th layer of material in the corresponding cross-section of the marine fiber reinforced thermoplastic composite pipe when the applied bending moment load is M.

[0101]

[0102] To verify the bending stiffness and stress analysis calculation method of the marine fiber-reinforced thermoplastic composite pipe proposed in this invention, a finite element model with a fiber winding angle of 55° / -55° and an axial length of 1000 mm was established using ABAQUS software, yielding numerical solutions for bending stiffness and stress. Simultaneously, the theoretical calculation expressions proposed in this invention were compiled into MATLAB programming language to calculate the theoretical solutions for bending stiffness and stress. The obtained numerical solutions were then compared and verified with the theoretical solutions obtained from the theoretical expressions proposed in this invention.

[0103] The material parameters and cross-sectional geometric parameters of marine fiber reinforced thermoplastic composite pipes are shown in Table 1 and Table 2, respectively.

[0104] Table 1 Material parameters of marine fiber reinforced thermoplastic composite pipe

[0105]

[0106] Table 2. Cross-sectional geometric parameters of marine fiber reinforced thermoplastic composite pipes

[0107]

[0108] like Figures 7-10 As shown, this embodiment specifically includes the following steps:

[0109] S1: Theoretical solution for bending stiffness and stress

[0110] Using MATLAB software, the theoretical expressions for solving the bending stiffness and bending stress of marine fiber reinforced thermoplastic composite pipes proposed in this invention are compiled into a programming language. The material parameters and cross-sectional geometric parameters of the marine fiber reinforced thermoplastic composite pipe are input into the program to obtain the bending stiffness of the marine fiber reinforced thermoplastic composite pipe and the stress on the cross section corresponding to different bending moments.

[0111] S2: Establishing the finite element model

[0112] Finite element model (see) Figure 7 The element type used in the finite element model is C3D8R because it is more efficient in handling nonlinear problems such as contact, plasticity, and large deformation. Figure 7As shown, reference point RP-1 and reference point RP-2 are respectively arranged at the cross-section center points of the two ends of the model. A bending moment load is respectively applied on the two reference points, the load size is equal and the direction is opposite, and the two reference points are all coupled with the motion of all nodes on the cross-section.

[0113] S3: comparing the numerical results obtained in S2 with the theoretical results obtained in S1, verifying the accuracy of the theoretical expression for solving the bending stiffness and bending stress proposed in the application.

[0114] The bending stiffness numerical results and the theoretical results are shown in Table 3.

[0115] Table 3: Bending stiffness calculation results of the marine fiber-reinforced thermoplastic composite pipe

[0116]

[0117] Since in the pure bending working condition, there is only bending moment in each cross-section of the marine fiber-reinforced thermoplastic composite pipe, the normal stress and shear stress along the length direction of the pipe are mainly discussed. The stress output path shown in Figure 9 When the applied bending moment size is 2000 Nm, the axial stress and shear stress of the inner liner layer, the first layer, the second layer, the fourth layer and the sixth layer in the fiber-reinforced layer and the outer sheath layer are respectively selected for comparative analysis.

[0118] The bending stiffness comparison results of Table 3 and Figure 10 The bending stress comparison results of Table 3 and

[0119] Although the specific embodiments of the application are described above with reference to the accompanying drawings, the description is not a limitation on the scope of protection of the application, and those skilled in the art should understand that various modifications or variations made by those skilled in the art on the basis of the technical solutions of the application without creative labor are still within the scope of protection of the application.

Claims

1. A method for calculating the bending stiffness and bending stress of an ocean fiber-reinforced thermoplastic composite pipe, characterized by, It comprises the following steps: S1, inputting cross-sectional geometric parameters and material parameters of the marine fiber-reinforced thermoplastic composite pipe; S2, establishing a constitutive relationship of each layer material of the marine fiber-reinforced thermoplastic composite pipe; S3, the constitutive relation of each layer and the axial stress of each layer material on the cross section of the marine fiber-reinforced thermoplastic composite pipe the generated strain and the normal stress of the i-th layer material and the shear stress of the i-th layer material where i is an integer greater than or equal to 1; S4, based on the functional principle, the work done by the bending moment on the marine fiber-reinforced thermoplastic composite pipe is equal to the total strain energy of the marine fiber-reinforced thermoplastic composite pipe, and the equilibrium equation of the marine fiber-reinforced thermoplastic composite pipe under bending load is established, and the stress and Expressions obtained in step S3 are associated with the above equilibrium equation and the theoretical expression for calculating the bending stiffness of the marine fiber-reinforced thermoplastic composite pipe is derived by summation. S5, the theoretical expression of the bending stiffness of the marine fiber-reinforced thermoplastic composite pipe is derived by simultaneously solving the geometric relationship expression, the statics relationship expression and the theoretical expression of the bending stiffness of the marine fiber-reinforced thermoplastic composite pipe obtained in step S4, to obtain the axial strain of the i-th layer of the marine fiber-reinforced thermoplastic composite pipe at any position under the action of the bending moment M S6, the stress at any position in the i-th layer of the cross section of the marine fiber reinforced thermoplastic composite pipe under the bending moment M is derived by substituting the stress expression of each layer in step S5 into the stress expression of each layer in step S3. S6, the stress at any position in the i-th layer of the cross section of the marine fiber reinforced thermoplastic composite pipe under the bending moment M is derived by substituting the stress expression of each layer in step S5 into the stress expression of each layer in step S3.

2. The method of calculating the bending stiffness and bending stress of the marine fiber reinforced thermoplastic composite pipe according to claim 1, characterized by, In the step S2, the constitutive relationship of the inner liner layer, the fiber-reinforced layer and the outer sheath layer of the marine fiber-reinforced thermoplastic composite pipe in the material principal coordinate system is established according to the material parameters, and the strain is expressed in the form of stress: In the above formula, 1 represents the direction of the fiber in the material principal coordinate system; 2 represents the direction perpendicular to the fiber direction in the material principal coordinate system; the 1-2 plane is the plane formed by the material principal coordinate axes 1 and 2; σ1 is the normal stress of the material in the 1 direction; σ2 is the normal stress of the material in the 2 direction; τ 12 is the shear stress of the material in the 1-2 plane; ε1 is the axial strain of the material in the 1 direction, and ε2 is the axial strain of the material in the 2 direction; γ 12 is the shear strain of the material in the 1-2 plane; is the compliance matrix of the material in the material principal coordinate system.

3. The method of calculating the bending stiffness and bending stress of the marine fiber reinforced thermoplastic composite pipe according to claim 2, characterized by, Since the homogeneous material can be considered as having infinite number of symmetry planes about any point, it can be treated as a composite material with a layup angle of 0° for matrix transformation; Each element in the matrix is calculated according to the following formula: In the above equations, E1and E2are the elastic moduli in the fiber direction and in the fiber in-plane tangential direction, respectively, in the material principal coordinate system; v 12 and v 21 are the Poisson's ratios in the fiber direction and in the fiber in-plane tangential direction, respectively, in the material principal coordinate system, G 12 is the shear modulus in the in-plane fiber direction in the material principal coordinate system; according to the reciprocal Beth's law, the Poisson's ratios v 12 and v 21 have the following relationship: The stiffness matrix can be obtained by inverting the compliance matrix in the material principal coordinate system Thus, the constitutive relation of strain represented by stress can be written as the constitutive relation of stress represented by strain: Qij= 1 V ∂U ∂xi ∂U ∂xj where Q is the stiffness matrix in the material principal coordinate system, and each element Q in the stiffness matrix is called a stiffness coefficient, which is calculated by the following independent elastic constants: For the isotropic material of the inner liner layer and the outer sheath layer, there are infinite symmetry planes about any point, which is considered to have a laying angle of 0°, so it can also be processed according to the above constitutive relationship.

4. The method of calculating the bending stiffness and bending stress of the marine fiber reinforced thermoplastic composite pipe according to claim 3, characterized by, The constitutive relationship expression of the material principal coordinate system is converted into the constitutive relationship expression in the Cartesian coordinate system through matrix operation; The conversion relationship between the material principal coordinate system and the Cartesian coordinate system; define the x-axis as the axial direction of the marine fiber-reinforced thermoplastic composite pipe; and the y-axis as the circumferential direction of the marine fiber-reinforced thermoplastic composite pipe; is the normal stress of the i-th layer of material of the marine fiber-reinforced thermoplastic composite pipe in the pipe axial direction in the plane; is the normal stress of the i-th layer of material of the marine fiber-reinforced thermoplastic composite pipe in the pipe axial direction in the plane, that is, the circumferential stress of the pipe; is the shear stress of the i-th layer of material of the marine fiber-reinforced thermoplastic composite pipe in the plane; θ (i) is the included angle between the axial direction of the marine fiber-reinforced thermoplastic composite pipe and the fiber winding direction of the i-th layer of material of the marine fiber-reinforced thermoplastic composite pipe, wherein i is an integer greater than or equal to 1; and the stiffness matrix of each layer of material in the principal coordinate system is The matrix operation is performed to obtain the stiffness matrix of each layer of material in the Cartesian coordinate system The matrix calculation formula is as follows: In the formula, is the stiffness matrix of the i-th layer material in the Cartesian coordinate system, T (i) is the stiffness matrix coordinate transformation matrix, which is represented by the following formula: According to the conversion relationship, the constitutive relationship of the i-th layer material of the marine fiber-reinforced thermoplastic composite pipe in the Cartesian coordinate system is as follows: In the above formulae, The elements in the middle are represented as: The above conversion relationship is also applicable to the inner liner layer and the outer sheath layer made of isotropic material; since the isotropic material has many symmetry planes at any point, when using the conversion relationship, it is assumed that the winding angle is 0°.

5. The marine fiber-reinforced thermoplastic composite pipe bending stiffness and bending stress calculation method according to claim 4, characterized in that: In the step S3, the ocean fiber-reinforced thermoplastic composite pipe is analyzed under bending load, the pipe axial direction is x direction, the pipe hoop direction is y direction, the axial normal stress of the i-th layer material is The following strain will be generated: In the above formulae represents the strain in the x-direction of the i-th layer material, represents the strain in the y-direction of the i-th layer material, represents the shear strain in the x-y plane, represents the elastic modulus of the i-th layer material, represents the Poisson's ratio of the i-th layer material, strain and strain ; the shear coupling coefficient represents and ; the ratio of and ; the ratio of In the above formula, S is the compliance coefficient of the material in the Cartesian coordinate system; The axial normal stress of the i-th layer material in the ocean fiber-reinforced thermoplastic composite pipe can be derived from the constitutive relation expression of the i-th layer material under the Cartesian coordinate system and the axial normal stress of the i-th layer material The generated strain expression The hoop normal stress The shear stress is represented by the following formula:

6. The method of calculating the bending stiffness and bending stress of the marine fiber reinforced thermoplastic composite pipe according to claim 5, characterized by, In the step S4, the work done by the external force on the unit length of the marine fiber-reinforced thermoplastic composite pipe under the bending load condition is obtained as: In the above formula, M is the bending moment acting on the marine fiber-reinforced thermoplastic composite pipe, is the central angle generated after the unit length marine fiber-reinforced thermoplastic composite pipe is bent, p is the radius of curvature of the marine fiber-reinforced thermoplastic composite pipe, E x is the axial overall elastic modulus of the marine fiber-reinforced thermoplastic composite pipe, I z is the moment of inertia of the cross section of the marine fiber-reinforced thermoplastic composite pipe, which is obtained according to the geometric relationship According to the statics relationship, M=E x I z / p.

7. The method of calculating the bending stiffness and bending stress of the marine fiber reinforced thermoplastic composite pipe according to claim 6, characterized by, The total strain energy of the marine fiber-reinforced thermoplastic composite pipe under the bending load condition is obtained as: First, the strain energy of the single layer material in the marine fiber reinforced thermoplastic composite pipe is calculated. In the bending working condition, the axial normal stress exists on the local micro unit hoop normal stress shear stress Therefore, the strain energy of the single layer material in the marine fiber reinforced thermoplastic composite pipe calculated by the S3 stress expression is the strain energy of the i-th layer material, which is: In the above formula, U i is the strain energy of the material single layer, i.e., the strain energy of the i-th layer material of the marine fiber-reinforced thermoplastic composite pipe; V i is a micro-volume unit of the i-th layer material in the marine fiber-reinforced thermoplastic composite pipe; r is the radius of the marine fiber-reinforced thermoplastic composite pipe, r i r is the radius of the marine fiber-reinforced thermoplastic composite pipe, r i r is the radius of the marine fiber-reinforced thermoplastic composite pipe, r i r is the radius of the marine fiber-reinforced thermoplastic composite pipe, r i r is The total strain energy of the unit length of the marine fiber-reinforced thermoplastic composite pipe is as follows: Wherein, the value range of n is n≥1, and n is an integer.

8. The method of calculating the bending stiffness and bending stress of the marine fiber reinforced thermoplastic composite pipe according to claim 7, characterized by, According to the principle of energy conservation, the work done by the external bending moment on the marine fiber-reinforced thermoplastic composite pipe is equal to the strain energy increased inside the marine fiber-reinforced thermoplastic composite pipe, and the following balance equation is established: U=W The above formula is written as: The bending stiffness calculation formula of the marine fiber-reinforced thermoplastic composite pipe is calculated as:

9. The marine fiber-reinforced thermoplastic composite pipe bending stiffness and bending stress calculation method according to claim 8, characterized in that: In the step S5, the axial strain of the i-th layer material of the marine fiber-reinforced thermoplastic composite pipe is calculated according to the geometric relationship as: In the above equation, y (i) is the distance from the i-th layer of material on the bend cross-section of the marine fiber-reinforced thermoplastic composite pipe to the neutral axis in the cross-section; according to the geometric relationship, y (i) is expressed as rsinα, and according to the statics relationship in material mechanics, the radius of curvature p of the marine fiber-reinforced thermoplastic composite pipe is expressed by the following equation: From the above expression, the axial strain at any position in the i-th layer of the marine fiber-reinforced thermoplastic composite pipe under the action of the bending moment M is derived 10. The method of calculating bending stiffness and bending stress of an ocean fiber reinforced thermoplastic composite pipe according to claim 9, characterized in that: In the step S6, the stress values of the marine fiber reinforced thermoplastic composite pipe at any position of each layer of the cross section under the applied bending moment load M are obtained by substituting the stress expressions of each layer in the step S5 into the stress expressions of each layer in the step S3. In the step S6, the stress values of the marine fiber reinforced thermoplastic composite pipe at any position of each layer of the cross section under the applied bending moment load M are obtained by substituting the stress expressions of each layer in the step S5 into the stress expressions of each layer in the step S3.

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