Strain field reconstruction method and related equipment for large deformation of pipeline structure

Abstract

The application discloses a strain field reconstruction method for large deformation of a pipeline structure and related equipment, and belongs to the technical field of pipelines. The method comprises the following steps: obtaining structural attribute data of a target pipeline; determining the rotation angle values of each pipe axis arc segment in the target pipeline according to the structural attribute data; reconstructing the three-dimensional displacement field data of each pipe axis arc segment under the Euler-Bernoulli beam three-dimensional orthogonal coordinate system according to the rotation angle values of each pipe axis arc segment; and processing the three-dimensional displacement field data of each pipe axis arc segment under the Euler-Bernoulli beam three-dimensional orthogonal coordinate system by using the Green-Lagrange strain tensor to obtain the strain field data of each pipe axis arc segment. The application describes the relationship between the pipeline strain field and the pipeline displacement field under the large deformation of the pipeline structure by using the Green-Lagrange strain tensor, and accordingly, the pipeline strain field under the large deformation of the pipeline structure can be reconstructed, so that the reconstruction efficiency of the pipeline strain field under the large deformation of the pipeline structure is effectively improved.

Description

Technical Field

[0001] This application relates to the field of pipeline technology, and in particular to a strain field reconstruction method and related equipment for pipeline structures under large deformation conditions. Background Technology

[0002] The strain field of a pipeline describes the degree of local deformation of each point within the pipeline structure relative to its initial configuration under external loads, temperature changes, or prestress. In related technologies, the inverse finite element method (iFEM) is typically used to solve the pipeline strain field under large deformation conditions. However, the implementation of the inverse finite element method often relies on iterative processing, resulting in low efficiency in reconstructing the pipeline strain field under large deformation conditions. Summary of the Invention

[0003] The main objective of this application is to propose a strain field reconstruction method and related equipment for pipeline structures under large deformation. The aim is to describe the relationship between the pipeline strain field and the pipeline displacement field under large deformation by using the Green-Lagrange strain tensor. Based on this, the pipeline strain field under large deformation can be reconstructed, thereby effectively improving the reconstruction efficiency of the pipeline strain field under large deformation.

[0004] To achieve the above objectives, one aspect of this application proposes a strain field reconstruction method for large deformation of pipeline structures, the method comprising: Obtain the structural attribute data of the target pipeline; Based on the structural attribute data, determine the rotation angle value of each pipe axis arc segment in the target pipe; Based on the rotation angle values ​​of each of the said pipe axis arc segments, reconstruct the three-dimensional displacement field data of each of the said pipe axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system; Using the Green-Lagrange strain tensor, the three-dimensional displacement field data of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system are processed to obtain the strain field data of each of the tube axis arc segments.

[0005] In some embodiments, reconstructing the three-dimensional displacement field data of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system based on the rotation angle value of each of the tube axis arc segments includes: Based on the rotation angle values ​​of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system, determine the central angle value and chord length value of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system. Based on the central angle and chord length of each arc segment of the tube axis in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam, determine the three-dimensional displacement value of each arc segment of the tube axis in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam. Based on the three-dimensional displacement values ​​of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system, the three-dimensional displacement field data of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system are reconstructed.

[0006] In some embodiments, the three-dimensional displacement values ​​include Directional displacement value Directional displacement value and Directional displacement values; the three-dimensional displacement field data includes Directional displacement field data Directional displacement field data and Directional displacement field data; the reconstructing of the three-dimensional displacement field data of each of the pipe axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system based on the three-dimensional displacement values ​​of each pipe axis arc segment in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system includes: Based on the arc segments of each tube axis in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam Directional displacement value Direction coordinates Direction coordinates, around The rotation angle value of the direction, and the rotation around The rotation angle values ​​of the directions are reconstructed for each of the aforementioned tube axis arc segments in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam. Displacement field data; Based on the arc segments of each tube axis in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam Directional displacement values, reconstructed in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system for each of the aforementioned pipe axis arc segments. Displacement field data; Based on the arc segments of each tube axis in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam Directional displacement values, reconstructed in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system for each of the aforementioned pipe axis arc segments. Directional displacement field data.

[0007] In some embodiments, the process of using the Green-Lagrange strain tensor to process the three-dimensional displacement field data of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system to obtain the strain field data of each of the tube axis arc segments includes: Construct the Green-Lagrange strain function between the strain field data and the three-dimensional displacement field data; The three-dimensional displacement field data of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system are substituted into the Green-Lagrange strain function, and higher-order infinitesimal terms are ignored to obtain the strain field data of each of the tube axis arc segments.

[0008] In some embodiments, the Green-Lagrange strain function satisfies the following formula: ; in, This represents the Green-Lagrange strain function; express Displacement field data; express Displacement field data; express Displacement field data; express Direction coordinates.

[0009] In some embodiments, after substituting the three-dimensional displacement field data and ignoring higher-order infinitesimal terms, the Green-Lagrange strain function is transformed into the following formula: ; in, This represents the Green-Lagrange strain function after substituting the three-dimensional displacement field data and ignoring higher-order infinitesimal terms; express Directional displacement value; express Directional displacement value; express Directional displacement value; Indicates circling The rotation angle value of the direction; Indicates circling The rotation angle value of the direction; express Direction coordinates.

[0010] In some embodiments, the strain field data includes membrane strain field data, which satisfies the following formula: ; in, This represents the membrane strain field data; express Directional displacement value; express Directional displacement value; express Directional displacement value; express Direction coordinates.

[0011] In some embodiments, the strain field data includes bending strain field data, which satisfies the following formula: ; in, This represents the bending strain field data; Indicates circling The rotation angle value of the direction; Indicates circling The rotation angle value of the direction; express Direction coordinates.

[0012] To achieve the above objectives, another aspect of this application proposes a strain field reconstruction device for large deformation of pipeline structures, the device comprising: The acquisition module is used to acquire the structural attribute data of the target pipeline; The first processing module is used to determine the rotation angle value of each pipe axis arc segment in the target pipe based on the structural attribute data. The second processing module is used to reconstruct the three-dimensional displacement field data of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system based on the rotation angle value of each of the tube axis arc segments. The third processing module is used to process the three-dimensional displacement field data of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system using the Green-Lagrange strain tensor, so as to obtain the strain field data of each of the tube axis arc segments.

[0013] To achieve the above objectives, another aspect of this application provides a computer program product, including a computer program that, when executed by a processor, implements the strain field reconstruction method for large deformation of pipeline structures described above.

[0014] According to an embodiment of this application, a strain field reconstruction method and related equipment for pipeline structures under large deformation conditions are provided. The method involves acquiring structural attribute data of the target pipeline; determining the rotation angle values ​​of each pipe axis arc segment in the target pipeline based on the structural attribute data; reconstructing the three-dimensional displacement field data of each pipe axis arc segment in a three-dimensional orthogonal coordinate system of an Euler-Bernoulli beam based on the rotation angle values ​​of each pipe axis arc segment; and processing the three-dimensional displacement field data of each pipe axis arc segment in the three-dimensional orthogonal coordinate system of an Euler-Bernoulli beam using the Green-Lagrange strain tensor to obtain the strain field data of each pipe axis arc segment. According to the technical solution of this application, the relationship between the pipeline strain field and the pipeline displacement field under large deformation conditions is described by the Green-Lagrange strain tensor, thereby enabling the reconstruction of the pipeline strain field under large deformation conditions, effectively improving the reconstruction efficiency of the pipeline strain field under such conditions.

[0015] Other features and advantages of this application will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the application. The objectives and other advantages of this application may be realized and obtained by means of the structures particularly pointed out in the description, claims and drawings. Attached Figure Description

[0016] Figure 1 This is a flowchart of a strain field reconstruction method for large deformation of pipeline structures provided in this application; Figure 2 This is an example diagram of measuring actual curvature using a dual-sided strain sensor, as provided in this application. Figure 3 This is an example diagram of measuring actual curvature using a single-sided strain sensor, as provided in this application. Figure 4 This is an example diagram of the coordinate relationship of the tube unit provided in this application; Figure 5 This is an example diagram of the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam provided in this application; Figure 6 This is an example diagram of the differential geometric reconstruction curve within the infinitesimal arc segment provided in this application; Figure 7 This is a structural diagram of a strain field reconstruction device for large deformation of pipeline structures provided in this application. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit it. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with those of this application; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this application as detailed in the appended claims.

[0018] It is understood that the terms “first,” “second,” etc., used in this application may be used herein to describe various concepts, but unless otherwise stated, these concepts are not limited by these terms. These terms are only used to distinguish one concept from another. For example, without departing from the scope of the embodiments of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the words “if,” “when,” or “in response to a determination” as used herein may be interpreted as “when…” or “when…” or “in response to a determination.”

[0019] As used in this application, the terms "at least one", "multiple", "each", "any", etc., "at least one" includes one, two or more, "multiple" includes two or more, "each" refers to each of the corresponding multiples, and "any" refers to any one of the multiples.

[0020] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0021] The strain field of a pipeline is typically used to describe the degree of local deformation of each point within a pipeline structure relative to its initial configuration under external loads, temperature changes, or prestress. In related technologies, the inverse finite element method (IFEM) is commonly used to solve for the strain field of a pipeline under large deformation conditions. The IFEM is a reverse calculation method that infers the structural displacement and strain fields based on measured strain data. It does not require knowledge of external loads or material properties; the structural strain field can be reconstructed in real time solely through surface or internal strain measurements. However, the implementation of the IFEM often relies on iterative processing, and it is not suitable for purely rotating pipeline models, resulting in low efficiency in reconstructing the pipeline strain field under large deformation conditions.

[0022] In view of this, embodiments of this application provide a strain field reconstruction method and related equipment for large deformation of pipeline structures. This method describes the relationship between the pipeline strain field and the pipeline displacement field under large deformation of pipeline structures using the Green-Lagrange strain tensor. Based on this, the pipeline strain field under large deformation of pipeline structures can be reconstructed, thereby effectively improving the reconstruction efficiency of the pipeline strain field under large deformation of pipeline structures. It is applicable to strain field reconstruction scenarios of structures such as wind turbine tower pipelines or marine risers.

[0023] First, the implementation steps of a strain field reconstruction method for large deformation of pipeline structures provided in this application will be described in detail below with reference to the accompanying drawings.

[0024] This application provides a strain field reconstruction method for large deformation of pipeline structures, which can be applied to terminals, servers, or software running on either terminal or server. Terminals can be tablets, laptops, desktop computers, etc., but are not limited to these. Servers can be independent physical servers, server clusters or distributed systems composed of multiple physical servers, or cloud servers providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, content delivery networks (CDNs), and big data and artificial intelligence platforms. Furthermore, a server can be a node server in a blockchain network, but is not limited to these. Blockchain is a new application model of computer technologies such as distributed data storage, peer-to-peer transmission, consensus mechanisms, and encryption algorithms.

[0025] Reference Figure 1 , Figure 1 This is a flowchart of a strain field reconstruction method for large deformation of pipeline structures provided in this application. The method may include the following steps S101-S104.

[0026] S101, Obtain the structural attribute data of the target pipeline.

[0027] It should be noted that the target pipeline refers to the pipeline whose strain field is to be reconstructed. In this embodiment, the plane layer containing the pipeline axis is defined as the neutral layer, and the surface of the target pipeline is defined as the surface layer. The pipeline axis is divided into a sufficiently large number of infinitesimal arc segments, which are defined as pipeline axis arc segments, thus forming multiple pipeline axis arc segments. Accordingly, the structural property data of the target pipeline may include, but is not limited to, the interlayer distance between the surface layer and the neutral layer of each pipeline axis arc segment, and the strain value of each pipeline axis arc segment.

[0028] S102, Based on the structural attribute data, determine the rotation angle value of each pipe axis arc segment in the target pipeline.

[0029] In this step, firstly, the actual curvature value of each pipe axis arc segment is determined based on the interlayer distance between the surface layer and the neutral layer of the target pipe, as well as the strain value of each pipe axis arc segment; then, an error functional model between the actual curvature value and the rotation angle value is constructed; subsequently, the error functional model is solved based on the actual curvature value of each pipe axis arc segment to obtain the rotation angle value of each pipe axis arc segment.

[0030] S103, based on the rotation angle values ​​of each pipe axis arc segment, reconstruct the three-dimensional displacement field data of each pipe axis arc segment in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system.

[0031] In this step, a three-dimensional orthogonal coordinate system is established based on the Euler–Bernoulli beam, denoted as the Euler–Bernoulli beam three-dimensional orthogonal coordinate system. Based on the rotation angle values ​​of each pipe axis arc segment, the three-dimensional displacement field data of each pipe axis arc segment under the Euler–Bernoulli beam three-dimensional orthogonal coordinate system are reconstructed. This represents the pipe displacement field under large deformation conditions of the pipe structure, thus achieving the reconstruction processing of the pipe displacement field under large deformation conditions.

[0032] S104 uses the Green-Lagrange strain tensor to process the three-dimensional displacement field data of each pipe axis arc segment in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system to obtain the strain field data of each pipe axis arc segment.

[0033] It should be noted that the Green-Lagrange strain tensor is used to describe the relationship between the strain field and displacement field of a pipeline under large deformation conditions.

[0034] In this step, the relationship between the pipeline strain field and the pipeline displacement field under large deformation of the pipeline structure is described by the Green-Lagrange strain tensor. Based on this, combined with the three-dimensional displacement field data of each pipeline axis arc segment in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system, the strain field data of each pipeline axis arc segment is reconstructed, which represents the pipeline strain field under large deformation of the pipeline structure, thereby realizing the reconstruction processing of the pipeline strain field under large deformation of the pipeline structure.

[0035] Therefore, compared with the inverse finite element method which relies on iterative processing, the embodiments of this application describe the relationship between the pipeline strain field and the pipeline displacement field under large deformation of the pipeline structure using the Green-Lagrange strain tensor. Based on this, the pipeline strain field under large deformation of the pipeline structure can be reconstructed. This method does not require iterative processing and is applicable to pure rotating pipeline models, thereby effectively improving the reconstruction efficiency of the pipeline strain field under large deformation of the pipeline structure.

[0036] In some embodiments, step S103 above, reconstructing the three-dimensional displacement field data of each pipe axis arc segment in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system based on the rotation angle value of each pipe axis arc segment, may include: Based on the rotation angle values ​​of each pipe axis arc segment in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system, determine the central angle value and chord length value of each pipe axis arc segment in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system. Based on the central angle and chord length of each pipe axis arc segment in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system, determine the three-dimensional displacement value of each pipe axis arc segment in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system. Based on the three-dimensional displacement values ​​of each pipe axis arc segment in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam, the three-dimensional displacement field data of each pipe axis arc segment in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam are reconstructed.

[0037] In some implementations, the above-mentioned three-dimensional displacement values ​​may include Directional displacement value Directional displacement value and Displacement values; the above three-dimensional displacement field data may include directional displacement values; Directional displacement field data Directional displacement field data and Directional displacement field data; the above-mentioned reconstruction of the three-dimensional displacement field data of each pipe axis arc segment in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system, based on the three-dimensional displacement values ​​of each pipe axis arc segment in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system, may include: Based on the arc segments of each pipe axis in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam Directional displacement value Direction coordinates Direction coordinates, around The rotation angle value of the direction, and the rotation around The rotation angle values ​​of the direction are used to reconstruct the arc segments of each pipe axis in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam. Displacement field data; Based on the arc segments of each pipe axis in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam Directional displacement values, reconstructed in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam for each pipe axis arc segment. Displacement field data; Based on the arc segments of each pipe axis in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam Directional displacement values, reconstructed in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam for each pipe axis arc segment. Directional displacement field data.

[0038] In some embodiments, step S104 above, which involves processing the three-dimensional displacement field data of each pipe axis arc segment in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system using the Green-Lagrange strain tensor to obtain the strain field data of each pipe axis arc segment, may include: Construct the Green-Lagrange strain function between strain field data and three-dimensional displacement field data; The three-dimensional displacement field data of each tube axis arc segment in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam are substituted into the Green-Lagrange strain function, and higher-order infinitesimal terms are ignored to obtain the strain field data of each tube axis arc segment.

[0039] In some implementations, the Green-Lagrange strain function described above satisfies the following formula: ; in, Represents the Green-Lagrange strain function; express Displacement field data; express Displacement field data; express Displacement field data; express Direction coordinates.

[0040] In some implementations, after substituting the three-dimensional displacement field data and neglecting higher-order infinitesimal terms, the Green-Lagrange strain function is transformed into the following formula: ; in, This represents the Green-Lagrange strain function after substituting three-dimensional displacement field data and ignoring higher-order infinitesimal terms; express Directional displacement value; express Directional displacement value; express Directional displacement value; Indicates circling The rotation angle value of the direction; Indicates circling The rotation angle value of the direction; express Direction coordinates.

[0041] In some embodiments, the strain field data mentioned above includes membrane strain field data, which satisfies the following formula: ; in, Represents membrane strain field data; express Directional displacement value; express Directional displacement value; express Directional displacement value; express Direction coordinates.

[0042] In some embodiments, the strain field data mentioned above includes bending strain field data, which satisfies the following formula: ; in, Represents bending strain field data; Indicates circling The rotation angle value of the direction; Indicates circling The rotation angle value of the direction; express Direction coordinates.

[0043] The specific implementation process of each of the above steps will be explained in detail below.

[0044] 1) Calculation of rotation angle.

[0045] The rotation angle can be determined by a least-squares error functional objective function of the rotation angle of the tube structure nodes. This objective function consists of two key parameters: the actual curvature calculated from the measured strain. and the theoretical curvature derived from the rotation angle of the tube structure nodes. As shown in the following formula (1): (1); In equation (1), The rotation angle vector represents the node of the tube element; Let represent the objective function of the least squares error functional.

[0046] Planar tube model, such as Figure 2 As shown, Figure 2 In the image, FBG (Fiber Bragg Grating) indicates a fiber Bragg grating sensor, i.e., a strain sensor; the dashed line represents the tube axis. This represents the interlayer distance between the surface layer and the neutral layer. This represents the actual strain on the surface of the upper surface layer. This represents the actual strain on the lower surface layer. Indicates the length of the tube unit. The tube length is represented by this model, which represents a classic configuration in shape-sensing research and is compatible with various cross-sectional geometries, including rectangular, circular, and tubular shapes. When strain sensors are arranged continuously and symmetrically on the upper and lower surfaces of the tube, the actual surface strain is... With membrane strain and bending strain (curvature) The coupling relationship shown in formula (2) exists: , (2).

[0047] The actual curvature can be calculated from the strain on the upper and lower surfaces of the tube using equation (2), as shown in formula (3) below: (3).

[0048] Therefore, the actual curvature obtained through two-sided strain calculation does not contain membrane strain interference, resulting in a pure actual curvature. Optionally, for slender, linearly elastic tube structures, these structures primarily undergo bending deformation. Even for large deformations under elastic deformation, the plane section assumption based on Euler-Bernoulli beams still holds, and the strain and curvature on the same section maintain a linear relationship. This effectiveness stems from the geometric relationships derived from the strain. Furthermore, the deformation caused by membrane strain is negligible compared to bending deformation; therefore, the influence of membrane strain on the calculation of actual curvature can be ignored. Figure 3 As shown, the actual curvature can be obtained by measuring the strain on one side of the surface, as shown in the following formula (4): (4).

[0049] In the definition of differential geometry, the curvature of a curve is the rate of rotation of the tangent direction angle about a point on the curve with respect to the arc length, indicating the degree to which the curve deviates from a straight line, as shown in the following formula (5): (5); In equation (5), The rotation angle of the tube structure, This represents the arc length corresponding to the rotation angle.

[0050] For pipe structures, the pipe units can be divided into elements, by... The tube is discretized using continuous shape functions, and the rotational displacement field of the tube element is defined using Lagrange polynomials. The expression for the rotational displacement of the tube element is shown in the following formula (6): (6); In equation (6), The rotation angle vector representing the node of the tube element. This indicates the rotation angle at the middle node of the tube element. , These are the rotation angles at the left and right endpoints of the pipe unit, respectively. The shape function matrix derived from the second-order Lagrange interpolation polynomial is shown in the following formula (7): (7).

[0051] The coordinate relationship of the tube element is as follows Figure 4 As shown, Figure 4 middle , , It is the length of the tube unit. It is the midpoint of the element. When the node to be found is at the left end of the element, Take -1 when the node in question is on the right side of the element. Take 1.

[0052] For slender tubes where bending deformation is dominant, the deformation of the tube length can be approximately ignored. In this case, the arc length corresponding to the rotation angle after tube deformation is... It can be approximated as the pipe length The variables in equation (5) The variables in equation (6) Equivalently, the theoretical curvature expression for any cross section can be obtained through equations (5)-(6), as shown in equation (8) below: (8); In equation (8), By shape function The derivation yields the following formula (9): (9); The above theoretical derivation process yields the precise expression for the theoretical curvature of any point inside the tube unit, determined by the node rotation angle. Therefore, according to equation (1), the least squares error functional objective function of the rotation angle can be expressed as the difference between the theoretical curvature and the actual curvature at all measured points inside the unit. This constitutes the Euclidean norm of the unit's least squares error functional, i.e., the error functional model, as shown in the following formula (10): (10); In equation (10), It is the length of the tube unit; This refers to the number of measurement points within the unit. This indicates the location of the measuring point.

[0053] Substituting equation (8) into equation (10), we obtain the quadratic expression of the error functional model, as shown in equations (11)-(13) below: (11); (12); (13).

[0054] In equations (11)-(13), The pseudo-stiffness matrix of the element is related to the position of the measuring point. The relevant functions are shown in equation (12); For the element pseudo-load vector, given the specific curvature The decision is as shown in equation (13); It is a constant.

[0055] Let the error functional model be paired with The variational equation can be obtained by taking the minimum value, as shown in formula (14) below: (14).

[0056] By sharing the boundary conditions of the connected nodes and the continuity of all elements, the pseudo-stiffness matrix and pseudo-load vector of the elements in equation (14) can be assembled into pseudo-stiffness and load vector. The stiffness matrix block and load vector corresponding to the shared node inside the element are superimposed and finally merged into the overall pseudo-stiffness matrix and pseudo-load vector, resulting in the global rotation angle equation without considering the overall constraint boundary conditions, as shown in the following equation (15): (15); In equation (15), Represents the global pseudo-stiffness matrix. It is a global pseudo-load vector. It is the rotation angle vector of all global unit nodes.

[0057] However, the global pseudo-stiffness matrix at this time It is a singular matrix that requires global boundary conditions to become a positive definite matrix, thereby obtaining a unique global node rotation angle vector. Boundary conditions can be applied based on the actual structure. For example, for a cantilever tube, the boundary conditions require the rotation angle of the fixed end. Based on the application of global boundary conditions, the final global rotation angle equation can be obtained, as shown in formula (16) below: (16).

[0058] In practical applications, the rotation angle of each unit node can be obtained through equation (16), and the rotation angle at each point along the pipe axis can be obtained using the shape function, i.e., equation (7). Then, based on the curve reconstruction algorithm, the displacement field of the pipe can be reconstructed.

[0059] 2) Pipe displacement field reconstruction based on rotation angle.

[0060] A three-dimensional orthogonal coordinate system is established based on the Euler-Bernoulli beam, defined as the Euler-Bernoulli beam three-dimensional orthogonal coordinate system, such as... Figure 5 As shown, this coordinate system includes three directions: along the tube axis. Direction, perpendicular to the pipe axis direction and Direction. To reconstruct the strain field of the pipeline, it is necessary to first reconstruct the direction in this coordinate system. direction, direction and The pipe displacement field in the direction of bending. In the assumption of an Euler-Bernoulli beam, the bending plane of this coordinate system... As a cross-section of the tube, its rigid rotation is determined by bending and torsion, and the spatial deformation of the tube axis is only related to the bending plane of this coordinate system. and Correlation. Therefore, in the reconstruction of the pipeline displacement field, it is necessary to consider the bending plane. Displacement field reconstruction is performed to obtain Displacement values ​​in the direction and Displacement values ​​in the direction, and also for the curved plane. Displacement field reconstruction is performed to obtain Displacement values ​​in the direction and The displacement value in the direction, then through two The displacement values ​​in the direction are integrated and processed to determine the direction. The final displacement value in the direction is obtained, thus yielding the coordinate system. direction, direction and The displacement value in the direction, i.e. the three-dimensional displacement value.

[0061] The following will use curved planes The process of displacement field reconstruction is illustrated using an example.

[0062] First, the pipe axis is divided into a sufficiently large number of infinitesimal arc segments, i.e., pipe axis arc segments. Then, any one of these infinitesimal arc segments is selected. ,like Figure 6 As shown, and These are the two endpoints of the infinitesimal arc segment, point The coordinates are ,point The coordinates are ; For point The tangent vector at that point, For point Tangent vector at point; For point Tangent vector at point and The included angle of the axis, For point Tangent vector at point and The included angle of the axis can be obtained by the rotation angle of the element node shown in equation (16) and the shape function shown in formula (7); For point Curvature at that point; For point Curvature at that point; It is a infinitesimal arc segment The corresponding chord length; It is a infinitesimal arc segment The corresponding central angle; For point and points Between Axis coordinate difference For point and points Between The difference in axis coordinates. Since the infinitesimal arc segment is short enough, it can be considered as a point. radius of curvature at point The radii of curvature at each point are approximately equal, therefore a point can be used. curvature at Instead of the curvature on this infinitesimal arc segment, It is the radius of the arc segment.

[0063] Then, the central angle can be obtained through geometric relationships. chord length , Axis coordinate difference and Axis coordinate difference As shown in the following formulas (17)-(20): (17); (18); (19); (20).

[0064] Due to the continuity of the deformation curve, the coordinates of the pipe's starting point and the rotation angle are used to deduce the recursive relationship points. coordinates of Available points coordinates of The following formulas (21)-(22) are obtained through recursion: (twenty one); (twenty two).

[0065] The coordinates of the endpoints of each pipe axis can be obtained using equations (21)-(22). For slender pipes, large deformations occur within the elastic deformation range, and the plane section assumption still holds. Based on the plane section assumption, the pipe section (bending plane) The displacement of any point on the pipe axis can be obtained from the displacement field of the pipe axis and the corresponding cross-sectional thickness and rotation angle, as shown in the following formulas (23)-(24): (twenty three); (twenty four); In equations (23)-(24), Point of Directional displacement value; Point of Directional displacement value; Indicating the axis of the tube Directional displacement value; Indicating the axis of the tube Directional displacement value; Let be the rotation angle. From this, we can determine the position of any point on the curved plane. In Directional displacement value and Directional displacement value.

[0066] It is worth noting that, in reconstructing the pipeline displacement field in this embodiment, for slender elastic pipes dominated by bending deformation, the influence of membrane strain on curvature calculation can be ignored. The curvature can be directly approximated by unilateral strain. Then, a least-squares error functional about the rotation angle is constructed using the theoretical curvature and the actual curvature, and the rotation displacement is obtained by solving for it. Based on this, the pipeline displacement field reconstruction is achieved. Theoretical analysis and numerical experiments show that the curvature error caused by membrane strain is effectively smoothed in this embodiment, and its impact on the final displacement is far less than its direct impact on the curvature itself.

[0067] It should be understood that, due to the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam... direction and The directions are all lateral, therefore for curved planes The displacement field reconstruction process is similar to that described above for curved planes. The displacement field reconstruction process is similar; simply reconstruct the above... Direction replaced with By determining the direction and performing the same calculations, any point on the curved plane can be obtained. In Directional displacement value and Directional displacement value. This is obtained through the above processing. There are two directional displacement values, therefore these two need to be... The directional displacement values ​​are integrated into the final value. Directional displacement value. The method of integration is not specifically limited; for example, it could be combining two... The mean value of the directional displacement is determined as the final value. The directional displacement value, for example, could be any one of the following. The directional displacement value is used as the final Directional displacement value, but not limited to this.

[0068] To obtain any point Directional displacement value Directional displacement value and After determining the directional displacement value, it is necessary to further determine the pipe displacement field in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system, thereby obtaining the displacement field at any point in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system. Directional displacement field data Directional displacement field data and The directional displacement field data, i.e., the three-dimensional displacement field data, is shown in the following formula (25): , , (25); In equation (25), Point of Displacement field data; Point of Displacement field data; Point of Displacement field data; Point of Directional displacement value; Point of Directional displacement value; Point of Directional displacement value; Indicates the pipe axis is wound around The rotation angle of the direction, i.e., the point The tangent vector in the curved plane Inner relative The rotation angle of the shaft; Indicates the pipe axis is wound around The rotation angle of the direction, i.e., the point The tangent vector in the curved plane Inner relative The rotation angle of the axis.

[0069] It should be understood that in practical applications, after discretizing the target pipeline into multiple pipe axis arc segments, the three-dimensional displacement values ​​of the endpoints of each pipe axis arc segment are first determined through the above process, and then the three-dimensional displacement field data of the endpoints of each pipe axis arc segment are determined, thereby realizing the reconstruction of the pipeline displacement field.

[0070] 3) Pipe strain field reconstruction based on pipe displacement field.

[0071] When a pipeline structure undergoes large deformation, the relationship between the pipeline strain field and the pipeline displacement field is no longer linear. To address this, this embodiment uses the Green-Lagrange strain tensor to describe the relationship between the pipeline strain field and the pipeline displacement field, which includes both linear and nonlinear terms, as shown in the following formula (26): (26); In equation (26), This represents the Green-Lagrange strain tensor, i.e., the Green-Lagrange strain function.

[0072] Substituting the pipe displacement field shown in equation (25) into equation (26) and ignoring higher-order infinitesimal terms, we can obtain the strain expression of the structure under geometric nonlinearity, i.e., the pipe strain field, as shown in the following formula (27): (27); In equation (27), This represents the Green-Lagrange strain tensor after substituting the pipe displacement field and neglecting higher-order infinitesimal terms.

[0073] Decoupling the pipe strain field shown in equation (27) yields the membrane strain field shown in equation (28) and the bending strain field shown in equation (29): (28); In equation (28), This represents the membrane strain field, which includes both linear and nonlinear terms.

[0074] (29); In equation (29), This represents the bending strain field.

[0075] Therefore, compared with the inverse finite element method which relies on iterative processing, the embodiments of this application do not require iterative processing. The relationship between the pipeline strain field and the pipeline displacement field under large deformation of the pipeline structure is described by the Green-Lagrange strain tensor. Based on this, the pipeline strain field under large deformation of the pipeline structure can be reconstructed, thereby effectively improving the reconstruction efficiency of the pipeline strain field under large deformation of the pipeline structure.

[0076] In addition, refer to Figure 7 This application also provides a strain field reconstruction device for large deformation of pipeline structures, which may include: Module 201 is used to acquire the structural attribute data of the target pipeline; The first processing module 202 is used to determine the rotation angle value of each pipe axis arc segment in the target pipe based on the structural attribute data. The second processing module 203 is used to reconstruct the three-dimensional displacement field data of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system based on the rotation angle value of each of the tube axis arc segments. The third processing module 204 is used to process the three-dimensional displacement field data of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system using the Green-Lagrange strain tensor to obtain the strain field data of each of the tube axis arc segments.

[0077] The content of the above method embodiments is applicable to the device embodiments. The specific functions implemented by the device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0078] Finally, this application also provides a computer program product, including a computer program that, when executed by a processor, implements the strain field reconstruction method described above for large deformation of pipeline structures.

[0079] The content of the above method embodiments is applicable to the embodiments of this program product. The specific functions implemented by the embodiments of this program product are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0080] The embodiments described in this application are for the purpose of more clearly illustrating the technical solutions of the embodiments of this application, and do not constitute a limitation on the technical solutions provided by the embodiments of this application. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this application are also applicable to similar technical problems.

[0081] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this application, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0082] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0083] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0084] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0085] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0086] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0087] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0088] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0089] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0090] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A strain field reconstruction method for large deformation of pipeline structures, characterized in that, The method includes: Obtain the structural attribute data of the target pipeline; Based on the structural attribute data, determine the rotation angle value of each pipe axis arc segment in the target pipe; Based on the rotation angle values ​​of each of the said pipe axis arc segments, reconstruct the three-dimensional displacement field data of each of the said pipe axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system; Using the Green-Lagrange strain tensor, the three-dimensional displacement field data of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system are processed to obtain the strain field data of each of the tube axis arc segments.

2. The method according to claim 1, characterized in that, The process of reconstructing the three-dimensional displacement field data of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system based on the rotation angle values ​​of each of the tube axis arc segments includes: Based on the rotation angle values ​​of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system, determine the central angle value and chord length value of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system. Based on the central angle and chord length of each arc segment of the tube axis in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system, determine the three-dimensional displacement value of each arc segment of the tube axis in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system. Based on the three-dimensional displacement values ​​of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system, the three-dimensional displacement field data of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system are reconstructed.

3. The method according to claim 2, characterized in that, The three-dimensional displacement values ​​include Directional displacement value Directional displacement value and Directional displacement values; the three-dimensional displacement field data includes Directional displacement field data Directional displacement field data and Displacement field data; The process of reconstructing the three-dimensional displacement field data of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system based on the three-dimensional displacement values ​​of each tube axis arc segment in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system includes: Based on the arc segments of each tube axis in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam Directional displacement value Direction coordinates Direction coordinates, around The rotation angle value of the direction, and the rotation around The rotation angle values ​​of the directions are reconstructed for each of the aforementioned tube axis arc segments in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam. Displacement field data; Based on the arc segments of each tube axis in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam Directional displacement values, reconstructed in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system for each of the aforementioned pipe axis arc segments. Displacement field data; Based on the arc segments of each tube axis in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam Directional displacement values, reconstructed in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system for each of the aforementioned pipe axis arc segments. Directional displacement field data.

4. The method according to claim 1, characterized in that, The process utilizes the Green-Lagrange strain tensor to process the three-dimensional displacement field data of each arc segment of the tube axis in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam, obtaining the strain field data of each arc segment of the tube axis, including: Construct the Green-Lagrange strain function between the strain field data and the three-dimensional displacement field data; The three-dimensional displacement field data of each of the tube axis arc segments in the three-dimensional orthogonal coordinate system of the Euler-Bernoulli beam are substituted into the Green-Lagrange strain function, and higher-order infinitesimal terms are ignored to obtain the strain field data of each of the tube axis arc segments.

5. The method according to claim 4, characterized in that, The Green-Lagrange strain function satisfies the following formula: ； in, This represents the Green-Lagrange strain function; express Displacement field data; express Displacement field data; express Displacement field data; express Direction coordinates.

6. The method according to claim 4, characterized in that, After substituting the three-dimensional displacement field data and ignoring higher-order infinitesimal terms, the Green-Lagrange strain function is transformed into the following formula: ； in, This represents the Green-Lagrange strain function after substituting the three-dimensional displacement field data and ignoring higher-order infinitesimal terms; express Directional displacement value; express Directional displacement value; express Directional displacement value; Indicates circling The rotation angle value of the direction; Indicates circling The rotation angle value of the direction; express Direction coordinates.

7. The method according to claim 4, characterized in that, The strain field data includes membrane strain field data, which satisfies the following formula: ； in, This represents the membrane strain field data; express Directional displacement value; express Directional displacement value; express Directional displacement value; express Direction coordinates.

8. The method according to claim 4, characterized in that, The strain field data includes bending strain field data, which satisfies the following formula: ； in, This represents the bending strain field data; Indicates circling The rotation angle value of the direction; Indicates circling The rotation angle value of the direction; express Direction coordinates.

9. A strain field reconstruction device for large deformation of pipeline structures, characterized in that, The device includes: The acquisition module is used to acquire the structural attribute data of the target pipeline; The first processing module is used to determine the rotation angle value of each pipe axis arc segment in the target pipe based on the structural attribute data. The second processing module is used to reconstruct the three-dimensional displacement field data of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system based on the rotation angle value of each of the tube axis arc segments. The third processing module is used to process the three-dimensional displacement field data of each of the tube axis arc segments in the Euler-Bernoulli beam three-dimensional orthogonal coordinate system using the Green-Lagrange strain tensor, so as to obtain the strain field data of each of the tube axis arc segments.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the strain field reconstruction method for large deformation of pipeline structures as described in any one of claims 1 to 8.

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