A method and apparatus for calculating the mechanical properties of pipes with irregular pipe sections.

Abstract

This invention provides a method and apparatus for calculating the mechanical properties of pipelines with irregularly shaped pipe segments. The method includes: generating a pipeline beam model composed of multiple connected pipeline beam elements based on the parameter information of each component in the pipeline; obtaining the mesh generation information of the irregularly shaped pipe segment to be analyzed in detail, as well as its node information in the pipeline beam model; generating a mesh model of the irregularly shaped pipe segment formed by splicing multiple shell elements; replacing the corresponding pipeline beam elements in the pipeline beam model with the mesh model of the irregularly shaped pipe segment to form a hybrid model; calculating the material density of the irregularly shaped pipe segment and replacing the linear density in the parameter information of the irregularly shaped pipe segment to form updated parameter information of the irregularly shaped pipe segment; performing finite element analysis on the hybrid model to obtain the displacement of each node in the hybrid model; and then calculating the stress of the pipeline beam elements and the target shell component respectively. This invention can complete the calculation and evaluation of pipelines and irregularly shaped shell components in one step, greatly improving the efficiency and accuracy of pipeline design.

Description

Technical Field

[0001] This invention relates to the field of pipeline design technology, and specifically to a method and apparatus for calculating the mechanical properties of pipelines with irregularly shaped pipe sections. Background Technology

[0002] Current piping calculation software typically uses one-dimensional pipe beam elements for model calculations, including straight and curved pipe beam elements, all of which are line elements. Furthermore, piping and equipment calculations are usually performed separately: first, the piping calculation is performed to obtain the thrust exerted by the pipe on the equipment, then load combination calculations are performed, and finally, the combined loads are used to perform stress analysis and evaluation on the equipment. Some programs can use shell elements for calculating special components. However, the methods for creating shell element components are quite complex. Some require inputting node coordinates node by node and providing a detailed description of each shell element. Others require using a separate modeling module to create the shell element model, and then the main program converts this shell element component into a stiffness matrix, which is then input into the piping model for calculation. In this calculation, the shell element model only provides the displacement and internal forces at the two connection points. After obtaining the piping solution, the forces on the component are then applied to the equipment for separate calculation of the shell element component. Therefore, the inability of existing piping calculation software to easily create shell element components is a major technical problem.

[0003] The method of directly placing shell element component models into piping problems is theoretically sound. Most common finite element programs can do this, but the problem lies in extremely low efficiency. This includes issues such as modeling efficiency, connection techniques between pipes and shell components, compliance with specifications during the process, and implementation of specifications during evaluation. These problems are why general-purpose finite element software cannot meet the needs of engineering design calculation and analysis applications. The technologies involved include: user interaction, or the definition of piping description methods, piping program calculations including support requirements for standard constraints, calculation methods for specification requirements and the correspondence between pipe loads, modeling methods for pipe components, especially irregularly shaped pipes, and the correspondence between pipe elements and shell elements. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to address the above-mentioned deficiencies in the prior art by providing a pipeline mechanics calculation method and device that can complete the calculation and evaluation of pipelines and irregular pipe shell components in one go, thereby greatly improving the efficiency of pipeline design.

[0005] The technical solution adopted to solve the technical problem of this invention is:

[0006] This invention provides a method for calculating the mechanical properties of a pipeline with irregularly shaped pipe sections, comprising:

[0007] Based on the parameter information of each component in the pipeline, a pipeline beam model composed of multiple pipeline beam elements is generated, along with the node information of each pipeline beam element. There is a one-to-one correspondence between components and pipeline beam elements.

[0008] Obtain the mesh generation information of the irregular pipe segment requiring detailed analysis, as well as its node information in the pipe beam model. Generate a mesh model of the irregular pipe segment formed by splicing multiple shell elements, and the mesh node information in the mesh model.

[0009] The corresponding pipe beam elements in the pipe beam model are replaced with the mesh model of the irregular pipe segment to form a hybrid model.

[0010] Calculate the material density of the irregular pipe segment and replace the linear density in the parameter information of the irregular pipe segment to generate updated parameter information for the irregular pipe segment.

[0011] Based on the operating conditions of the pipeline to be calculated and the parameter information of each component in the pipeline, finite element analysis is performed on the hybrid model to obtain the displacement of each node in the hybrid model. Based on the node displacements of the pipeline beam elements, the nodal internal forces of the pipeline beam elements are calculated. Based on the mesh node displacements of the mesh model of the irregular pipe segment, the stress of each shell element is calculated.

[0012] Calculate the stress of the pipe beam element based on the nodal internal forces of the pipe beam element.

[0013] Optionally, the irregular pipe section includes a bend.

[0014] Calculating the material density of the bend includes:

[0015] Based on the linear density w of the bend a Determine the theoretical material density w of the bend. a ′, its calculation formula is: w a ′=w a / g a / t a Among them, after the bend is segmented circumferentially, the end face circle forms N arc segments, g a Let g be the length of the arc. a =πD a / N,t a D represents the wall thickness of the bend. a The diameter of the bend is [the diameter of the pipe].

[0016] Calculate the circumferential reduced density coefficient fac of the bend based on the number of circumferential segments. a Its calculation formula is: fac a =g a / g a ′, where g a′ represents the length of the broken line segment corresponding to the arc after the bend is segmented circumferentially, and g is the length of the broken line segment. a ′=2D a ×sin(180 / N),

[0017] Calculate the axial reduced density coefficient fac of the bend based on the number of axial segments. a After axial segmentation of the bend, the bend forms n bend segments. Let L be the length of the line connecting the center points of the beginning and end faces of each bend segment, where L = 2R × sin(β / 2n), R is the bending radius of the bend, β is the turning angle of the bend, and the circumference of the ellipse containing the axial center point of each bend segment is l, where the major axis length of the ellipse is a = r, the minor axis length is b = r × cos(β / 2n), and the axial reduced density coefficient is fac. a The formula for calculating ′ is: fac a ′=s / (n×L×l), where s is the surface area of ​​the bend.

[0018] Then calculate the material density w of the bend according to the following formula. a ":

[0019] w a "=w a ′×fac a ×fac a ′.

[0020] Optionally, the irregularly shaped pipe section includes a tee pipe.

[0021] Calculating the material density of the tee pipe specifically includes:

[0022] Based on the linear density w of the main pipe or branch pipe b Determine the theoretical material density w of the main pipe or branch pipe. b ′, its calculation formula is: w b ′=w b / g b / t b Among them, after the main pipe or branch pipe is segmented circumferentially, the end face circle forms multiple arc segments, g b Let t be the length of the arc. b For the wall thickness of the main pipe or branch pipe,

[0023] Calculate the area conversion factor fac for the main or branch pipe based on the area before and after the replacement model. b Its calculation formula is: fac b =A / A′, where,

[0024] A represents the area calculated before replacing the main or branch pipe model, without considering any missing or extra area, where A = π × D. b ×L bD is the diameter of the main or branch pipe, L b It is the length of the line connecting the center of the end circle of the main pipe or branch pipe to the intersection point of the central axes of the three pipes in the tee.

[0025] A′ is the area calculated after replacing the main pipe or branch pipe model, taking into account the missing or extra area. Specifically, A′ is the sum of the shell element areas of the main pipe or branch pipe calculated based on the mesh node information of the main pipe or branch pipe in the mesh model.

[0026] Then calculate the material density of the main pipe or branch pipe according to the following formula:

[0027] w b "=w b ′×fac b .

[0028] Optionally, the irregularly shaped pipe section includes a tapered pipe.

[0029] Calculating the material density of the tapered tube specifically includes:

[0030] Calculate the weight of the tapered tube W = w c ×L c ,

[0031] Based on the average wall thickness of the tapered tube, the calculation formula is t. c = (T+t) / 2, where T is the wall thickness of the large end of the tapered tube and t is the wall thickness of the small end of the tapered tube.

[0032] The formula for calculating the surface area of ​​the tapered tube after meshing is as follows:

[0033] Among them, R c r is the radius of the large end of the tapered tube. c L is the radius of the small end of the tapered tube. c N is the length of the tapered tube. c The number of circumferential segments in the tapered tube.

[0034] Based on the average wall thickness of the tapered tube and the surface area of ​​the tapered tube after meshing, calculate the volume V = A of the tapered tube. c ×t c ,

[0035] Then calculate the material density w of the tapered tube according to the following formula. c ′:

[0036] w c = W / V.

[0037] Optionally, the nodes of the pipe beam elements at the connection between the mesh model of the irregular pipe segment and the pipe beam element are designated as master nodes, and the nodes of the mesh model of the irregular pipe segment corresponding to the master nodes at the connection between the mesh model of the irregular pipe segment and the pipe beam element are designated as slave nodes.

[0038] Finite element analysis was performed on the hybrid model to obtain the displacements of each node, including: at the connection between the mesh model of the irregular pipe segment and the pipe beam element, only the displacements of the main nodes were calculated.

[0039] The calculation of stress in each shell element based on the mesh node displacements of the irregular pipe segment mesh model specifically includes:

[0040] Based on the displacement of the master node, calculate the displacement of each slave node corresponding to the master node.

[0041] The displacements of each slave node, along with the displacements of other mesh nodes in the mesh model of the irregular pipe segment obtained from the finite element calculation, constitute the mesh node displacements of the mesh model of the irregular pipe segment.

[0042] The stress of each shell element is calculated based on the mesh node displacements of the mesh model of the irregular pipe segment.

[0043] Optionally, before calculating the displacements of each slave node corresponding to the master node based on the displacement of the master node, the method further includes: determining whether the operating condition is a non-temperature operating condition or a temperature operating condition.

[0044] If the operating condition is determined to be non-temperature-related, the displacement of each slave node corresponding to the master node is calculated using the following formula based on the displacement of the master node:

[0045] d′=d×a

[0046] Where d is the displacement of the master node, d′ is the displacement of the slave node corresponding to the master node, and a is the transformation matrix that converts the displacement of the master node to the displacement of the slave node.

[0047] If the operating condition is determined to be a temperature-related condition, the displacement of each slave node corresponding to the master node is calculated using the following formula based on the displacement of the master node:

[0048] d′=d×(a×(1+alf))

[0049] Where alf is the coefficient of thermal expansion of the pipe material.

[0050] The present invention also provides a pipe mechanics calculation device with irregularly shaped pipe sections, comprising:

[0051] The pipe beam generation module is used to generate a pipe beam model composed of multiple pipe beam elements connected together, based on the parameter information of each component in the pipe, as well as the node information of each pipe beam element. There is a one-to-one correspondence between components and pipe beam elements.

[0052] The shell generation module is used to obtain the mesh generation information of the irregular pipe segment that needs to be analyzed in detail, as well as its node information in the pipe beam model, and generate a mesh model of the irregular pipe segment formed by splicing multiple shell elements, along with the mesh node information in the mesh model.

[0053] The replacement module is used to replace the pipe beam elements at corresponding positions in the pipe beam model with the mesh model of the irregular pipe segment to form a hybrid model.

[0054] The shell parameter generation module is used to calculate the material density of the irregular pipe segment and replace the linear density in the parameter information of the irregular pipe segment to generate updated parameter information for the irregular pipe segment.

[0055] The finite element method (FEM) module is used to perform FEM calculations on the hybrid model based on the operating conditions of the pipeline and the parameter information of each component in the pipeline. This yields the displacements of each node in the hybrid model. Based on the node displacements of the pipeline beam elements, the module calculates the nodal internal forces of the pipeline beam elements. Furthermore, based on the mesh node displacements of the irregularly shaped pipe segment mesh model, the module calculates the stresses of each shell element.

[0056] The stress calculation module calculates the stress of the pipe beam element based on the nodal internal forces of the pipe beam element.

[0057] Optionally, it also includes an interface module for receiving the operating condition information of the pipeline to be calculated and the parameter information of each component and transmitting them to the pipeline beam generation module and the finite element calculation module, and also transmitting the parameter information of the irregular pipe section to the shell generation module and the shell parameter formation module respectively.

[0058] It is also used to receive the numbering information and mesh division information of irregular pipe segments and transmit them to the shell generation module, and to transmit the numbering information of irregular pipe segments to the shell parameter forming module.

[0059] Optionally, the irregular pipe section includes a bend.

[0060] The shell parameter forming module calculates the material density of the bend, specifically including:

[0061] Based on the linear density w of the bend a Determine the theoretical material density w of the bend. a ′, its calculation formula is: w a ′=w a / g a / t a Among them, after the bend is segmented circumferentially, the end face circle forms N arc segments, g a Let g be the length of the arc. a =πD a / N,t a D represents the wall thickness of the bend.a The diameter of the bend is [the diameter of the pipe].

[0062] Calculate the circumferential reduced density coefficient fac of the bend based on the number of circumferential segments. a Its calculation formula is: fac a =g a / g a ′, where g a ′ represents the length of the broken line segment corresponding to the arc after the bend is segmented circumferentially, and g is the length of the broken line segment. a ′=2D a ×sin(180 / N),

[0063] Calculate the axial reduced density coefficient fac of the bend based on the number of axial segments. a After axial segmentation of the bend, the bend forms n bend segments. Let L be the length of the line connecting the center points of the beginning and end faces of each bend segment, where L = 2R × sin(β / 2n), R is the bending radius of the bend, β is the turning angle of the bend, and the circumference of the ellipse containing the axial center point of each bend segment is l, where the major axis length of the ellipse is a = r, the minor axis length is b = r × cos(β / 2n), and the axial reduced density coefficient is fac. a The formula for calculating ′ is: fac a ′=s / (n×L×l), where s is the surface area of ​​the bend.

[0064] Then calculate the material density w of the bend according to the following formula. a ":

[0065] w a "=w a ′×fac a ×fac a ′.

[0066] Optionally, the irregularly shaped pipe section includes a tee pipe.

[0067] The shell parameter forming module is also electrically connected to the shell generation module, and it calculates the material density of the tee pipe, specifically including:

[0068] Based on the linear density w of the main pipe or branch pipe b Determine the theoretical material density w of the main pipe or branch pipe. b ′, its calculation formula is: w b ′=w b / g b / t b Among them, after the main pipe or branch pipe is segmented circumferentially, the end face circle forms multiple arc segments, g b Let t be the length of the arc. b For the wall thickness of the main pipe or branch pipe,

[0069] Calculate the area conversion factor fac for the main or branch pipe based on the area before and after the replacement model. b Its calculation formula is: fac b =A / A′, where,

[0070] A represents the area calculated before replacing the main or branch pipe model, without considering any missing or extra area, where A = π × D. b ×L b D is the diameter of the main or branch pipe, L b It is the length of the line connecting the center of the end circle of the main pipe or branch pipe to the intersection point of the central axes of the three pipes in the tee.

[0071] A′ is the area calculated after replacing the main pipe or branch pipe model, taking into account the missing or extra area. Specifically, A′ is the sum of the shell element areas of the main pipe or branch pipe calculated based on the mesh node information of the main pipe or branch pipe in the mesh model.

[0072] Then calculate the material density of the main pipe or branch pipe according to the following formula:

[0073] w b "=w b ′×fac b .

[0074] Optionally, the irregularly shaped pipe section includes a tapered pipe.

[0075] The shell parameter forming module is also electrically connected to the shell generation module, and it calculates the material density of the tapered tube, specifically including:

[0076] Calculate the weight of the tapered tube W = w c ×L c ,

[0077] Based on the average wall thickness of the tapered tube, the calculation formula is t. c = (T+t) / 2, where T is the wall thickness of the large end of the tapered tube and t is the wall thickness of the small end of the tapered tube.

[0078] The formula for calculating the surface area of ​​the tapered tube after meshing is as follows:

[0079] Among them, R c r is the radius of the large end of the tapered tube. c L is the radius of the small end of the tapered tube. c N is the length of the tapered tube. c The number of circumferential segments in the tapered tube.

[0080] Based on the average wall thickness of the tapered tube and the surface area of ​​the tapered tube after meshing, calculate the volume V = A of the tapered tube. c ×t c ,

[0081] Then calculate the material density w of the tapered tube according to the following formula. c ′:

[0082] w c = W / V.

[0083] Optionally, the shell parameter forming module includes a material density calculation module and a parameter updating module.

[0084] The material density calculation module is electrically connected to the interface module and is used to calculate the material density of the irregular pipe section based on its parameter information.

[0085] The parameter update module is electrically connected to the material density calculation module and is used to replace the linear density in the parameter information of the irregular pipe segment with the material density of the irregular pipe segment to form the updated parameter information of the irregular pipe segment.

[0086] Optionally, the nodes of the pipe beam elements at the connection between the mesh model of the irregular pipe segment and the pipe beam element are designated as master nodes, and the nodes of the mesh model of the irregular pipe segment corresponding to the master nodes at the connection between the mesh model of the irregular pipe segment and the pipe beam element are designated as slave nodes.

[0087] The finite element calculation module includes a total nodal displacement calculation module, a mesh nodal displacement generation module, a beam element internal force calculation module, and a shell element stress calculation module.

[0088] The total node displacement calculation module is used to perform finite element calculations on the hybrid model to obtain the displacement of each node in the hybrid model. This includes calculating the displacement of only the main nodes at the connection points between the mesh model of the irregular pipe segment and the pipe beam element.

[0089] The mesh node displacement generating module is electrically connected to the total node displacement calculation module. It is used to calculate the displacements of each slave node corresponding to the master node based on the master node's displacement. It is also used to aggregate the displacements of each slave node, along with the other mesh node displacements of the irregular pipe segment's mesh model obtained from finite element calculations, to form the mesh node displacements of the irregular pipe segment's mesh model.

[0090] The beam element internal force calculation module is electrically connected to the total nodal displacement calculation module, and is used to calculate the nodal internal forces of the pipe beam element based on the nodal displacements of the pipe beam element.

[0091] The shell element stress calculation module is electrically connected to the mesh node displacement forming module, and is used to calculate the stress of each shell element based on the mesh node displacement of the mesh model of the irregular pipe segment.

[0092] Optionally, the finite element calculation module further includes a judgment module, which is electrically connected between the interface module and the mesh node displacement forming module, and is used to determine whether the working condition is a non-temperature working condition or a temperature working condition.

[0093] If the operating condition is determined to be non-temperature-related, the mesh node displacement generation module is triggered to calculate the displacement of each slave node corresponding to the master node using the following formula:

[0094] d′=d×a

[0095] Where d is the displacement of the master node, d′ is the displacement of the slave node corresponding to the master node, and a is the transformation matrix that converts the displacement of the master node to the displacement of the slave node.

[0096] If the operating condition is determined to be a temperature-related condition, the mesh node displacement generation module is triggered to calculate the displacement of each slave node corresponding to the master node using the following formula:

[0097] d′=d×(a×(1+alf))

[0098] Where alf is the coefficient of thermal expansion of the pipe material.

[0099] Optionally, the mesh node displacement forming module includes a shell slave node displacement calculation module and a shell node displacement summarization module.

[0100] The shell slave node displacement calculation module is electrically connected to the total node displacement calculation module. It is used to calculate the displacement of each slave node corresponding to the master node based on the displacement of the master node. The shell node displacement summarization module is electrically connected to both the shell slave node displacement calculation module and the total node displacement calculation module. It is used to summarize the displacement of each slave node and the displacement of other mesh nodes of the mesh model of the irregular pipe segment obtained in the finite element calculation to form the mesh node displacement of the mesh model of the irregular pipe segment.

[0101] In this invention, for irregularly shaped pipe components requiring detailed mechanical analysis, a finite element mesh model (with each four adjacent nodes forming a shell element after meshing) is generated to replace the corresponding pipe beam elements in the pipe beam model. After determining the material density of the irregularly shaped pipe segment, finite element calculations are performed on the resulting hybrid model to obtain the displacements of each node in the hybrid model. Based on the nodal displacements of the beam elements in the hybrid model, the nodal internal forces of the pipe beam elements can be calculated, followed by the stress of the pipe beam elements. Based on the mesh node displacements of the irregularly shaped pipe segment mesh model, the internal forces (i.e., stresses) of each shell element can be calculated. Thus, this invention completes the calculation and evaluation of both the pipe beam elements and the irregularly shaped pipe shell components in one step, eliminating unnecessary conservative combination processes and greatly improving the efficiency of pipeline design. Furthermore, compared to methods using one-dimensional pipe beam elements for model calculation, the calculation accuracy of this invention is significantly improved. Attached Figure Description

[0102] Figure 1 A flowchart of a pipeline mechanical calculation method with irregularly shaped pipe sections provided in Embodiment 1 of the present invention;

[0103] Figure 2 A schematic diagram of the cross-section of the pipeline being divided into grids;

[0104] Figure 3 A schematic diagram of axial segmentation and meshing of a bend;

[0105] Figure 4 for Figure 3 aa cross section diagram;

[0106] Figure 5 This is a schematic diagram of the structure of a tee pipe;

[0107] Figure 6 A schematic diagram for calculating the actual area of ​​the three-way main pipe;

[0108] Figure 7 This is a schematic diagram of a tapered tube mesh.

[0109] Figure 8 A schematic diagram of the master-slave nodes at the connection surface between the tube beam element and the shell element;

[0110] Figure 9 This is a block diagram of a pipe mechanics calculation device with irregularly shaped pipe sections provided in Embodiment 2 of the present invention;

[0111] Figure 10 A pipeline model diagram with irregularly shaped pipe shell components, created for the pipeline program of this invention;

[0112] Figure 11 This is a diagram illustrating the statements for the pipe beam title in the pipe program of this invention. Detailed Implementation

[0113] The technical solutions of the invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the invention, not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without creative effort are within the scope of the invention.

[0114] In the description of this invention, it should be noted that the use of terms such as "above" to indicate orientation or positional relationship is based on the orientation or positional relationship shown in the accompanying drawings and is only for the purpose of facilitating and simplifying the description. It does not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0115] In the description of this invention, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0116] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "connection," "setting," "installation," "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0117] This invention provides a method for calculating the mechanical properties of a pipeline with irregularly shaped pipe sections, comprising:

[0118] Based on the parameter information of each component in the pipeline, a pipeline beam model composed of multiple pipeline beam elements is generated, along with the node information of each pipeline beam element. There is a one-to-one correspondence between components and pipeline beam elements.

[0119] Obtain the mesh generation information of the irregular pipe segment requiring detailed analysis, as well as its node information in the pipe beam model. Generate a mesh model of the irregular pipe segment formed by splicing multiple shell elements, and the mesh node information in the mesh model.

[0120] The corresponding pipe beam elements in the pipe beam model are replaced with the mesh model of the irregular pipe segment to form a hybrid model.

[0121] Calculate the material density of the irregular pipe segment and replace the linear density in the parameter information of the irregular pipe segment to generate updated parameter information for the irregular pipe segment.

[0122] Based on the operating conditions of the pipeline to be calculated and the parameter information of each component in the pipeline, finite element analysis is performed on the hybrid model to obtain the displacement of each node in the hybrid model. Based on the node displacements of the pipeline beam elements, the nodal internal forces of the pipeline beam elements are calculated. Based on the mesh node displacements of the mesh model of the irregular pipe segment, the stress of each shell element is calculated.

[0123] Calculate the stress of the pipe beam element based on the nodal internal forces of the pipe beam element.

[0124] The present invention also provides a pipe mechanics calculation device with irregularly shaped pipe sections, comprising:

[0125] The pipe beam generation module is used to generate a pipe beam model composed of multiple pipe beam elements connected together, based on the parameter information of each component in the pipe, as well as the node information of each pipe beam element. There is a one-to-one correspondence between components and pipe beam elements.

[0126] The shell generation module is used to obtain the mesh generation information of the irregular pipe segment that needs to be analyzed in detail, as well as its node information in the pipe beam model, and generate a mesh model of the irregular pipe segment formed by splicing multiple shell elements, along with the mesh node information in the mesh model.

[0127] The replacement module is used to replace the pipe beam elements at corresponding positions in the pipe beam model with the mesh model of the irregular pipe segment to form a hybrid model.

[0128] The shell parameter generation module is used to calculate the material density of the irregular pipe segment and replace the linear density in the parameter information of the irregular pipe segment to generate updated parameter information for the irregular pipe segment.

[0129] The finite element method (FEM) module is used to perform FEM calculations on the hybrid model based on the operating conditions of the pipeline and the parameter information of each component in the pipeline. This yields the displacements of each node in the hybrid model. Based on the node displacements of the pipeline beam elements, the module calculates the nodal internal forces of the pipeline beam elements. Furthermore, based on the mesh node displacements of the irregularly shaped pipe segment mesh model, the module calculates the stresses of each shell element.

[0130] The stress calculation module calculates the stress of the pipe beam element based on the nodal internal forces of the pipe beam element.

[0131] Example 1:

[0132] like Figure 1 As shown, this embodiment provides a method for calculating the mechanical properties of a pipeline with irregularly shaped pipe sections, including:

[0133] Based on the parameter information of each component in the pipeline, a pipeline beam model composed of multiple pipeline beam elements is generated, along with the node information of each pipeline beam element. There is a one-to-one correspondence between components and pipeline beam elements.

[0134] Obtain the mesh generation information of the irregular pipe segment requiring detailed analysis, as well as its node information in the pipe beam model. Generate a mesh model of the irregular pipe segment formed by splicing multiple shell elements, and the mesh node information in the mesh model.

[0135] The corresponding pipe beam elements in the pipe beam model are replaced with the mesh model of the irregular pipe segment to form a hybrid model.

[0136] Calculate the material density of the irregular pipe segment and replace the linear density in the parameter information of the irregular pipe segment to generate updated parameter information for the irregular pipe segment.

[0137] Based on the operating conditions of the pipeline to be calculated and the parameter information of each component in the pipeline, finite element analysis is performed on the hybrid model to obtain the displacement of each node in the hybrid model. Based on the node displacements of the pipeline beam elements, the nodal internal forces of the pipeline beam elements are calculated. Based on the mesh node displacements of the mesh model of the irregular pipe segment, the stress of each shell element is calculated.

[0138] Calculate the stress of the pipe beam element based on the nodal internal forces of the pipe beam element.

[0139] In engineering design, whether it's a nuclear power plant, thermal power plant, or petrochemical project, there are typically numerous pipelines. The analysis and calculation of these pipelines constitute a significant portion of the plant design work. Computer software is needed to perform mechanical analysis and calculations on the pipeline layout to prove the rationality of the design. This invention is one of several processes within a computer program algorithm for pipeline calculation. Previous pipeline programs mostly used one-dimensional beam elements to simulate pipelines, including straight pipe beam elements and irregular pipe (including bends, tees, tapered pipes, etc.) beam elements, all of which are line elements. This invention addresses the technical means required to convert irregular pipe beam elements into a three-dimensional shell element model, meeting the requirements of finite element calculations for hybrid models of pipeline beams and shell element components.

[0140] For irregularly shaped pipe components requiring detailed mechanical analysis and calculations, a finite element mesh model is generated (after meshing, every four adjacent nodes constitute a shell element) to replace the corresponding pipe beam elements in the pipe beam model. After determining the material density of the irregularly shaped pipe segment, finite element calculations are performed on the resulting hybrid model to obtain the displacements of each node in the hybrid model. Based on the nodal displacements of the beam elements in the hybrid model, the nodal internal forces of the pipe beam elements can be calculated, followed by the stress of the pipe beam elements. Based on the mesh nodal displacements of the irregularly shaped pipe segment mesh model, the internal forces (i.e., stresses) of each shell element can be calculated. Thus, this invention completes the calculation and evaluation of pipe beam elements and irregularly shaped pipe shell components in one step, without unnecessary conservative combination processing, greatly improving the efficiency of pipeline design. Furthermore, compared with the method of using one-dimensional pipe beam elements for model calculation, the calculation accuracy of this invention is significantly improved.

[0141] To address the weaknesses commonly found in current pipeline programs, this invention proposes the aforementioned pipeline mechanics calculation method. By adding simple input requirements to the existing pipeline calculation problem data, the pipeline program can automatically convert irregular pipe segments, such as one-dimensional curved beam element elbows (note: although they are one-dimensional line elements, they actually describe a partial circular loop of a pipe with a known bending radius and diameter), into three-dimensional shell element models. The original curved pipe element only has three nodes (start point, end point, and reference point). After conversion, it may become hundreds or thousands of nodes. Every four adjacent nodes are connected end to end to form a shell element, and multiple shell elements are spliced ​​together to form a three-dimensional shell element model.

[0142] The discretization of a smooth circular pipe into a finite number of three-dimensional shell elements is a pre-processing mesh generation technique used in finite element analysis programs, a well-known technique in this field. The end of a beam element is a node, while the end of a shell element is a surface composed of multiple nodes; the technique of associating a point with a surface composed of multiple points is also well-known in this field. This invention integrates these techniques into the modeling module of a pipe calculation program. The model automatically built using this method can simultaneously and automatically calculate both pipe beam elements and shell elements during the pipe calculation process. To achieve this function, the program structure needs to meet the functional requirements of various elements, and in this case, it must meet the various requirements of pipe and shell element calculations. This includes methods for handling pipe beams and their connection to shell components, as well as a precise method for converting the mass density of components in the pipe into shell elements.

[0143] When converting a pipe model into a shell element, the material density of the target shell component needs to be determined. For pipe models, all commercially available programs require the linear density of the pipe to be given, which includes the material weight of the pipe, typically steel, the working medium, and the insulation material. However, the calculation for shell elements is different. It requires the material density of the target shell component. When calculating weight, the program usually multiplies the shell's area by its thickness and then by its material density to obtain the weight of the shell element.

[0144] When calculating the material density of the target shell component based on the linear weight provided by the pipe, the common algorithm is to divide the linear density per unit length by the pipe circumference and pipe thickness to obtain the material density of the target shell component. The problem with this approach is that the results are not accurate enough, especially when the number of segments is small, which can lead to significant errors. The applicant initially proposed the following method:

[0145] Pipe cross-section as Figure 2 As shown: The circle in the figure is a schematic diagram of the pipe's mid-surface. The pipe's wall thickness is ignored here, and the mid-surface radius is R. The figure below shows the pipe divided into six segments along its circumference. The length L is one side length of the shell element, which is the length of the segmented polygonal line.

[0146] If a circular pipe is divided into six segments along its circumference, 360 / 6 = 60, and α = 60 degrees per segment. As shown in the diagram, the length of a broken line segment g′ in the actual pipe is less than the corresponding arc length g. The arc length g = 2 × r × π × 60 / 360 = r × π / 3. The broken line length g′ = r × sin(30) × 2 = r. The ratio of the arc length to the broken line length is π / 3 = 1.047198. Extending this to any number of circumferential segments, the algorithm for converting the linear density w of a given pipe into the material density of a straight pipe is:

[0147] The equivalent density for the circular arc segment is: w′=w / g / t, where w is the given linear density of the pipe and t is the pipe wall thickness;

[0148] The arc length of the circular segment is: g = D × π / N, where D is the pipe diameter and N is the number of segments.

[0149] π = 3.1415926;

[0150] The corresponding length of the broken line segment is: g′=(D / 2×sin(2×π / N / 2))×2=D / sin(π / N);

[0151] According to the relationship between g and g′: fac=g / g′=D×π / N / (D / sin(π / N))=π / N / sin(π / N);

[0152] Shell element density: w″=w′×fac.

[0153] The applicant's preliminary research indicates that this method of processing straight pipe shell element density yields accurate pipe weight calculations regardless of the number of circumferentially divided pipe segments. However, this method has limitations for irregularly shaped pipes, such as elbows, tees, and tapered pipes, as the weight of the converted model differs from the initial pipe beam model weight. Analysis reveals that the weight difference in the elbow shell element model is due to the fact that the weight of the curved pipe element equals the linear weight of the pipe multiplied by the elbow's arc length. Furthermore, the shell element density calculated using the above method, after considering the shell element area, results in a shell element elbow weight that is less than the actual weight of the elbow. This error arises because discretizing the bend into small rectangular planar elements not only transforms the circumferential (circumferential) curve into a broken line but also the axial direction. For elbows, changing the bending trajectory from a smooth curve to a broken line alters the pipe's cross-section, requiring consideration of this factor during shell element density conversion. Adaptive modifications are also necessary for components such as tapered pipes (also known as converging pipes) and tees, making the above method unsuitable for direct application.

[0154] In this embodiment, the irregular pipe section includes a bend.

[0155] The parameters of the bend include:

[0156] The node information of the bend in the pipe beam model includes the node numbers and coordinate values ​​of the start, end, and reference nodes.

[0157] Calculating the material density of the bend includes:

[0158] Based on the linear density w of the bend a Determine the theoretical material density w of the bend. a ′, its calculation formula is: w a ′=w a / g a / t a Among them, after the bend is segmented circumferentially, the end face circle forms N arc segments, g a Let g be the length of the arc. a =πD a / N,t a D represents the wall thickness of the bend. a The diameter of the bend is [the diameter of the pipe].

[0159] Calculate the circumferential reduced density coefficient fac of the bend based on the number of circumferential segments. a Its calculation formula is: fac a =g a / g a ′, where g a ′ represents the length of the broken line segment corresponding to the arc after the bend is segmented circumferentially, and g is the length of the broken line segment. a ′=2D a ×sin(180 / N),

[0160] Calculate the axial reduced density coefficient fac of the bend based on the number of axial segments. a After axial segmentation of the bend, the bend forms n bend segments. Let L be the length of the line connecting the center points of the beginning and end faces of each bend segment, where L = 2R × sin(β / 2n), R is the bending radius of the bend, β is the turning angle of the bend, and the circumference of the ellipse containing the axial center point of each bend segment is l, where the major axis length of the ellipse is a = r, the minor axis length is b = r × cos(β / 2n), and the axial reduced density coefficient is fac. a The formula for calculating ′ is: fac a ′=s / (n×L×l), where s is the surface area of ​​the bend.

[0161] Then calculate the material density w of the bend according to the following formula. a ":

[0162] w a "=w a ′×fac a ×faca ′.

[0163] The material density w of the above-mentioned bent pipe a The calculation and analysis process is as follows:

[0164] When converting a curved pipe into shell elements, it's necessary to determine the material density of the shell elements. For pipe models, all commercially available programs provide the linear density of the pipe, which includes the weight of the pipe material, typically steel, the working medium, and insulation. However, for shell elements, the process is different; the material density of the shell element must be specified. When calculating weight, programs usually multiply the shell's area by its thickness and then by the material density to obtain the weight of a shell element. When calculating the material density of the shell element from the linear weight provided by the pipe, a common algorithm is to divide the linear density per unit length by the pipe's perimeter and thickness. This method is not accurate enough, especially when the number of segments is small, leading to significant errors. For curved pipes, the problem becomes even more complex. For example, if the curved pipe is like... Figure 3 As shown:

[0165] If this 180-degree rotated curved pipe is divided into three sections, as follows: Figure 3 First, for the circumferential segmentation (assuming it is divided into six segments, not shown in the diagram), in Figure 2 The analysis already considered the case of circumferential segmentation of the pipeline. Here, we only analyze the case of axial segmentation. Assuming this 180-degree bend is divided into three segments and modeled using shell elements, the program assumes the circumferential segmentation is divided into six segments during mesh generation. It only calculates the node coordinates at sections 0-0 and 1-1, which are circular. However, section aa is no longer circular; it becomes an ellipse, as shown below. Figure 4 As shown. The major semi-axis of the ellipse is the radius r of the pipe, while the length of the minor semi-axis is related to the number of axial segments.

[0166] L=2R×sin(β / 2n), a=r, b=r×cos(β / 2n).

[0167] Figure 3 In the equation, the length L of each axial broken line segment is: 2R×sin(60 / 2)=R, and its corresponding arc length is =R×π / 3.

[0168] Therefore, the material density of the bent pipe should also have a coefficient fac. a = Smooth area / Broken line area = Smooth area / (Circumference of ellipse × Total length of broken line).

[0169] There is no simple elementary mathematical expression to describe the perimeter of an ellipse. However, the perimeter of the ellipse at the bend aa can be calculated using the following more precise expression:

[0170] circumference of ellipse

[0171] Where: q = a + b

[0172] In summary, the first step, as described in the analysis of the straight tube above, yields the material density of the shell element: w a "=w a ′×fac a .

[0173] These are the results of the above analysis of the density of straight tube shell units.

[0174] The second step, adding to the previous treatment of the pipe cross-section becoming elliptical, is the density of the elbow shell element: w a "=w a ′×fac a ×fac a ′:

[0175] fac a = Smooth area of ​​the bend s / Area of ​​the bend with broken lines = Smooth area s / (Circumference of the ellipse l × Total length of the broken lines n × L) = = s / (n × L × l).

[0176] In this embodiment, the irregular pipe section includes a tee pipe.

[0177] The parameters of the tee pipe include:

[0178] The node information of the tee pipe in the pipe beam model includes the node where the branch pipe and the two main pipes intersect, as well as the node number and coordinate value of their respective end nodes.

[0179] Calculating the material density of the irregularly shaped pipe section specifically includes:

[0180] Based on the linear density w of the main pipe or branch pipe b Determine the theoretical material density w of the main pipe or branch pipe. b ′, its calculation formula is: w b ′=w b / g b / t b Among them, after the main pipe or branch pipe is segmented circumferentially, the end face circle forms multiple arc segments, g b Let t be the length of the arc. b For the wall thickness of the main pipe or branch pipe,

[0181] Calculate the area conversion factor fac for the main or branch pipe based on the area before and after the replacement model. b Its calculation formula is: fac b =A / A′, where,

[0182] A represents the area calculated before replacing the main or branch pipe model, without considering any missing or extra area, where A = π × D. b ×L b D is the diameter of the main or branch pipe, L b It is the length of the line connecting the center of the end circle of the main pipe or branch pipe to the intersection point of the central axes of the three pipes in the tee.

[0183] A′ is the area calculated after replacing the main pipe or branch pipe model, taking into account the missing or extra area. Specifically, A′ is the sum of the shell element areas of the main pipe or branch pipe calculated based on the mesh node information of the main pipe or branch pipe in the mesh model.

[0184] Then calculate the material density of the main pipe or branch pipe according to the following formula:

[0185] w b "=w b ′×fac b .

[0186] For T-junctions, such as Figure 5 As shown, because the connection between the branch pipe and the main pipe is missing material after the shell element model is made, neither of the aforementioned two calculation methods (straight pipe and elbow) can accurately describe the weight of the pipe tee. The shell element density must be calculated considering the number of segments in the shell element, based on the model's construction conditions. There are two issues here: first, during discretization, the curve at the connection between the main and branch pipes becomes a straight line; second, the number of segments in the main pipe and branch pipe may differ, both of which must be taken into account when calculating the area.

[0187] For the supervisor, the number of segments in the branch system needs to be considered, such as... Figure 6 As shown in the diagram, for ease of explanation, the main pipe is divided into 6 segments circumferentially (only three segments are shown in the diagram). Their influence should be considered when calculating the area of ​​the main pipe. Material is missing at the connection between the main pipe and the branch pipe; this influence must also be considered when calculating the area. The entire branch pipe is divided into 12 segments, but only 6 segments need to be considered in the diagram (the other 6 segments intersect with another main pipe). When calculating the area of ​​the main pipe, the pipe can be divided into two parts: a part of length L1 and a part of length l1. The dividing point is determined by the branch pipe diameter, l1 = d / 2. The area of ​​the L part is calculated as a standard straight pipe (circumferential hexagon perimeter × L1). The part of l1 below r is also calculated as a standard straight pipe ((circumferential hexagon perimeter / 2) × l1). For the part below r, the coordinates of each vertex of each shell element must be calculated point by point to obtain the average height and area of ​​each trapezoid. Alternatively, the coordinate values ​​of each node of the main pipe can be directly used to calculate the sum of the areas of all shell elements of the main pipe.

[0188] In previous piping problems, tees were described using the same method as straight pipes in terms of linear density, making the calculation of the tee's weight relatively simple: length multiplied by linear weight. However, when calculating the density of a tee shell element, the area A obtained from the pipe beam element calculation (A = D × π × (L1 + l1)) is used. Considering the number of shell elements for the main and branch pipes in this problem, the actual total area A′ is calculated. Therefore, the material density w of the shell element is... b "=w b ′×A / A′. The algorithm for A′ is calculated using the two methods described above.

[0189] For branch pipes, additional material is added at the connection between the branch pipe and the main pipe, and this effect must also be considered in the calculation. The calculation method is the same as the two calculation methods for the main pipe mentioned above, and will not be repeated here.

[0190] In this embodiment, the irregularly shaped pipe segment includes a tapered pipe.

[0191] The parameters of the tapered tube include:

[0192] The node information of the tapered tube in the pipe beam model includes the node numbers and coordinate values ​​of the beginning and end nodes.

[0193] Calculating the material density of the tapered tube specifically includes:

[0194] Calculate the weight of the tapered tube W = w c ×L c ,

[0195] Based on the average wall thickness of the tapered tube, the calculation formula is t. c = (T+t) / 2, where T is the wall thickness of the large end of the tapered tube and t is the wall thickness of the small end of the tapered tube.

[0196] The formula for calculating the surface area of ​​the tapered tube after meshing is as follows:

[0197] Among them, R c r is the radius of the large end of the tapered tube. c L is the radius of the small end of the tapered tube. c N is the length of the tapered tube. c The number of circumferential segments in the tapered tube.

[0198] Based on the average wall thickness of the tapered tube and the surface area of ​​the tapered tube after meshing, calculate the volume V = A of the tapered tube. c ×t c ,

[0199] Then calculate the material density w of the tapered tube according to the following formula. c ′:

[0200] w c = W / V.

[0201] While the algorithm for tapered pipes (also known as converging pipes) appears to be the same as for straight pipes in principle, it is not actually the same. Besides needing to consider the average wall thickness and average diameter, the length of the shell element is not the same as the length of the user-input tapered pipe element. Figure 7 L in c .

[0202] like Figure 7 As shown, the wall thickness of the tapered tube can be considered as the average of the wall thickness at the large end and the wall thickness at the small end. c = (T+t) / 2. The linear weight of this component is given in the input data of the piping program. Its calculated weight W is equal to the product of the linear weight and the component length: W = w c ×L c When converting to shell element material density, the required total volume V of the shell elements is given by shell element density = W / V. The number of circumferential segments when dividing into shell elements affects the result. The volume of each segment is calculated by multiplying its area by the average wall thickness. The width of each segment is calculated using the average width b, and the segment length is not L. c It is not the edge length of the intersection of the two segments, but rather the length C of the centerline (drawn as a dashed line in the diagram) of the dividing section. Its length is:

[0203]

[0204] Where H = R c cos(360 / 2N), h=r c cos(360 / 2N),

[0205] A = a c ×N, a c =b c ×C, b=(R) c +r c sin(360 / 2N), a c For one

[0206] The area of ​​each segment, where N is the number of circumferential segments in the tapered tube.

[0207] Therefore, given the weight W of the asymmetrical head, the volume of the asymmetrical head after being divided into shells can be calculated as: V = A c ×t c Its material density: shell element density = W / V.

[0208] In this embodiment, the nodes of the pipe beam elements at the connection between the mesh model of the irregular pipe segment and the pipe beam element are designated as master nodes, and the nodes of the mesh model of the irregular pipe segment corresponding to the master nodes at the connection between the mesh model of the irregular pipe segment and the pipe beam element are designated as slave nodes.

[0209] Finite element analysis was performed on the hybrid model to obtain the displacements of each node, including: at the connection between the mesh model of the irregular pipe segment and the pipe beam element, only the displacements of the main nodes were calculated.

[0210] The calculation of stress in each shell element based on the mesh node displacements of the irregular pipe segment mesh model specifically includes:

[0211] Based on the displacement of the master node, calculate the displacement of each slave node corresponding to the master node.

[0212] The displacements of each slave node, along with the displacements of other mesh nodes in the mesh model of the irregular pipe segment obtained from the finite element calculation, constitute the mesh node displacements of the mesh model of the irregular pipe segment.

[0213] The stress of each shell element is calculated based on the mesh node displacements of the mesh model of the irregular pipe segment.

[0214] When creating a pipe model, if a section of the pipe needs to be treated as a shell element component, then the connections to its two ends must be treated. It is assumed that the cross-section of the pipe at any point is always a plane, and this plane is rigid; this is a fundamental assumption in pipe calculations using beam elements. Therefore, at the end of a one-dimensional pipe, there is only one node (let's call it node n), and the component connected to it is changed to a shell element component. There are no nodes at this point, but there is a ring of nodes along the outer diameter of the pipe, and this ring of nodes is not independent; their displacements are entirely determined by node n. For example, Figure 8 This illustrates the connection between the pipe beam and shell elements. Nodes 8 and 9 form the pipe beam element, a one-dimensional line element. Nodes 21 to 26 represent a ring of nodes on the shell element boundary. The displacement solutions for these nodes are not included in the displacement unknowns of the structural equations in the finite element model; they are indirectly obtained from the displacement of node 9. The typical solution process usually ends here. However, this result is incomplete for temperature loads, lacking the effect of thermal expansion on rigid surfaces. The influence of thermal expansion can be considered when calculating the displacements of subordinate nodes, as each subordinate node is affected by thermal expansion, resulting in a change in its corresponding length R.

[0215] In this embodiment, before calculating the displacements of each slave node corresponding to the master node based on the displacement of the master node, the method further includes: determining whether the operating condition is a non-temperature operating condition or a temperature operating condition.

[0216] If the operating condition is determined to be non-temperature-related, the displacement of each slave node corresponding to the master node is calculated using the following formula based on the displacement of the master node:

[0217] d′=d×a

[0218] Where d is the displacement of the master node, d′ is the displacement of the slave node corresponding to the master node, and a is the transformation matrix that converts the displacement of the master node to the displacement of the slave node.

[0219] If the operating condition is determined to be a temperature-related condition, the displacement of each slave node corresponding to the master node is calculated using the following formula based on the displacement of the master node:

[0220] d′=d×(a×(1+alf))

[0221] Where alf is the coefficient of thermal expansion of the pipe material.

[0222] The aforementioned master node and its slave nodes form a rigid surface. Because this rigid surface does not deform, it is correct for general load solutions, but it causes problems for temperature loads. For the pipe beam model, the program only considers thermal expansion along the axial direction during calculation, and cannot calculate the circumferential thermal expansion of the pipe. However, for shell element components, after applying a temperature load, the shell element component can obtain both axial and circumferential thermal expansion displacements. At this time, unrealistic results will appear at the connection between the pipe beam element and the shell element component, due to this rigid surface. Therefore, it is necessary to consider the thermal displacement effect of each slave node. Without considering the temperature effect, the displacement of the auxiliary node is equal to the displacement of the master node transferred to the corresponding position: d′=d×a. When thermal expansion displacement needs to be considered: d′=d×(a×(1+alf)), where alf is the coefficient of thermal expansion of the material.

[0223] Current pipeline calculation and analysis software cannot directly combine pipeline elements and pipeline components described by shell elements for analysis and calculation. Pipeline calculations must be performed under various operating conditions, such as self-weight, temperature, and seismic conditions. Different operating conditions and operational levels require different evaluation standards, which are reflected in different standard formulas. The formulas used in pipeline evaluation employ many coefficients. The bending moment of the pipeline beam obtained from the pipeline calculation is directly input into the standard formulas; therefore, the actual stress is not directly obtained from the pipeline beam element. The limits required by the standard evaluation are allowable stresses. The program must consider various factors (such as welding, component type, number of loading cycles, etc.). The influence of these conditions is sometimes considered by coefficients given in the standard, such as the weld coefficient, which is related to the welding process and connecting components. Some conservative factors are unavoidable when using pipeline beams for calculations.

[0224] For equipment constructed from shell elements, stress is used directly for evaluation. However, this involves differentiating between membrane stress, bending stress, and membrane plus bending stress, which are related not only to the nature of the load but also to the evaluation location. A piping calculation program using this technique can conveniently complete the calculation of piping and equipment components in one go. The weight of the elbow shell element component model obtained using this technique is completely consistent with the weight of the pipe beam, with no calculation discrepancy. This is crucial for dynamic analysis because the dynamic response of the problem (usually analyzed using the response spectrum method) is closely related to the mode shapes. The modes of the piping problem are closely related to the model's mass distribution. Another technique is to use density equivalence between irregularly shaped pipe beam elements and shell elements. This technique ensures that the weight calculated from these components is consistent with the piping problem, meeting the overall calculation requirements. The requirements for piping evaluation are naturally met, and shell elements can directly provide element stresses, including membrane stress and bending stress. The software developed using these two techniques provides more realistic local results than conventional software and can complete the calculation and evaluation of piping and equipment components in one go. Because the program is very easy to use, work efficiency is greatly improved. At the same time, it eliminated many of the conservative aspects of the design, making the design and construction of pipelines and the entire project more economical and efficient.

[0225] The specific implementation requires the assistance of computer software. The following implementation steps refer to the implementation process of any computer pipeline design calculation software that uses the technology of this invention.

[0226] 1) The first step is the standard pipe calculation. Based on the pipe problem to be calculated, pipe beam elements are generated. This step is standard in pipe calculation and is not relevant to this invention. However, it is a fundamental condition for this invention. The problem includes elbows, tees, and / or tapered pipes. Using this invention, it is necessary to first define how to determine the shell element components in the problem, and to be able to distinguish the inlets and outlets of elbows and tees, as well as branch pipes.

[0227] 2) When a pipe bend element is required to be calculated as a shell element, the software needs to determine the original start and end points of the element, reference node numbers, coordinate values ​​of each node, and various information such as the diameter, bending radius, material, temperature, and pressure of the pipe element. The next step is to create a finite element solution model file, which must include all the information of the shell element, and the corresponding pipe bend beam element must be removed.

[0228] 3) For tees, it should be defined whether they are main pipes or branch pipes, and the number of units required for the three parts should be specified. The three units must be logically connected. In the problem, these three tee pipe beam units need to be removed.

[0229] 4) For the coordinates of the start and end points in the second step, the coordinates of the shell element mesh nodes and the element number group should be generated to describe the shell element here. The shell element component type should be marked to distinguish between straight pipe or curved pipe elements, and the main and branch pipes of the tee should also be distinguished.

[0230] 5) Divide the pipe bend element into element meshes according to circumferential segments N and axial segments n respectively, and obtain the mass correction factor fac. a and fac a In standard pipe description files, the linear density of the pipe is defined when defining the pipe cross-section, typically in units of mass per unit length, such as kilograms per meter. However, shell element calculations require the material density of the shell element. During this model conversion, the principle to ensure is that the weight of the converted shell element components matches the weight of the original input pipe element. The original pipe weight is W = pipe length × linear weight. Theoretically, the total area of ​​the shell model of this pipe should equal the lateral surface area of ​​the cylinder within this pipe element. For bends, a mass correction factor fac needs to be added. a and fac a ′.

[0231] 6) For the tee, calculate the material density of each shell element according to the tee inlet, outlet, and branch pipe, w b "=w b ′×A / A′.

[0232] 7) Prepare the finite element file for pipeline calculation, start the finite element calculation for each calculation case, and the program solves the finite element equations.

[0233] 8) Perform stress calculations for the piping unit and shell unit together, and conduct stress assessments for each unit in accordance with the piping and equipment specifications.

[0234] Step 5) above yields the theoretical material density value for the bent pipe shell element. However, in reality, because each shell element is a plane, it differs from the curved surface of the pipe's cylindrical surface. Therefore, the theoretical density for the pipe surface can be calculated: w a ′=w a / (D×π) / t, considering the shell element's substitution of a curved surface for a planar element, the above theoretical density needs to be multiplied by a coefficient fac. a fac a =π / N / sin(π / N). Coefficient fac a When constructing shell units, the reduced surface area necessitates increasing the pipe density. Furthermore, the effect of the pipe cross-section becoming elliptical must be considered. Ultimately, w a "=w a ′×fac a ′:

[0235] faca = Smooth area of ​​the bend / Area of ​​the bend's broken line = Smooth area / (Circumference of the ellipse × Total length of the broken line).

[0236] In step 6), when calculating the material density of the tee, the calculation is performed based on both the pipe beam area and the total area of ​​the shell unit. Then, the material density calculated based on the pipe weight is converted to the material density w of the shell unit tee. b "=w b ′×A / A′, where A is the cylindrical lateral surface area of ​​the tee main pipe beam, and A′ is the total area of ​​the actual tee main pipe after being divided into shell elements. The algorithm for tee branch pipes is similar.

[0237] Example 2:

[0238] like Figure 9 As shown, the present invention also provides a pipe mechanics calculation device with irregularly shaped pipe sections, comprising:

[0239] Pipe beam generation module 1 is used to generate a pipe beam model composed of multiple pipe beam elements connected together, as well as the node information of each pipe beam element, based on the parameter information of each component in the pipe. Each component corresponds one-to-one with a pipe beam element.

[0240] Shell generation module 2 is used to obtain the mesh generation information of the irregular pipe segment that needs to be analyzed in detail, as well as its node information in the pipe beam model, and generate a mesh model of the irregular pipe segment formed by splicing multiple shell elements, and the mesh node information in the mesh model.

[0241] Replacement module 3 is used to replace the pipe beam elements at corresponding positions in the pipe beam model with the mesh model of the irregular pipe segment to form a hybrid model.

[0242] Shell parameter generation module 6 is used to calculate the material density of the irregular pipe segment and replace the linear density in the parameter information of the irregular pipe segment to generate updated parameter information of the irregular pipe segment.

[0243] Finite element calculation module 4 is used to perform finite element calculations on the hybrid model based on the operating condition information of the pipeline to be calculated and the parameter information of each component in the pipeline, to obtain the displacement of each node of the hybrid model, to calculate the nodal internal forces of the pipeline beam elements based on the nodal displacements of the pipeline beam elements, and to calculate the stress of each shell element based on the mesh nodal displacements of the mesh model of the irregular pipe segment.

[0244] Stress calculation module 5 calculates the stress of the pipe beam element based on the nodal internal forces of the pipe beam element.

[0245] In this embodiment, an interface module 7 is also included, which is used to receive the working condition information of the pipeline to be calculated and the parameter information of each component and transmit them to the pipeline beam generation module 1 and the finite element calculation module 4, and also transmit the parameter information of the irregular pipe section to the shell generation module 2 and the shell parameter forming module 6 respectively.

[0246] It is also used to receive the numbering information and mesh division information of irregular pipe segments and transmit them to the shell generation module, and to transmit the numbering information of irregular pipe segments to the shell parameter forming module 6.

[0247] In this embodiment, the irregular pipe section includes a bend.

[0248] The parameters of the bend include:

[0249] The node information of the bend in the pipe beam model includes the node numbers and coordinate values ​​of the start, end, and reference nodes.

[0250] The shell parameter forming module 6 calculates the material density of the bend, specifically including:

[0251] Based on the linear density w of the bend a Determine the theoretical material density w of the bend. a ′, its calculation formula is: w a ′=w a / g a / t a Among them, after the bend is segmented circumferentially, the end face circle forms N arc segments, g a Let g be the length of the arc. a =πD a / N,t a D represents the wall thickness of the bend. a The diameter of the bend is [the diameter of the pipe].

[0252] Calculate the circumferential reduced density coefficient fac of the bend based on the number of circumferential segments. a Its calculation formula is: fac a =g a / g a ′, where g a ′ represents the length of the broken line segment corresponding to the arc after the bend is segmented circumferentially, and g is the length of the broken line segment. a ′=2D a ×sin(180 / N),

[0253] Calculate the axial reduced density coefficient fac of the bend based on the number of axial segments. aAfter axial segmentation of the bend, the bend forms n bend segments. Let L be the length of the line connecting the center points of the beginning and end faces of each bend segment, where L = 2R × sin(β / 2n), R is the bending radius of the bend, β is the turning angle of the bend, and the circumference of the ellipse containing the axial center point of each bend segment is l, where the major axis length of the ellipse is a = r, the minor axis length is b = r × cos(β / 2n), and the axial reduced density coefficient is fac. a The formula for calculating ′ is: fac a ′=s / (n×L×l), where s is the surface area of ​​the bend.

[0254] Then calculate the material density w of the bend according to the following formula. a ":

[0255] w a "=w a ′×fac a ×fac a ′.

[0256] In this embodiment, the irregular pipe section includes a tee pipe.

[0257] The parameters of the tee pipe include:

[0258] The node information of the tee pipe in the pipe beam model includes the node where the branch pipe and the two main pipes intersect, as well as the node number and coordinate value of their respective end nodes.

[0259] The shell parameter forming module 6 is also electrically connected to the shell generation module 2, and it calculates the material density of the tee pipe, specifically including:

[0260] Based on the linear density w of the main pipe or branch pipe b Determine the theoretical material density w of the main pipe or branch pipe. b ′, its calculation formula is: w b ′=w b / g b / t b Among them, after the main pipe or branch pipe is segmented circumferentially, the end face circle forms multiple arc segments, g b Let t be the length of the arc. b For the wall thickness of the main pipe or branch pipe,

[0261] Calculate the circumferential reduced density coefficient fac of the main pipe or branch pipe based on the number of circumferential segments. b Its calculation formula is: fac b =g b / g b ′, where g b ′ represents the length of the broken line segment corresponding to the arc after the main pipe or branch pipe is segmented circumferentially.

[0262] Calculate the area conversion factor fac for the main or branch pipe based on the area before and after the replacement model. b ′, its calculation formula is: fac b ′=A / A′, where,

[0263] A represents the area calculated before replacing the main or branch pipe model, without considering any missing or extra area, where A = π × D. b ×L b D is the diameter of the main or branch pipe, L b It is the length of the line connecting the center of the end circle of the main pipe or branch pipe to the intersection point of the central axes of the three pipes in the tee.

[0264] A′ is the area calculated after replacing the main pipe or branch pipe model, taking into account the missing or extra area. Specifically, A′ is the sum of the shell element areas of the main pipe or branch pipe calculated based on the mesh node information of the main pipe or branch pipe in the mesh model.

[0265] Then calculate the material density of the main pipe or branch pipe according to the following formula:

[0266] w b "=w b ′×fac b ×fac b ′.

[0267] In this embodiment, the irregularly shaped pipe segment includes a tapered pipe.

[0268] The parameters of the tapered tube include:

[0269] The node information of the tapered tube in the pipe beam model includes the node numbers and coordinate values ​​of the beginning and end nodes.

[0270] The shell parameter forming module 6 calculates the material density of the tapered tube, specifically including:

[0271] Calculate the weight of the tapered tube W = w c ×L,

[0272] Based on the average wall thickness of the tapered tube, the calculation formula is t. c = (T+t) / 2, where T is the wall thickness of the large end of the tapered tube and t is the wall thickness of the small end of the tapered tube.

[0273] The formula for calculating the surface area of ​​the tapered tube after meshing is as follows:

[0274] Among them, R c r is the radius of the large end of the tapered tube. c Where N is the radius of the small end of the tapered tube, L is the length of the tapered tube, and N is the radius of the small end of the tapered tube. c The number of circumferential segments in the tapered tube.

[0275] Based on the average wall thickness of the tapered tube and the surface area of ​​the tapered tube after meshing, calculate the volume V = A of the tapered tube. c ×t c ,

[0276] Then calculate the material density w of the tapered tube according to the following formula. c ′:

[0277] w c = W / V.

[0278] In this embodiment, the shell parameter forming module 6 includes a material density calculation module 61 and a parameter updating module 62.

[0279] The material density calculation module 61 is electrically connected to the interface module 7 and is used to calculate the material density of the irregular pipe section based on the parameter information of the irregular pipe section.

[0280] The parameter update module 62 is electrically connected to the material density calculation module 61 and is used to replace the linear density in the parameter information of the irregular pipe segment with the material density of the irregular pipe segment to form the updated parameter information of the irregular pipe segment.

[0281] In this embodiment, the nodes of the pipe beam elements at the connection between the mesh model of the irregular pipe segment and the pipe beam element are designated as master nodes, and the nodes of the mesh model of the irregular pipe segment corresponding to the master nodes at the connection between the mesh model of the irregular pipe segment and the pipe beam element are designated as slave nodes.

[0282] The finite element calculation module 4 includes a total nodal displacement calculation module 41, a mesh nodal displacement formation module 42, a beam element internal force calculation module 44, and a shell element stress calculation module 43.

[0283] The total node displacement calculation module 41 is used to perform finite element calculations on the hybrid model to obtain the displacement of each node in the hybrid model. This includes: at the connection between the mesh model of the irregular pipe segment and the pipe beam element, only the displacement of the main node is calculated.

[0284] The mesh node displacement forming module 42 is electrically connected to the total node displacement calculation module 41. It is used to calculate the displacements of each slave node corresponding to the master node based on the displacement of the master node. It is also used to summarize the displacements of each slave node, along with the other mesh node displacements of the irregular pipe segment mesh model obtained from the finite element calculation, to form the mesh node displacements of the irregular pipe segment mesh model.

[0285] The beam element internal force calculation module 44 is electrically connected to the total nodal displacement calculation module 41, and is used to calculate the nodal internal forces of the pipe beam element based on the nodal displacements of the pipe beam element.

[0286] The shell element stress calculation module 43 is electrically connected to the mesh node displacement forming module 42, and is used to calculate the internal force of each shell element based on the mesh node displacement of the mesh model of the irregular pipe segment, so as to obtain the stress of the irregular pipe.

[0287] In this embodiment, the finite element calculation module 4 further includes a judgment module 45, which is electrically connected between the interface module 7 and the mesh node displacement forming module 42, and is used to determine whether the working condition is a non-temperature working condition or a temperature working condition.

[0288] If the operating condition is determined to be non-temperature-related, the mesh node displacement generation module is triggered to calculate the displacement of each slave node corresponding to the master node using the following formula:

[0289] d′=d×a

[0290] Where d is the displacement of the master node, d′ is the displacement of the slave node corresponding to the master node, and a is the transformation matrix that converts the displacement of the master node to the displacement of the slave node.

[0291] If the operating condition is determined to be a temperature-related condition, the mesh node displacement generation module is triggered to calculate the displacement of each slave node corresponding to the master node using the following formula:

[0292] d′=d×(a×(1+alf))

[0293] Where alf is the coefficient of thermal expansion of the pipe material.

[0294] In this embodiment, the mesh node displacement forming module 42 includes a shell node displacement calculation module 421 and a shell node displacement summarization module 422.

[0295] The shell slave node displacement calculation module 421 is electrically connected to the total node displacement calculation module 41 and is used to calculate the displacement of each slave node corresponding to the master node based on the displacement of the master node. The shell node displacement summarization module 422 is electrically connected to the shell slave node displacement calculation module 421 and the total node displacement calculation module 41 respectively and is used to summarize the displacement of each slave node and the other mesh node displacements of the mesh model of the irregular pipe segment obtained in the finite element calculation to form the mesh node displacement of the mesh model of the irregular pipe segment.

[0296] Application Cases

[0297] The problem established using the technology of this invention can very conveniently generate calculations for shelled units of various devices and components, such as... Figure 10 As shown, these calculations are performed in one go.

[0298] The total weight calculated using this shell element model is completely consistent with the mass of the pipe beam problem. Moreover, the calculations for each working condition are completed in one go, and the stress assessment of the pipe beam and shell elements under each working condition can be completed automatically in one go.

[0299] Generating and calculating shell element components requires only a single statement. Removing this statement results in a pipe beam problem; adding it introduces shell element components. For example, consider the following partial data from a problem: the second and fifth statements, `RSHL, LX = 1`, indicate a straight pipe and require shell element calculation. The eighth statement, `RSHL, LX = 2`, requests that the preceding bend elements be calculated using shell elements. Removing these three statements, or adding the comment symbol "*", transforms the problem into a pipe beam problem without any modifications. Figure 11 As shown.

[0300] Crucially, existing shell element programs, when converting shell models to stiffness matrices, cannot perform temperature and internal pressure calculations. Furthermore, static and dynamic calculations cannot be achieved using only a single stiffness matrix. Its advantage lies in its fast computation speed. During each overall calculation, aside from considering the stiffness matrix, no further work related to shell elements is required. However, it also has significant drawbacks. While it saves computing time, it introduces challenges for analysts, requiring model building, analysis, and evaluation to be performed in stages, along with load simplification. This invention effectively solves these problems.

[0301] It is understood that the above embodiments are merely exemplary implementations used to illustrate the principles of the present invention, and the present invention is not limited thereto. For those skilled in the art, various modifications and improvements can be made without departing from the spirit and essence of the present invention, and these modifications and improvements are also considered to be within the scope of protection of the present invention.

Claims

1. A method for calculating the mechanical properties of a pipeline with irregularly shaped pipe sections, characterized in that, include: Based on the parameter information of each component in the pipeline, a pipeline beam model composed of multiple pipeline beam elements is generated, along with the node information of each pipeline beam element. There is a one-to-one correspondence between components and pipeline beam elements. Obtain the mesh generation information of the irregular pipe segment requiring detailed analysis, as well as its node information in the pipe beam model. Generate a mesh model of the irregular pipe segment formed by splicing multiple shell elements, and the mesh node information in the mesh model. The corresponding pipe beam elements in the pipe beam model are replaced with the mesh model of the irregular pipe segment to form a hybrid model. Calculate the material density of the irregular pipe segment and replace the linear density in the parameter information of the irregular pipe segment to generate updated parameter information for the irregular pipe segment. Based on the operating conditions of the pipeline to be calculated and the parameter information of each component in the pipeline, finite element analysis is performed on the hybrid model to obtain the displacement of each node in the hybrid model. Based on the node displacements of the pipeline beam elements, the nodal internal forces of the pipeline beam elements are calculated. Based on the mesh node displacements of the mesh model of the irregular pipe segment, the stress of each shell element is calculated. Calculate the stress of the pipe beam element based on the nodal internal forces of the pipe beam element; The irregular pipe section includes a bend. Calculating the material density of the bend includes: Based on the linear density w of the bend a Determine the theoretical material density w of the bend. a ′, its calculation formula is: w a ′=w a / g a / t a Among them, after the bend is segmented circumferentially, the end face circle forms N arc segments, g a Let g be the length of the arc. a =πD a / N,t a D represents the wall thickness of the bend. a The diameter of the bend is [the diameter of the pipe]. Calculate the circumferential reduced density coefficient fac of the bend based on the number of circumferential segments. a Its calculation formula is: fac a =g a / g a ′, where g a ′ represents the length of the broken line segment corresponding to the arc after the bend is segmented circumferentially, and g is the length of the broken line segment. a ′=2D a ×sin(180 / N), Calculate the axial reduced density coefficient fac of the bend based on the number of axial segments. a After axial segmentation of the bend, the bend forms n bend segments. Let L be the length of the line connecting the center points of the beginning and end faces of each bend segment, where L = 2R × sin(β / 2n), R is the bending radius of the bend, β is the turning angle of the bend, and the circumference of the ellipse containing the axial center point of each bend segment is l, where the major axis length of the ellipse is a = r, the minor axis length is b = r × cos(β / 2n), and the axial reduced density coefficient is fac. a The formula for calculating ′ is: fac a ′=s / (n×L×l), where s is the surface area of ​​the bend. Then calculate the material density w of the bend according to the following formula. a ": In a ″=w a ′×fac a ×fac a ′。 2. The pipe mechanics calculation method with irregularly shaped pipe sections according to claim 1, characterized in that, The irregular pipe section includes a tee pipe. The parameters of the tee pipe include: Calculating the material density of the tee pipe specifically includes: Based on the linear density w of the main pipe or branch pipe b Determine the theoretical material density w of the main pipe or branch pipe. b ′, its calculation formula is: w b ′=w b / g b / t b Among them, after the main pipe or branch pipe is segmented circumferentially, the end face circle forms multiple arc segments, g b Let t be the length of the arc. b For the wall thickness of the main pipe or branch pipe, Calculate the area conversion factor fac for the main or branch pipe based on the area before and after the replacement model. b Its calculation formula is: fac b =A / A′, where, A represents the area calculated before replacing the main or branch pipe model, without considering any missing or extra area, where A = π × D. b ×L b D is the diameter of the main or branch pipe, L b It is the length of the line connecting the center of the end circle of the main pipe or branch pipe to the intersection point of the central axes of the three pipes in the tee. A′ is the area calculated after replacing the main pipe or branch pipe model, taking into account the missing or extra area. Specifically, A′ is the sum of the shell element areas of the main pipe or branch pipe calculated based on the mesh node information of the main pipe or branch pipe in the mesh model. Then calculate the material density of the main pipe or branch pipe according to the following formula: In b ″=w b ′×fac b 。 3. The pipe mechanics calculation method with irregularly shaped pipe sections according to claim 1, characterized in that, The irregularly shaped pipe section includes a tapered pipe. Calculating the material density of the tapered tube specifically includes: Calculate the weight of the tapered tube W = w c ×L c , Based on the average wall thickness of the tapered tube, the calculation formula is t. c = (T+t) / 2, where T is the wall thickness of the large end of the tapered tube and t is the wall thickness of the small end of the tapered tube. The formula for calculating the surface area of ​​the tapered tube after meshing is as follows: Among them, R c r is the radius of the large end of the tapered tube. c L is the radius of the small end of the tapered tube. c N is the length of the tapered tube. c The number of circumferential segments in the tapered tube. Based on the average wall thickness of the tapered tube and the surface area of ​​the tapered tube after meshing, calculate the volume V = A of the tapered tube. c ×t c , Then calculate the material density w of the tapered tube according to the following formula. c ′: w c ′=W / V。 4. The pipe mechanics calculation method with irregularly shaped pipe sections according to any one of claims 1-3, characterized in that, Let the nodes of the pipe beam elements at the connection between the mesh model of the irregular pipe segment and the pipe beam elements be the master nodes, and let the nodes of the mesh model of the irregular pipe segment corresponding to the master nodes at the connection between the mesh model of the irregular pipe segment and the pipe beam elements be the slave nodes. Finite element analysis was performed on the hybrid model to obtain the displacements of each node, including: at the connection between the mesh model of the irregular pipe segment and the pipe beam element, only the displacements of the main nodes were calculated. The calculation of stress in each shell element based on the mesh node displacements of the irregular pipe segment mesh model specifically includes: Based on the displacement of the master node, calculate the displacement of each slave node corresponding to the master node. The displacements of each slave node, along with the displacements of other mesh nodes in the mesh model of the irregular pipe segment obtained from the finite element calculation, constitute the mesh node displacements of the mesh model of the irregular pipe segment. The stress of each shell element is calculated based on the mesh node displacements of the mesh model of the irregular pipe segment.

5. The pipe mechanics calculation method with irregularly shaped pipe sections according to claim 4, characterized in that, Before calculating the displacements of each slave node corresponding to the master node based on the displacement of the master node, the process further includes: determining whether the operating condition is a non-temperature operating condition or a temperature operating condition. If the operating condition is determined to be non-temperature-related, the displacement of each slave node corresponding to the master node is calculated using the following formula based on the displacement of the master node: d′=d×a Where d is the displacement of the master node, d′ is the displacement of the slave node corresponding to the master node, and a is the transformation matrix that converts the displacement of the master node to the displacement of the slave node. If the operating condition is determined to be a temperature-related condition, the displacement of each slave node corresponding to the master node is calculated using the following formula based on the displacement of the master node: d′=d×(a×(1+alf)) Where alf is the coefficient of thermal expansion of the pipe material.

6. A pipe mechanics calculation device with irregularly shaped pipe sections, characterized in that, include: The pipe beam generation module is used to generate a pipe beam model composed of multiple pipe beam elements connected together, based on the parameter information of each component in the pipe, as well as the node information of each pipe beam element. There is a one-to-one correspondence between components and pipe beam elements. The shell generation module is used to obtain the mesh generation information of the irregular pipe segment that needs to be analyzed in detail, as well as its node information in the pipe beam model, and generate a mesh model of the irregular pipe segment formed by splicing multiple shell elements, along with the mesh node information in the mesh model. The replacement module is used to replace the pipe beam elements at corresponding positions in the pipe beam model with the mesh model of the irregular pipe segment to form a hybrid model. The shell parameter generation module is used to calculate the material density of the irregular pipe segment and replace the linear density in the parameter information of the irregular pipe segment to generate updated parameter information for the irregular pipe segment. The finite element method (FEM) module is used to perform FEM calculations on the hybrid model based on the operating conditions of the pipeline and the parameter information of each component in the pipeline. This yields the displacements of each node in the hybrid model. Based on the node displacements of the pipeline beam elements, the module calculates the nodal internal forces of the pipeline beam elements. Furthermore, based on the mesh node displacements of the irregularly shaped pipe segment mesh model, the module calculates the stresses of each shell element. The stress calculation module calculates the stress of the pipe beam element based on the nodal internal forces of the pipe beam element. The irregular pipe section includes a bend. The shell parameter forming module calculates the material density of the bend, specifically including: Based on the linear density w of the bend a Determine the theoretical material density w of the bend. a ′, its calculation formula is: w a ′=w a / g a / t a Among them, after the bend is segmented circumferentially, the end face circle forms N arc segments, g a Let g be the length of the arc. a =πD a / N,t a D represents the wall thickness of the bend. a The diameter of the bend is [the diameter of the pipe]. Calculate the circumferential reduced density coefficient fac of the bend based on the number of circumferential segments. a Its calculation formula is: fac a =g a / g a ′, where g a ′ represents the length of the broken line segment corresponding to the arc after the bend is segmented circumferentially, and g is the length of the broken line segment. a ′=2D a ×sin(180 / N), Calculate the axial reduced density coefficient fac of the bend based on the number of axial segments. a After axial segmentation of the bend, the bend forms n bend segments. Let L be the length of the line connecting the center points of the beginning and end faces of each bend segment, where L = 2R × sin(β / 2n), R is the bending radius of the bend, β is the turning angle of the bend, and the circumference of the ellipse containing the axial center point of each bend segment is l, where the major axis length of the ellipse is a = r, the minor axis length is b = r × cos(β / 2n), and the axial reduced density coefficient is fac. a The formula for calculating ′ is: fac a ′=s / (n×L×l), where s is the surface area of ​​the bend. Then calculate the material density w of the bend according to the following formula. a ": In a ″=w a ′×fac a ×fac a ′。 7. The pipe mechanics calculation device with irregularly shaped pipe sections according to claim 6, characterized in that, It also includes an interface module, which receives the operating condition information of the pipeline to be calculated and the parameter information of each component and transmits them to the pipeline beam generation module and the finite element calculation module. It also transmits the parameter information of the irregular pipe section to the shell generation module and the shell parameter formation module respectively. It is also used to receive the numbering information and mesh division information of irregular pipe segments and transmit them to the shell generation module, and to transmit the numbering information of irregular pipe segments to the shell parameter forming module.

8. The pipe mechanics calculation device with irregularly shaped pipe sections according to claim 6, characterized in that, The irregular pipe section includes a tee pipe. The parameters of the tee pipe include: The shell parameter forming module is also electrically connected to the shell generation module, and it calculates the material density of the tee pipe, specifically including: Based on the linear density w of the main pipe or branch pipe b Determine the theoretical material density w of the main pipe or branch pipe. b ′, its calculation formula is: w b ′=w b / g b / t b Among them, after the main pipe or branch pipe is segmented circumferentially, the end face circle forms multiple arc segments, g b Let t be the length of the arc. b For the wall thickness of the main pipe or branch pipe, Calculate the area conversion factor fac for the main or branch pipe based on the area before and after the replacement model. b Its calculation formula is: fac b =A / A′, where, A represents the area calculated before replacing the main or branch pipe model, without considering any missing or extra area, where A = π × D. b ×L b D is the diameter of the main or branch pipe, L b It is the length of the line connecting the center of the end circle of the main pipe or branch pipe to the intersection point of the central axes of the three pipes in the tee. A′ is the area calculated after replacing the main pipe or branch pipe model, taking into account the missing or extra area. Specifically, A′ is the sum of the shell element areas of the main pipe or branch pipe calculated based on the mesh node information of the main pipe or branch pipe in the mesh model. Then calculate the material density of the main pipe or branch pipe according to the following formula: In b ″=w b ′×fac b 。 9. The pipe mechanics calculation device with irregularly shaped pipe sections according to claim 6, characterized in that, The irregularly shaped pipe section includes a tapered pipe. The shell parameter forming module is also electrically connected to the shell generation module, and it calculates the material density of the bent pipe, specifically including: Calculating the material density of the tapered tube specifically includes: Calculate the weight of the tapered tube W = w c ×L c , Based on the average wall thickness of the tapered tube, the calculation formula is t. c = (T+t) / 2, where T is the wall thickness of the large end of the tapered tube and t is the wall thickness of the small end of the tapered tube. The formula for calculating the surface area of ​​the tapered tube after meshing is as follows: Among them, R c r is the radius of the large end of the tapered tube. c L is the radius of the small end of the tapered tube. c N is the length of the tapered tube. c The number of circumferential segments in the tapered tube. Based on the average wall thickness of the tapered tube and the surface area of ​​the tapered tube after meshing, calculate the volume V = A of the tapered tube. c ×t c , Then calculate the material density w of the tapered tube according to the following formula. c ′: w c ′=W / V。 10. The pipe mechanics calculation device with irregularly shaped pipe sections according to any one of claims 6-9, The shell parameter formation module includes a material density calculation module and a parameter update module. The material density calculation module is electrically connected to the interface module and is used to calculate the material density of the irregular pipe section based on its parameter information. The parameter update module is electrically connected to the material density calculation module and is used to replace the linear density in the parameter information of the irregular pipe segment with the material density of the irregular pipe segment to form the updated parameter information of the irregular pipe segment.

11. The pipe mechanics calculation device with irregularly shaped pipe sections according to any one of claims 6-9, characterized in that, Let the nodes of the pipe beam elements at the connection between the mesh model of the irregular pipe segment and the pipe beam elements be the master nodes, and let the nodes of the mesh model of the irregular pipe segment corresponding to the master nodes at the connection between the mesh model of the irregular pipe segment and the pipe beam elements be the slave nodes. The finite element calculation module includes a total nodal displacement calculation module, a mesh nodal displacement generation module, a beam element internal force calculation module, and a shell element stress calculation module. The total node displacement calculation module is used to perform finite element calculations on the hybrid model to obtain the displacement of each node in the hybrid model. This includes calculating the displacement of only the main nodes at the connection points between the mesh model of the irregular pipe segment and the pipe beam element. The mesh node displacement generating module is electrically connected to the total node displacement calculation module. It is used to calculate the displacements of each slave node corresponding to the master node based on the master node's displacement. It is also used to aggregate the displacements of each slave node, along with the other mesh node displacements of the irregular pipe segment's mesh model obtained from finite element calculations, to form the mesh node displacements of the irregular pipe segment's mesh model. The beam element internal force calculation module is electrically connected to the total nodal displacement calculation module, and is used to calculate the nodal internal forces of the pipe beam element based on the nodal displacements of the pipe beam element. The shell element stress calculation module is electrically connected to the mesh node displacement forming module, and is used to calculate the stress of each shell element based on the mesh node displacement of the mesh model of the irregular pipe segment.

12. The pipe mechanics calculation device with irregularly shaped pipe sections according to claim 11, characterized in that, The finite element calculation module also includes a judgment module, which is electrically connected between the interface module and the mesh node displacement forming module, and is used to determine whether the working condition is a non-temperature condition or a temperature condition. If the operating condition is determined to be non-temperature-related, the mesh node displacement generation module is triggered to calculate the displacement of each slave node corresponding to the master node using the following formula: d′=d×a Where d is the displacement of the master node, d′ is the displacement of the slave node corresponding to the master node, and a is the transformation matrix that converts the displacement of the master node to the displacement of the slave node. If the operating condition is determined to be a temperature-related condition, the mesh node displacement generation module is triggered to calculate the displacement of each slave node corresponding to the master node using the following formula: d′=d×(a×(1+alf)) Where alf is the coefficient of thermal expansion of the pipe material.

13. The pipe mechanics calculation device with irregularly shaped pipe sections according to claim 11, characterized in that, The mesh node displacement generation module includes a shell node displacement calculation module and a shell node displacement aggregation module. The shell slave node displacement calculation module is electrically connected to the total node displacement calculation module. It is used to calculate the displacement of each slave node corresponding to the master node based on the displacement of the master node. The shell node displacement summarization module is electrically connected to both the shell slave node displacement calculation module and the total node displacement calculation module. It is used to summarize the displacement of each slave node and the displacement of other mesh nodes of the mesh model of the irregular pipe segment obtained in the finite element calculation to form the mesh node displacement of the mesh model of the irregular pipe segment.

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