Method for calculating buckling instability pressure of continuous fiber composite external-pressure-resistant reinforcing layer

Abstract

The invention discloses a method for calculating buckling instability pressure of a continuous fiber composite external-pressure-resistant reinforcing layer. The method comprises the following steps: establishing a motion equation of the fiber composite external-pressure-resistant reinforcing layer; calculating an integral point displacement increment; calculating an integral point strain increment based on the integral point displacement increment; calculating an integral point stress increment based on the orthotropic stiffness matrix and a rotation axis formula, and determining the maximum stress of the integral point; judging whether the maximum stress of the integral point meets a Hashin damage criterion or not; establishing an equilibrium equation set based on the virtual work equation; adopting a Newton-Raphson method to iteratively solve the equation set; carrying out convergence test; and updating the equilibrium state until the continuous fiber composite external pressure resistant reinforcing layer reaches buckling instability, and outputting a calculation result. By adopting the technical scheme provided by the invention, the buckling instability pressure and the section deformation of the continuous fiber composite external-pressure-resistant reinforcing layer under the action of external pressure can be quickly and accurately evaluated.

Description

Technical Field

[0001] The present invention belongs to the technical field of crushing instability prediction of deep-sea flexible riser structures, and in particular relates to a method for calculating the buckling instability pressure of a continuous fiber composite external pressure-resistant reinforcement layer. Background Art

[0002] The ocean is rich in mineral resources, and deep-sea mineral resource development has gradually become a hot topic in academia and engineering. The pipeline hoisting mining system is currently recognized as the most commercially promising marine mineral development solution, with the upper transport pipeline being considered the core of the mining system. During deep-sea operations, the upper transport pipeline will be subjected to complex loads, placing high demands on the pipeline's mechanical properties. Traditional rigid pipes cannot meet the needs of mining operations due to their high bending stiffness, difficulty in recycling, and susceptibility to corrosion. Flexible pipes, however, offer low bending stiffness, ease of installation and recycling, and corrosion resistance, making them a more advantageous option.

[0003] Flexible pipes can be divided into metal flexible pipes and non-metallic flexible pipes according to material type, and can be divided into bonded flexible pipes and non-bonded flexible pipes according to processing technology. Among them, non-metallic non-bonded flexible pipes have the advantages of being lightweight, corrosion-resistant, permeation-resistant, flexible, high-pressure-resistant, and easy to process and install. They can adapt to the harsh environment of the ocean and have broad application prospects in the field of deep-sea mining. Non-metallic non-bonded flexible pipes are generally composed of an inner lining layer, an internal pressure-resistant reinforcement layer, an external pressure-resistant reinforcement layer, an anti-wear layer, a tensile reinforcement layer, an outer sheath, etc. Among them, the external pressure-resistant reinforcement layer is composed of a continuous fiber-reinforced composite shell or a fiber-reinforced composite winding tape, which is mainly used to resist external high hydrostatic pressure and is an important component of non-metallic non-bonded flexible pipes.

[0004] Flexible pipes used in deep-sea mining operate at depths of approximately 4,000 to 6,000 meters. Under high-pressure conditions, flexible pipes are highly susceptible to local buckling instability. When the external pressure is sufficiently high, this local buckling can rapidly propagate along the pipe's axis, potentially leading to failure of the entire pipeline. The ability of flexible pipes used in deep-sea mining to withstand high external hydrostatic pressures is primarily provided by the fiber-composite pressure-resistant reinforcement layer. Currently, research on the buckling instability of fiber-composite pressure-resistant reinforcement layers is scarce, and a rapid and effective method for assessing the load-bearing capacity of these layers remains lacking, presenting a critical scientific and technological challenge that needs to be addressed urgently. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for calculating the buckling instability pressure of a continuous fiber composite external pressure resistant reinforcement layer.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for calculating the buckling instability pressure of a continuous fiber composite external pressure-resistant reinforcement layer includes:

[0008] Step S1, measuring the geometric parameters of the continuous fiber composite external pressure resistant reinforcement layer of the deep-sea flexible pipe;

[0009] Step S2: obtaining material characteristic parameters of the continuous fiber composite external pressure resistant reinforcement layer of the deep-sea flexible pipe;

[0010] Step S3: constructing the motion equation of the continuous fiber composite external pressure resistant reinforcement layer according to the nonlinear ring theory;

[0011] Step S4: Applying volume increment Calculate the displacement increment of the integration point

[0012] Step S5: Based on the integral point displacement increment Calculate the strain increment at the integration point based on the equation of motion

[0013] Step S6: Calculate the stress increment at the integration point based on the strain increment at the integration point And by comparing the maximum stress {σ max} i ;

[0014] Step S7: Determine the maximum stress at the integration point {σ max} i Whether the Hashin damage criterion is satisfied; if the Hashin damage criterion is satisfied, stiffness reduction is performed on the stiffness matrix of the anti-external pressure reinforcement layer; if the Hashin damage criterion is not satisfied, proceed to step S8;

[0015] Step S8: establishing a set of equilibrium equations based on the virtual work equation;

[0016] Step S9, using the Newton-Raphson method to iteratively solve the equations;

[0017] Step S10: Check whether the displacement value has converged. Check the change in displacement between two iterations. If the change is less than a set small value, it is considered that the iterative calculation of this load substep has converged. If it has not converged, use the displacement value calculated in the previous iteration as an estimate and return to step S4 for calculation until convergence.

[0018] Step S11: Update the equilibrium state, calculate the current external pressure P and the cross-sectional ellipticity Δ, and repeat steps S4 to S8 until the continuous external pressure-resistant reinforcement layer reaches buckling instability, and output the theoretical calculation results.

[0019] Preferably, the step S3 is specifically as follows:

[0020] Step S31: According to the relationship between the material mechanical curvature and the axial strain and the cross-sectional elliptical deformation displacement relationship, the axial strain is obtained, that is:

[0021]

[0022] in, is the distance from any point on the deformed cross section to the geometric mid-plane,

[0023] Step S32: Obtain the hoop strain according to the initial ellipticity Δ0, the hoop infinitesimal segment node displacement relationship, and the geometric relationship, namely:

[0024]

[0025] in, ε θ0 is the hoop strain caused by the initial radial displacement of the pipeline.

[0026] Preferably, in step S5, if the main direction of the fiber forms an angle α with the axial direction of the external pressure resistant reinforcement layer, then:

[0027]

[0028] in: is the strain increment in the longitudinal direction of the fiber, is the strain increment in the transverse direction of the fiber, Axial strain increment of the cross section of the continuous fiber composite external pressure reinforcement layer, Hoop strain increment of the cross section of continuous fiber composite external pressure reinforcement layer.

[0029] Preferably, the step S6 is specifically as follows:

[0030] Step S61: Calculate the longitudinal and transverse stress increments of the fiber based on the orthotropic stiffness matrix:

[0031]

[0032] Where: is the stress increment in the longitudinal direction of the fiber, is the stress increment in the transverse direction of the fiber;

[0033] Step S62: If the main direction of the fiber forms an angle α with the axial direction of the continuous fiber composite external pressure-resistant reinforcement layer, the axial stress increment and the hoop stress increment of the cross section are:

[0034]

[0035] Preferably, in step S8, the balance equation is obtained based on the fact that the internal force work is equal to the external force work:

[0036] in,

[0037]

[0038] Preferably, the geometric parameters of the continuous fiber composite anti-external pressure reinforcement layer of the deep-sea flexible pipe are measured, including the outer diameter D, thickness t, fiber winding angle α and initial ellipticity Δ0 of the anti-external pressure reinforcement layer.

[0039] As a preference, the material characteristic parameters of the continuous fiber composite anti-external pressure reinforcement layer of the deep-sea flexible pipe include: elastic modulus E1 in the longitudinal direction of the fiber, elastic modulus E2 in the transverse direction of the fiber, in-plane Poisson's ratio v 12 and v 21 , Fiber longitudinal tensile strength X T , fiber longitudinal compressive strength X C , fiber transverse tensile strength Y T And the fiber transverse compressive strength Y C .

[0040] The beneficial effects of the present invention are:

[0041] (1) The nonlinear theoretical model proposed in the present invention can quickly calculate the buckling instability pressure of the continuous fiber composite anti-external pressure reinforcement layer, and its calculation efficiency and convergence are significantly better than the traditional finite element method.

[0042] (2) The present invention takes into account the winding direction and damage failure of fiber composite materials, and can accurately calculate the buckling instability pressure of different fiber composite materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0044] Figure 1 is the cross-section calculation parameter of the continuous external pressure-resistant reinforcement layer;

[0045] Figure 2 It is a schematic diagram of the deformation and displacement of the cross section of the continuous external pressure-resistant reinforcement layer;

[0046] Figure 3 is the distribution of Gaussian integral points;

[0047] Figure 4 It is a flow chart of the method for calculating the buckling instability pressure of the continuous fiber composite anti-external pressure reinforcement layer disclosed in the present invention. DETAILED DESCRIPTION

[0048] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0049] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0050] Example 1:

[0051] like Figure 4 As shown, an embodiment of the present invention provides a method for calculating the buckling instability pressure of a continuous fiber composite anti-external pressure reinforcement layer, comprising:

[0052] Step S1, measuring the geometric parameters of the continuous fiber composite anti-external pressure reinforcement layer of the deep-sea flexible pipe, including the outer diameter D, thickness t, fiber winding angle α and initial ellipticity Δ0 of the anti-external pressure reinforcement layer;

[0053] Step S2: Obtain the material properties of the continuous fiber composite anti-external pressure reinforcement layer of the deep-sea flexible pipe, including the elastic modulus E1 in the longitudinal direction of the fiber, the elastic modulus E2 in the transverse direction of the fiber, the in-plane Poisson's ratio v 12 and v 21 , Fiber longitudinal tensile strength X T , fiber longitudinal compressive strength X C , fiber transverse tensile strength Y T And the fiber transverse compressive strength Y C ;

[0054] Step S3: Establish the motion equation of the continuous fiber composite anti-external pressure reinforcement layer according to the nonlinear ring theory. Only the axial strain and the hoop strain are considered, and the radial strain and the shear strain are ignored. Figure 1 As shown in the figure, according to the relationship between the material mechanics curvature and axial strain, and the relationship between the cross-sectional elliptical deformation and displacement, the axial strain can be derived as:

[0055]

[0056] in, is the distance from any point on the deformed cross section to the geometric mid-plane. Figure 2 It is deduced that:

[0057] According to the displacement relationship and geometric relationship of the nodes of the circumferential infinitesimal segment, the circumferential strain can be derived as follows:

[0058]

[0059] in,

[0060] Assuming that the initial ovality Δ0 is a certain initial radial displacement w0 of the continuous fiber composite anti-external pressure reinforcement layer before loading, this displacement does not cause the generation of internal stress in the anti-external pressure reinforcement layer and only affects the hoop strain. The hoop strain considering the initial ovality is:

[0061] Step S4: Applying volume increment Calculate the displacement increment of the integration point Specifically, it can be written as:

[0062]

[0063] Step S5: Based on the integral point displacement increment Calculate the strain increment at the integration point based on the derived motion equation If the main direction of the fiber forms an angle α with the axial direction of the external pressure-resistant reinforcement layer, then:

[0064]

[0065] Where: is the strain increment in the longitudinal direction of the fiber, is the strain increment in the transverse direction of the fiber, Axial strain increment of the cross section of the continuous fiber composite external pressure reinforcement layer, Hoop strain increment of the cross section of continuous fiber composite external pressure reinforcement layer.

[0066] Step S6: Calculate the integral point stress increment based on the orthotropic stiffness matrix and the rotation axis formula And by comparing the maximum stress {σ max} i ;

[0067] First, the longitudinal and transverse stress increments of the fiber are calculated based on the orthotropic stiffness matrix:

[0068]

[0069] Where: is the stress increment in the longitudinal direction of the fiber, is the stress increment in the transverse direction of the fiber.

[0070] If the main direction of the fiber forms an angle α with the axial direction of the continuous fiber composite external pressure reinforcement layer, the axial stress increment and hoop stress increment of the cross section are:

[0071]

[0072] Calculate the fiber longitudinal stress σ1 and fiber transverse stress σ2 at the integration point, and determine the maximum stress {σ max} i .

[0073] Step S7: Determine the maximum stress at the integration point {σ max} i Whether the Hashin damage criterion is met; if the Hashin damage criterion is met, the stiffness reduction is performed on the stiffness matrix of the anti-external pressure reinforcement layer; if the Hashin damage criterion is not met, proceed to the next step.

[0074] Specifically, it is to judge whether the maximum stress at the integration point meets the following conditions:

[0075] When σ1≥0,

[0076] When σ1<0,

[0077] When σ2≥0,

[0078] When σ2<0,

[0079] If the maximum stress at the integration point meets any of the above conditions, it is considered that the fiber composite material has been damaged and failed, and the stiffness of the fiber composite material should be reduced:

[0080] when or When E1=E1·λ, E2=E2;

[0081] when or When E1=E1, E2=E2·λ;

[0082] Among them, λ is the stiffness reduction coefficient, which can be set according to different fiber materials and the range is: 0<λ<1.

[0083] Step S8: Establish a group of equilibrium equations based on the virtual work equation; according to the internal work being equal to the external work, the equilibrium equation can be obtained:

[0084]

[0085] in,

[0086]

[0087] Step S9: Use the Newton-Raphson method to iteratively solve the equations. Assuming that the pipeline circumferential displacement v and radial displacement w are both functions of θ, they can be approximately expressed using trigonometric series as follows:

[0088]

[0089] Substituting the above displacement function into the strain expression can calculate the strain increment. To load the pressure-resistant reinforcement layer, it is impossible to describe the process of the hydrostatic pressure gradually decreasing after the pressure-resistant reinforcement layer reaches its ultimate bearing capacity. Therefore, the pressure-resistant reinforcement layer is loaded by applying displacement increments. The hydrostatic pressure is also regarded as an unknown quantity, and the increment of the pipe volume V is specified. You can get 4N+1 about Then, the Newton-Raphson method is applied to iteratively solve the nonlinear algebraic equations.

[0090] Formula (8) includes the integral of the cross section of the compression reinforcement layer, which is solved by the numerical calculation method of Gaussian integral. The cross section of the compression reinforcement layer is divided into k and l Gaussian integral points in the circumferential direction and radial wall thickness direction, respectively, as follows: Figure 3 The number of integration points needs to be adjusted according to the different stress conditions of the pipeline and the severity of the initial geometric defects.

[0091] Step S10: Convergence test. Verify that the displacement values ​​have converged. Specifically, the change between two iterations of the displacement is checked. If the change is less than a set minimum value, the iterative calculation of this load substep is considered to have converged. If not, the displacement value calculated in the previous iteration is used as an estimate, and the calculation returns to step S4 until convergence is achieved.

[0092] Step S11: Update the equilibrium state, calculate the current external pressure P and the cross-sectional ellipticity Δ, and repeat steps S4 to S8 until the continuous external pressure-resistant reinforcement layer reaches buckling instability, and output the theoretical calculation results.

[0093] External pressure:

[0094] Cross-sectional ellipticity:

[0095] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A method for calculating the buckling instability pressure of a continuous fiber composite external pressure-resistant reinforcement layer, characterized in that: include: Step S1, measuring the geometric parameters of the continuous fiber composite external pressure resistant reinforcement layer of the deep-sea flexible pipe; Step S2: obtaining material characteristic parameters of the continuous fiber composite external pressure resistant reinforcement layer of the deep-sea flexible pipe; Step S3: constructing the motion equation of the continuous fiber composite external pressure resistant reinforcement layer according to the nonlinear ring theory; Step S4: Applying volume increment Calculate the displacement increment of the integration point Step S5: Based on the integral point displacement increment Calculate the strain increment at the integration point based on the equation of motion Step S6: Calculate the stress increment at the integration point based on the strain increment at the integration point And by comparing the maximum stress {σ max } i ; Step S7: Determine the maximum stress at the integration point {σ max } i Whether the Hashin damage criterion is satisfied; if the Hashin damage criterion is satisfied, stiffness reduction is performed on the stiffness matrix of the anti-external pressure reinforcement layer; if the Hashin damage criterion is not satisfied, proceed to step S8; Step S8: establishing a set of equilibrium equations based on the virtual work equation; Step S9, using the Newton-Raphson method to iteratively solve the equations; Step S10: Check whether the displacement value has converged. Check the change in displacement between two iterations. If the change is less than a set small value, it is considered that the iterative calculation of this load substep has converged. If it has not converged, use the displacement value calculated in the previous iteration as an estimate and return to step S4 for calculation until convergence. Step S11: Update the equilibrium state, calculate the current external pressure P and the cross-sectional ellipticity Δ, and repeat steps S4 to S8 until the continuous external pressure-resistant reinforcement layer reaches buckling instability, and output the theoretical calculation results.

2. The method for calculating the buckling instability pressure of the continuous fiber composite anti-external pressure reinforcement layer according to claim 1, characterized in that: The step S3 is specifically as follows: Step S31: According to the relationship between the material mechanical curvature and the axial strain and the cross-sectional elliptical deformation displacement relationship, the axial strain is obtained, that is: in, is the distance from any point on the deformed cross section to the geometric mid-plane, Step S32: Obtain the hoop strain according to the initial ellipticity Δ0, the hoop infinitesimal segment node displacement relationship, and the geometric relationship, namely: in, ε θ0 is the hoop strain caused by the initial radial displacement of the pipeline.

3. The method for calculating the buckling instability pressure of the continuous fiber composite anti-external pressure reinforcement layer according to claim 2, characterized in that: In step S5, if the main direction of the fiber forms an angle α with the axial direction of the external pressure-resistant reinforcement layer, then: in: is the strain increment in the longitudinal direction of the fiber, is the strain increment in the transverse direction of the fiber, Axial strain increment of the cross section of the continuous fiber composite external pressure reinforcement layer, Hoop strain increment of the cross section of continuous fiber composite external pressure reinforcement layer.

4. The method for calculating the buckling instability pressure of a continuous fiber composite external pressure-resistant reinforcement layer according to claim 3, characterized in that: The step S6 is specifically as follows: Step S61: Calculate the longitudinal and transverse stress increments of the fiber based on the orthotropic stiffness matrix: Where: is the stress increment in the longitudinal direction of the fiber, is the stress increment in the transverse direction of the fiber; Step S62: If the main direction of the fiber forms an angle α with the axial direction of the continuous fiber composite external pressure-resistant reinforcement layer, the axial stress increment and the hoop stress increment of the cross section are:

5. The method for calculating the buckling instability pressure of the continuous fiber composite anti-external pressure reinforcement layer according to claim 4, characterized in that: In step S8, based on the fact that the internal force work is equal to the external force work, the equilibrium equation is obtained: in, 6. The method for calculating the buckling instability pressure of the continuous fiber composite anti-external pressure reinforcement layer according to claim 5, characterized in that: The geometric parameters of the continuous fiber composite anti-external pressure reinforcement layer of the deep-sea flexible pipe were measured, including the outer diameter D, thickness t, fiber winding angle α and initial ellipticity Δ0 of the anti-external pressure reinforcement layer.

7. The method for calculating the buckling instability pressure of the continuous fiber composite anti-external pressure reinforcement layer according to claim 6, characterized in that: The material characteristic parameters of the continuous fiber composite anti-external pressure reinforcement layer of the deep-sea flexible pipe include: elastic modulus E1 in the longitudinal direction of the fiber, elastic modulus E2 in the transverse direction of the fiber, in-plane Poisson's ratio v 12 and v 21 , Fiber longitudinal tensile strength X T , fiber longitudinal compressive strength X C , fiber transverse tensile strength Y T And the fiber transverse compressive strength Y C .

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