Finite Element Model Establishment Method for Pressure-bearing Equipment with Nozzles Based on Non-uniform Springs

Abstract

The present invention discloses a method for establishing a finite element model of a pressure-bearing device with a nozzle based on a non-uniform spring. The technical solution includes parametric modeling of the pressure-bearing device with a head, structural mesh and swept mesh division, inside and outside surface recognition based on an undirected graph, surface node offset based on node projection, analysis area restriction based on an undirected graph, solution of the minimum potential energy problem of the non-uniform spring system based on the gradient descent method, updating nodes, adjusting spring stiffness, and generating the final finite element mesh. It mainly aims at the problem that when dividing the finite element mesh of the structure with the weld fillet detail, the weld fillet structure significantly changes the geometric topology relationship of the model, which requires manual meshing and cannot achieve high-efficiency automation. It realizes the function of generating a finite element mesh with weld fillet details only by meshing the reference model without weld fillets and without manual meshing of the target model with weld fillets, which has application value for improving the efficiency in related fields.

Description

Technical Field

[0001] The present invention relates to the technical field of a method for establishing a finite element mesh model of a pressure-bearing equipment with nozzles, in particular to the technical field of a method for establishing a finite element mesh model of a pressure-bearing equipment with nozzles based on non-uniform springs. Background Art

[0002] In the field of special equipment, cylinders, heads and nozzles are conventional components of pressure-bearing equipment, which are usually designed and manufactured according to the conventional design standard GB-150 or the analytical design standard GB / T-4732. During the design process, finite element analysis and verification are usually required. Finite element analysis and verification require a series of steps such as establishing a geometric model, dividing meshes, performing calculations, extracting stress data, and evaluating according to standards. Among them, the establishment of geometric models and mesh division work is complicated and time-consuming for manual labor, which significantly limits the work efficiency of related verification. In terms of mesh division, since the connection parts between the nozzles and the cylinders and heads are welded structures, in order to avoid stress singularities, especially in fatigue analysis, it is necessary to divide fillets with a certain radius. For example, in the boiler standard GB / T-16508, it is stipulated that when applying the finite element analysis verification method, all corners of the components should have appropriate fillets, and the fillet radius should not be less than the smaller value of 10 mm and 1 / 4 of the thickness of the thicker part. However, the fillets significantly change the geometric topology structure of the nozzle area. The prior art generally simplifies the topology structure through complex manual dissection. The related operations have high requirements for personnel and the process is complex. Usually, special mesh division software (such as Hypermesh software) is required, and different dissection methods are usually adopted according to different fillet situations. Therefore, it is difficult to achieve programming and automation, which significantly limits the related work efficiency. Summary of the Invention

[0003] The purpose of the present invention is to solve the problems in the prior art, and propose a method for establishing a finite element model of a pressure-bearing equipment with nozzles based on non-uniform springs, which can realize the function of generating regular meshes of the target model through node projection offset and non-uniform stiffness spring analysis from the meshes of the reference geometric model without fillets that are easy to divide, without manual dissection, significantly reducing the difficulty of mesh division of the filleted model, and having certain reference value for related fields.

[0004] To achieve the above purpose, the present invention proposes a method for establishing a finite element model of a pressure-bearing equipment with nozzles based on non-uniform springs, including the following steps:

[0005] Step 101, geometric parameterization and automatic generation of the reference geometric model of the pressure-bearing equipment with nozzles; the following steps are automatically realized by the program;

[0006] Step 101-1, Component Modeling and Assembly: First, generate the nozzle, cylindrical shell, and head components in sequence according to the parametric modeling method; rigidly rotate and translate the nozzle model and the cylindrical shell model based on the center point parameters of the two end sections; rigidly rotate and translate the head based on the center point coordinates of the end and the top orientation direction vector; perform Boolean merging on all components that have been rigidly rotated and translated.

[0007] Step 101-2, Cutting of the Local Area of the Nozzle: For each nozzle, based on the outer diameter of the nozzle , set the scale factor , and use an auxiliary cylindrical surface with a diameter of to cut the cylindrical shell to form an annular area around the nozzle; for each nozzle, create two auxiliary planes that pass through the center points of the two end sections of the nozzle and are perpendicular to each other, and cut the nozzle and the nozzle annular area based on the auxiliary planes.

[0008] Step 102, Automatic Identification of the Inner and Outer Surfaces of the Reference Geometric Model and Mesh Generation of the Reference Geometric Model: Extract all geometric surfaces of the reference geometric model, obtain the number of entities corresponding to each surface, that is, count the number of entities with this surface as the boundary, and call the surface with a count of 1 the manifold surface; eliminate all manifold surfaces that are planes, and form an undirected graph for the remaining manifold surfaces according to the adjacent relationship; obtain the connected components of the undirected graph, and after removing the connected components corresponding to the inner wall surfaces of each nozzle, the remaining two connected components are the inner surface and the outer surface, and distinguish the inner and outer by the area size relationship; divide structured grids in the nozzle and the annular area, and generate swept grids along the wall thickness in the remaining area.

[0009] Step 103, Import of the Target Geometric Model with Welding Fillet Details and Automatic Identification of the Inner and Outer Surfaces of the Target Geometric Model: Compared with the reference geometric model, the target geometric model with welding fillet details only differs in the welding fillet area and does not require mesh division, and can be obtained by adding fillet features to the reference geometric model generated in Step 101; the method for automatically identifying the inner and outer surfaces of the target geometric model is the same as that for the reference geometric model.

[0010] Step 104, Mesh Node Offset Based on Node Projection and Mesh Smoothing Based on the Principle of Minimum Potential Energy of Non-uniform Springs.

[0011] Among them, for the mesh node offset based on node projection, obtain the mesh nodes of the outer surface and the inner surface of the reference geometric model respectively; delete the association relationship between the reference geometric model mesh and the reference geometric model to generate isolated meshes; import the inner and outer geometric surfaces of the target geometric model, and project the outer surface nodes and the inner surface nodes onto the outer surface and the inner surface of the target geometry respectively by the shortest distance method; record the coordinates of the projected outer surface and inner surface nodes.

[0012] The mesh smoothing based on the principle of minimum potential energy of non-uniform springs includes:

[0013] Step 104-1: Narrowing of the analysis region, calculating the coordinate differences of all outer and inner surface nodes s before and after projection , setting a threshold , and defining the nodes s with Euclidean norm greater than eps as the set of significantly deformed nodes ; Defining two nodes contained in the same mesh element as adjacent nodes, and constructing an undirected graph G of all nodes; Specifying a positive integer N, starting from , performing a breadth-first search BFS on G, and respectively obtaining all nodes within distance N and exactly at distance N from the set of significantly deformed nodes , denoted as S′ and S′′ respectively, and respectively obtaining the relevant element sets E′ and E′′ of S′ and S′′; Taking all the nodes in E′ and E′′ and denoting them as , denoting all the relevant nodes of E′′ as S′′′, taking the nodes in P that belong to the manifold surface in the reference geometric model, and denoting them as P′; Taking the set of nodes that are in P′ but not in S as P′′, and denoting ;

[0014] Step 104-2: Constructing the initial spring system, traversing the elements in E′, setting the internal node numbers of each element as , for any pair of nodes , where , M is the number of nodes contained in the element, obtaining the distance between the two nodes in the reference geometric model, and adding a linear spring with an initial stiffness of between the nodes ;

[0015] Step 104-3: Optimization calculation based on the principle of minimum potential energy, setting the stiffness of the linear spring as , setting the total potential energy as , where represents the summation over all springs, is the current length of the spring in the iteration step, is the original length of the spring in the initial reference geometric model, are the node numbers at both ends of the spring, is the current three-dimensional coordinate of the node to be optimized, is the three-dimensional coordinate of the node in the reference geometric model, setting the boundary conditions: For the node , setting the zero-value boundary condition, , for the node , setting , based on the gradient descent method, iteratively calculate to make the minimum ;

[0016] Step 104-4, adding the non-uniform stiffness gain coefficient. Based on the topological characteristics near the intersection region of the nozzle, take the mesh elements of the body in the intersection region in Step 101-1 as , take the relevant elements of the significant deformation element set S as , take the set intersection , denoted as the key mesh element set ; Define two mesh elements sharing a mesh face as adjacent elements; take the adjacent element set of , take , where is the set difference operation; similarly, take the adjacent element set of , take ; Respectively set the stiffness gain coefficient of , and multiply the stiffness of the linear spring generated by the elements in in Step 104-2 by times the initial stiffness; Preferably, it is recommended to initially take ;

[0017] Step 104-5, adjust the gain coefficient to optimize the mesh quality, set value, carry out calculations in the method of Step 104-3, obtain the optimal value, update the node coordinates with , and correct value based on the mesh quality under this node index, and iterate repeatedly to obtain the final smoothed mesh.

[0018] Preferably, the nozzle in Step 101 is parameterized by the three-dimensional coordinates of the center points of both ends of the cross-section, wall thickness, and outer diameter; the cylindrical body is parameterized by the three-dimensional coordinates of the center points of both ends of the cross-section, wall thickness, and outer diameter; the elliptical head is parameterized by the straight edge section height, wall thickness, top orientation direction vector, end center point coordinates, head height, and head diameter; the hemispherical head is parameterized by the inner diameter, wall thickness, top orientation direction vector, and three-dimensional coordinates of the end face center point.

[0019] Preferably, during the Boolean union in Step 101-1, the internal boundary faces should be retained, and for each nozzle, the additional faces contained within the nozzle should be deleted.

[0020] Preferably, in Step 104-1, the value is not greater than mm.

[0021] Preferably, in step 104-1, N is an integer between 6 and 10.

[0022] Beneficial effects of the method for establishing a finite element model of a pressure-bearing device with a nozzle based on a non-uniform spring: In view of the problem that when meshing a finite element of a structure with a weld fillet detail, the weld fillet structure significantly changes the geometric topology relationship of the model, requires manual meshing, and cannot achieve high-efficiency automation, the present invention only needs to mesh a reference geometric model without a nozzle weld fillet detail, and finally the target geometric model with a fillet is automatically obtained by the program by solving a minimum potential energy problem based on a non-uniform spring, avoiding manual meshing of the target geometric model with a fillet, significantly improving the automation and programming level of generating a finite element mesh model of a pressure-bearing device with a nozzle, and improving work efficiency; By introducing an initial stiffness inversely proportional to the original length of the spring (the first source of non-uniformity) and setting three spring stiffness gain coefficients (the second source of non-uniformity), the mesh can be interactively modified by adjusting the three spring stiffness gain coefficients to further improve the mesh quality; The modeling and mesh smoothing method proposed by the present invention is convenient for development and software encapsulation on a secondary development platform such as Abaqus Python, etc., and is convenient for direct later calls; The method for automatically identifying the inner and outer surfaces based on an undirected graph proposed by the present invention can realize automatic identification of the inner and outer surfaces of the reference geometric model and the target geometric model without manual operation; The method for solving the minimum potential energy problem of a non-uniform spring system based on the gradient descent method proposed by the present invention avoids solving a matrix equation and can be conveniently compiled and implemented in the form of a C language dynamic link library, etc., with a fast operation speed; The analysis region reduction method proposed by the present invention reduces the region that needs mesh smoothing, and only needs to perform mesh smoothing calculations on the region near significantly deformed nodes, further improving the calculation efficiency.

[0023] The features and advantages of the present invention will be described in detail through embodiments in conjunction with the drawings. Description of the Drawings

[0024] Figure 1 is the overall step block diagram of the method for establishing a finite element model of a pressure-bearing device with a nozzle based on a non-uniform spring of the present invention.

[0025] Figure 2 is the automatic identification framework diagram of the inner and outer surfaces of the present invention.

[0026] Figure 3 is the step diagram of the analysis region reduction method based on undirected graph BFS of the present invention.

[0027] Figure 4 is the overall dimension schematic diagram of an engineering example diagram of a pressure-bearing device with a nozzle.

[0028] Figure 5 It is a schematic diagram of the local dimensions of the nozzle in the engineering example drawing of the pressure-bearing equipment with a nozzle.

[0029] Figure 6 It is a three-dimensional modeling structure diagram of the component.

[0030] Figure 7 It is a three-dimensional modeling structure diagram of the whole.

[0031] Figure 8 It is a three-dimensional schematic diagram of the segmentation method for the local area of the nozzle.

[0032] Figure 9 It is a planar schematic diagram of the segmentation method for the local area of the nozzle.

[0033] Figure 10 It is the structural grid in the local area of the nozzle and the swept grid in the area outside the nozzle.

[0034] Figure 11 It is a mesh division diagram near the intersection area of the nozzle.

[0035] Figure 12 It is the undirected graph and connected components in this case.

[0036] Figure 13 It is a schematic diagram of the outer surface in the automatic recognition effect of the inner and outer surfaces.

[0037] Figure 14 It is a schematic diagram of the inner surface in the automatic recognition effect of the inner and outer surfaces.

[0038] Figure 15 It is a fillet geometric model with an external diameter change of 7.5mm.

[0039] Figure 16 It is the mesh before the projection of the intersection area.

[0040] Figure 17 It is the mesh after the projection of the intersection area.

[0041] Figure 18 It is a set of significantly deformed nodes Schematic diagram.

[0042] Figure 19 It is a schematic diagram of the mesh element E' to be smoothed.

[0043] Figure 20 It is a schematic diagram of the boundary element set E''.

[0044] Figure 21 It is the mesh division effect diagram of the area near the intersection of nozzle 1 (without considering the influence of the original length of the spring on the initial stiffness).

[0045] Figure 22It is the rendering of the meshing in the area near the intersection of nozzle 2 (without considering the influence of the original spring length on the initial stiffness).

[0046] Figure 23 It is the rendering of the meshing in the area near the intersection of nozzle 1 (the initial stiffness is inversely proportional to the original spring length).

[0047] Figure 24 It is the rendering of the meshing in the area near the intersection of nozzle 2 (the initial stiffness is inversely proportional to the original spring length).

[0048] Figure 25 It is based on the stiffness gain coefficient The meshing situation in the area near the intersection of nozzle 1.

[0049] Figure 26 It is based on the stiffness gain coefficient The meshing situation in the area near the intersection of nozzle 2.

[0050] Figure 27 It is based on the stiffness gain coefficient The meshing situation in the area near the intersection of nozzle 1.

[0051] Figure 28 It is based on the stiffness gain coefficient The meshing situation in the area near the intersection of nozzle 2.

[0052] Figure 29 It is based on the stiffness gain coefficient The meshing situation in the area near the intersection of nozzle 1.

[0053] Figure 30 It is based on the stiffness gain coefficient The meshing situation in the area near the intersection of nozzle 2.

[0054] Figure 31 It is the local dimension drawing of the nozzle in Embodiment 3.

[0055] Figure 32 It is the meshing situation diagram of the area near the intersection with internal and external fillet structures, the meshing situation before projection.

[0056] Figure 33 It is the meshing situation diagram of the area near the intersection with internal and external fillet structures, the meshing situation before smoothing after projection.

[0057] Figure 34 It is the meshing situation diagram of the area near the intersection with internal and external fillet structures The meshing situation under the parameters.

[0058] Figure 35 It is the meshing situation diagram of the area near the intersection with internal and external fillet structures The meshing situation under the parameters.

[0059] Figure 36 It is a grid diagram of the area near the intersection with internal and external rounded structures. The grid conditions under the parameters. Specific implementation manners

[0060] To make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. However, it should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the scope of the present invention. In addition, in the following description, the descriptions of well-known structures and technologies are omitted to avoid unnecessarily confusing the concepts of the present invention.

[0061] In the description of the present invention, it should be noted that when an element is referred to as being "fixed to" or "disposed on" another element, it can be directly on the other element or indirectly on the other element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or indirectly connected to the other element.

[0062] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "center", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the product of the present invention is usually placed during use. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus cannot be understood as a limitation to the present invention. In addition, the terms "first", "second", "third", etc. are only used for distinguishing descriptions and cannot be understood as indicating or implying relative importance. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, the meaning of "a plurality" is two or more unless otherwise specifically defined. The meaning of "several" is one or more unless otherwise specifically defined.

[0063] In the description of the present invention, it should also be noted that unless otherwise clearly defined and limited, the terms "set", "installed", "connected", "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations. Embodiment 1:

[0064] Refer to Figures 1-5 , the method for establishing a finite element model of a pressure-bearing device with a nozzle based on a non-uniform spring includes the following four main steps:

[0065] Step 101, geometric parameterization and automatic generation of the reference geometric model of the pressure-bearing device with a nozzle;

[0066] Step 102, automatic identification of the inner and outer surfaces of the reference geometric model and mesh generation of the reference geometric model;

[0067] Step 103, import of the target geometric model with welded fillet details and automatic identification of the inner and outer surfaces of the target geometric model;

[0068] Step 104, mesh node offset based on node projection and mesh smoothing based on the minimum potential energy principle of non-uniform springs.

[0069] Among them, in Step 101, the nozzle is parameterized by the three-dimensional coordinates of the center points of the two end sections, wall thickness, and outer diameter; the cylindrical body is parameterized by the three-dimensional coordinates of the center points of the two end sections, wall thickness, and outer diameter; the elliptical head is parameterized by the height of the straight edge section, wall thickness, top-facing direction vector, end center point coordinates, head height, and head diameter; the hemispherical head is parameterized by the inner diameter, wall thickness, top-facing direction vector, and three-dimensional coordinates of the end face center point. By calling the three-dimensional modeling software through the API, the three-dimensional geometric models of the nozzle and the main cylindrical body are generated through the stretching command, and the three-dimensional geometric model of the head is generated through the revolved body command to generate separate component models.

[0070] Since the component models are generated in the component's own coordinate system, it is necessary to rotate and translate each component subsequently. The specific method is as follows: for the nozzle and the cylindrical body, according to the coordinates of the center points of the two end faces (denoted as , denoted as ), determine the direction vector of the center line, and the head is arranged according to the end face center point coordinates and the top-facing direction vector (denoted as ).

[0071] Denote the end face center point and the stretching direction vector of the nozzle and the cylindrical body when the components are generated as and , similarly, denote the end face center point and the top-facing direction vector of the head when the components are generated as and . Take the angular bisector direction vector , of the two vectors , first translate the component with the vector , then rotate it 180 degrees around the vector , and finally, use the vector By translating the components, you can move them to positions consistent with the parameters. Boolean merge operations are then used to generate the overall 3D model. For subsequent automatic meshing, the internal interfaces must be retained during merging.

[0072] The subsequent automatic meshing method is as follows: for each nozzle, based on the nozzle outer diameter , set the scale factor , usually taken , as the diameter The auxiliary cylindrical surface cuts the cylinder to form an annular area around the pipe. For each pipe, two auxiliary planes are made through the center points of the cross sections at both ends of the pipe and are perpendicular to each other. The pipe and the annular area of ​​the pipe are cut based on the auxiliary planes. The pipe and the annular area are divided into structural grids, and the remaining area is generated along the wall thickness. Sweep grid

[0073] The specific method of automatic inner and outer surface identification described in step 102 and step 103 is as follows. The step diagram is as follows: Figure 2 As shown in the figure: all geometric faces of the reference geometric model or the target geometric model are extracted to obtain the number of entities corresponding to each face, that is, the number of entities with the face as the boundary is counted, and the face with the number 1 is called a manifold face; since the inner and outer surfaces of the conventional cylindrical tube structure are non-planar, all planar manifold faces are eliminated, and two manifold faces that share at least one edge are defined as adjacent, and the remaining manifold faces are constructed into an undirected graph according to the adjacent relationship; the connected branches of the undirected graph are obtained, and after removing the connected branches corresponding to the inner wall surface of each tube, the remaining two connected branches are the inner surface and the outer surface, and the inner and outer surfaces are distinguished by the relationship between the area sizes (wherein the outer wall surface of the tube needs to be eliminated when counting the area), and the larger area is recorded as the outer surface, and the smaller area is recorded as the inner surface.

[0074] In the import of the target geometric model with welding chamfer details described in step 103, it is necessary to ensure that the target geometric model with welding chamfer details is different from the reference geometric model only in the welding chamfer area. The imported target geometric model does not need to be meshed in advance. Preferably, it can be obtained by adding chamfer features to the reference geometric model generated in step 101.

[0075] The specific method of the grid node offset based on node projection described in step 104 is as follows: obtain the grid nodes of the outer surface and inner surface of the reference geometric model respectively; delete the association between the reference geometric model grid and the reference geometric model, make the grid independent of the reference geometric model, and generate an isolated grid; import the inner and outer geometric surfaces of the target geometric model, and project the outer surface nodes and the inner surface nodes onto the outer surface and inner surface of the target geometry respectively according to the shortest distance method; record the coordinates of the outer surface and inner surface nodes after projection.

[0076] The mesh fairing based on the principle of minimum potential energy of non-uniform springs in step 104 is the core content of the present invention, which realizes the generation of a finite element mesh model with fillet details without manual meshing. The specific implementation steps are as follows:

[0077] Step 104-1, reduction of the analysis area. Calculate the coordinate differences of all outer and inner surface nodes s before and after projection , set a threshold , and define the nodes s with Euclidean norm greater than as the set of significantly deformed nodes ; preferably, is taken not to be greater than 0.1 mm.

[0078] Define two nodes contained in the same mesh element as adjacent nodes, and construct an undirected graph G of all nodes.

[0079] Specify a positive integer N, starting from , perform a breadth-first search BFS on G, and respectively obtain all nodes within distance N and exactly at distance N from the set of significantly deformed nodes (denoted as S' and S'' respectively), and respectively obtain the relevant element sets E' and E'' of S' and S'', and the relevant step block diagram is as Figure 3 shown. It can be seen that through BFS, the final analysis area only contains the mesh elements E' close to S, reducing the calculation amount and improving the calculation efficiency.

[0080] In the conventional assessment of pressure-bearing equipment (refer to GB / T-4732 or ASME standard BPVC Ⅷ.2), not only the average stress on the wall thickness section is required, but also the bending stress linearly varying along the wall thickness. Usually, at least 4 layers of meshes are required in the wall thickness direction of the pressure-bearing equipment and the nozzle to accurately capture the bending stress. Therefore, it is appropriate for N to take an integer between 6 and 10, which can, on the one hand, include all the meshes in the wall thickness direction of the local area in the calculation, and on the other hand, avoid taking too large a value and increasing the calculation amount.

[0081] Denote all the nodes in E' and E'' as , denote all the relevant nodes of E'' as S''', take the nodes in that belong to the manifold surface in the reference geometric model, denoted as P'; take the set of nodes that are in P' but not in S as P'', and denote , the main purpose is to determine different boundary conditions. Among them, the non-significantly deformed nodes and the nodes on the surface (H) are set as zero displacement boundaries, while the significantly deformed nodes need to maintain the projected coordinate values.

[0082] Step 104-2: Construct the initial spring system. Traverse the elements in E′. Let the internal node number of each element be . For any pair of nodes , where , where is restricted to ensure that a spring is added to a pair of nodes only once. M is the number of nodes included in the element. Obtain the distance between two nodes in the reference geometric model . Add a linear spring with an initial stiffness of between the nodes .

[0083] It should be noted that is the first source of the non-uniformity of the spring stiffness in the present invention. Taking the value of is to ensure that the spring force is proportional to the stretching or compression rate of the spring.

[0084] Step 104-3: Optimization calculation based on the principle of minimum potential energy. The nodes participating in the calculation are . Let the stiffness of the linear spring be . Let the total potential energy be , where represents the summation over all springs, is the current length of the spring in the iteration step, is the original length of the spring in the initial reference geometric model, are the node numbers at both ends of the spring, is the current three-dimensional coordinate of the node to be optimized, is the three-dimensional coordinate of the node in the reference geometric model. Set the boundary conditions: For the node , set the zero-value boundary condition, . For the node , set . Based on the gradient descent method, iteratively calculate the that minimizes under the boundary conditions. The execution method of the specific method is as follows:

[0085] For a single spring, the potential energy is . Respectively take the derivatives of each component of and :

[0086]

[0087] Traverse all the springs, accumulate the relevant derivatives of the nodes with the same number, and obtain the gradient vector of the total potential energy with respect to the node coordinates (since each node has three coordinate components, the dimension of the gradient vector is 3 times the number of nodes, ), denoted as where is the number of nodes in, represents the three-dimensional gradient component of the th node in (corresponding to three directions). To satisfy the boundary conditions, if , obtain the number of s, and set to 0, thereby obtaining a modified gradient vector that is consistent with the boundary conditions, denoted as (a -dimensional vector). To control the size of each iteration step, normalize as follows: Similarly, let , take the maximum value , and obtain the normalized .

[0088] Set the number of iterations and the step size of each iteration. Let be the three-dimensional coordinate values of the nodes in. The iterative calculation method is as follows: In each iteration, first calculate the normalized gradient vector , and update according to , , represents the three-dimensional component of the th node; when the number of iterations reaches the set number , exit the iteration and return the current three-dimensional coordinate values of the nodes in. can be set manually. When setting a larger , each iteration causes a larger change in the coordinate values, and the number of iterations can be reduced. It is recommended for preliminary rapid calculations. When setting a smaller , each iteration causes a smaller change in the coordinate values, and it is recommended for fine-tuning the mesh elements.

[0089] Step 104-4, addition of non-uniform stiffness gain coefficients. Based on the topological characteristics near the intersection region of the nozzle, take the mesh elements of the nozzle and the main body intersection region in Step 101 as , take the relevant elements of the significantly deformed element set as , and take the set intersection , denoted as the key grid unit set ; Define two mesh cells that share a mesh surface as adjacent cells.

[0090] Pick The set of adjacent cells ,Pick ,in, Performs the difference operation on a set.

[0091] Similarly, take The set of adjacent cells ,Pick .

[0092] Set up separately The stiffness gain coefficient is , the unit set in step [4.2] The stiffness of the generated linear spring, which is a factor of the initial stiffness times; as a preferred option, it is recommended to initially take .

[0093] Step 104-5, adjust the gain coefficient to optimize the mesh quality. value, and calculate using the method in step 104.3 to obtain the optimal value under the current stiffness distribution. value (i.e. the coordinate value returned by step 104.3), Update node coordinates, based on the mesh quality at the node coordinates, correct Numerical,iteration, to obtain the final smoothed mesh. Embodiment 2:

[0094] As an example, based on the first embodiment, the implementation method and specific effects of the present invention are described in detail based on the Python secondary development platform of ABAQUS software.

[0095] like Figure 4 , Figure 5 As shown, the pressure-bearing equipment consists of a cylinder with an outer diameter of 1000mm and a length of 1000mm and an elliptical head with a height of 250mm and a straight side section length of 10mm. There are two connecting pipes of the same size on the left and right sides. The outer diameter of the connecting pipe is 200mm, the center line is 500mm away from the end of the cylinder, the outer end face of the connecting pipe is 600mm away from the center line of the cylinder, the length of the connecting pipe is 200mm, and a 7.5mm chamfer is opened on the outside. The wall thickness of the pressure-bearing equipment and the connecting pipe is 5mm.

[0096] Parametric 3D modeling of the reference geometric model. As an example of parameterization, according to the parameterization method of nozzles and pressure-bearing equipment, the structure is divided into main components (motherComponents) and nozzles (pipes). Since the Python secondary development platform of Abaqus software provides an interpreter for the Python language, the parameterization method of this embodiment is represented by a Python list as follows:

[0097] (1) Parametric scheme for main components (represented by a Python list, each component is represented by a Python dictionary):

[0098] motherComponents=

[0099] {'motherType':'mainPipe', 'parameters': {'point1': (0, 0, 0), 'point2': (0, 0, 1000), 'thickness': 5, 'outerDiameter': 1000}},

[0100] {'motherType': 'cap', 'parameters': {'capType': 'elliptic', 'diameter': 1000, 'thickness': 5, 'orientationUp': [0, 0, 1], 'center':(0, 0, 1000), 'type': 'outerBased', 'h': 10, 'Height': 250}},]

[0101] It can be seen from this that the main component contains two Python dictionaries: the first dictionary is about the cylinder. Among them, the motherType attribute represents the type of the component (using mainPipe to represent the main cylinder), and the parameters attribute gives the geometric parameters of the cylinder. point1 and point2 specify the coordinates of the centers of the two ends of the cylinder. According to Figure 4Take the values (0, 0, 0) and (0, 0, 1000mm) respectively. The thickness attribute gives the wall thickness of the cylinder, with a value of 5mm. The second dictionary is about the head. The motherType attribute indicates that the type of the component is a head (cap). The parameters parameter gives the geometric parameters of the head. Among them, capType represents the type of the head (here it is an elliptical head). According to the standard "GB / T - 25198 Pressure Equipment Heads", elliptical heads can be divided into two types: inner - based heads and outer - based heads. For inner - based heads, the type parameter is set to innerBased. At this time, the diameter parameter diameter is the inner diameter, and the height parameter Height is the height of the inner wall surface. For outer - based heads, the type parameter is set to outerBased, the diameter parameter diameter is the outer diameter, and the height parameter Height is the height of the outer wall surface. According to Figure 4 , the head is an outer - based head, with an outer diameter diameter = 1000mm, a height Height = 250mm, a wall thickness thickness = 5mm, the center coordinates center of the end face is (0, 0, 1000mm), the straight - side section length h = 10mm, and the top - facing direction vector orientationUp is (0, 0, 1), which represents the direction vector of the line connecting the top of the head and the center point of the end face.

[0102] (2) Parametric scheme for nozzles (represented by a Python list pipes, and each nozzle is represented by a Python dictionary):

[0103] pipes = [{'point1': (-600, 0, 500), 'point2': (-400, 0, 500), 'thickness': 5, 'outerDiameter': 200},

[0104] {'point1': (600, 0, 500), 'point2': (400, 0, 500), 'thickness': 5, 'outerDiameter': 200}].

[0105] Here, the pipes list contains two nozzles. The thickness thickness is 5mm for both, and the outer diameter outerDiameter is 200mm for both. The positions of the nozzles are determined by the two end - center points point1 and point2.

[0106] Call the stretching modeling command of Abaqus software to establish the nozzles and the main cylinder, and call the revolved - body modeling command to establish the head.

[0107] (3)Rigid rotation, translation and Boolean union of components

[0108] Figure 6 , Figure 7 The three - dimensional modeling results of the single nozzle component on the left - hand side nozzle and the three - dimensional modeling results of the overall pressure - bearing equipment with nozzles are given. It can be seen that after the component is modeled by extrusion, The axis is the coordinate system when modeling the component. Since the nozzle is generated by an extrusion feature, the length direction of the component is consistent with the axis. However, in the overall model, the length direction of the nozzle is the axis direction, and rotation and translation are still required to ensure the coordinate values of nozzle point1 and point2. The general method is as follows: For the nozzle and the cylinder, according to the center - point coordinates of the two end faces (denoted as , denoted as ), the direction vector of the center line is determined. For the head, according to the center - point coordinates of the end face and the top - facing direction vector (denoted as ). Obviously, in this nozzle , , , .

[0109] Denote the center - point of the end face of the nozzle and the cylinder and the extrusion direction vector when the component is generated as , . For this nozzle , . Take the angular - bisector direction vector of the two vectors . Here, there is . First, translate the component with the vector (here, the translation with has no effect. For the general case of , translation cannot be ignored). Subsequently, rotate 180 degrees around the unit vector . Finally, translate the component with the vector , and the nozzle can be moved to a position consistent with the parameters. The rotation and translation operation methods for other components are similar. After moving all components to the specified position through rigid rotation and translation, a Boolean union operation is performed to generate the overall three - dimensional model. For subsequent mesh generation, the internal interface needs to be retained during the union. The cylinder region contained within the inner wall of the nozzle is removed by extrusion deletion to generate the final three - dimensional model (as shown in

[0110] ). Figure 7 ).

[0111] (4) Cutting of the local area of the nozzle.

[0112] Since the nozzle area is a key area, a finer grid is required to capture stress changes. For each nozzle, based on the outer diameter of the nozzle , set the scale factor , in this example, , as the diameter The auxiliary cylindrical surface cuts the cylinder to form an annular area around the pipe; for each pipe, two auxiliary planes are made through the center points of the cross-sections at both ends of the pipe and are perpendicular to each other. The pipe and the annular area of ​​the pipe are cut based on the auxiliary planes. The effect is as follows Figure 8 , Figure 9 shown.

[0113] (5) Mesh generation method: For the local area of ​​the pipe, since the Boolean merge retains the internal boundaries, each body in the local area can be divided into a structural hexahedral mesh. The area outside the pipe can be divided into a swept mesh along the wall thickness direction. Using the Abaqus software platform, in order to capture the stress distribution in the wall thickness direction, it is necessary to divide more than 4 layers of mesh in the wall thickness direction. The meshing effect of this case is shown in the figure below. Figure 10 He Ru Figure 11 As shown in the figure, due to the existence of the annular area near the take-over pipe, a structured mesh can be generated, which is convenient for controlling the mesh quality and meeting the analysis requirements of the discontinuous area.

[0114] Automatic identification of internal and external surfaces based on undirected graphs.

[0115] Extract all geometric faces of the reference geometric model or the target geometric model, obtain the number of entities corresponding to each face, that is, count the number of entities with the face as the boundary, and call the face with the number 1 a manifold face; eliminate all manifold faces that are planes, and construct an undirected graph for the remaining manifold faces according to adjacency, wherein two manifold faces are defined as adjacent when they share any edge; obtain the connected branches of the undirected graph, and after removing the connected branches corresponding to the inner wall surface of each connecting pipe, the remaining two connected branches are the inner surface and the outer surface. After eliminating the outer surface of each connecting pipe, the inner and outer surfaces are distinguished based on the principle that the remaining total area of ​​the outer surface is greater than the remaining total area of ​​the inner surface.

[0116] In this case, the total number of faces in the model is 161, of which the total number of manifold faces after removing the plane is 68. According to the adjacent relationship of the faces, an undirected graph is constructed for the 68 manifold faces and connected branches are extracted. The results are as follows: Figure 12 As shown: Figure 12 The numbers in the figure represent the number of the surface. There are four connected branches, of which branch 2 and branch 3 represent the inner wall surfaces of the two nozzles, and the remaining branch 1 and branch 4 represent the inner and outer wall surfaces. However, only the connected branches are not enough to determine the inner and outer relationship of branches 1 and 4. After eliminating all the outer wall surfaces of the nozzles, the remaining total areas of branches 1 and 4 are , , therefore, it is determined that branch 4 is the outer surface and branch 1 is the inner surface. Figure 13 、 14 The effects of automatic recognition and classification of the inner and outer surfaces are given. It can be seen that the method of the present invention can accurately identify the inner and outer surfaces. Since the inner and outer surfaces are the surfaces that require subsequent node projection offset, accurately identifying the inner and outer surfaces is one of the key contents of the present invention.

[0117] Generate the target geometric model with fillets and identify the inner and outer surfaces.

[0118] As Figure 5 shown, there is a fillet with a radius of 7.5 mm on the outside between the nozzle and the cylinder. The feature of the present invention is that the fillet details make the topology of the nozzle and the cylinder complex in the relevant area. The prior art requires manual meshing, which is not conducive to automation and programming. The present invention only needs to generate the fillet geometric model without considering mesh division, greatly reducing manual operations. In this example, the same parametric method and modeling method as the above steps (1), (2), and (3) are adopted to generate the reference geometric model, and then a 7.5 mm fillet is set outside the intersection position. The effect is as Figure 15 shown. The inner and outer surfaces can be automatically recognized according to the same method as step (6) above.

[0119] Node offset of the inner and outer surfaces based on projection.

[0120] Let the outer surface of the reference geometric model be Surf-1, the inner surface be Surf-2, the outer surface of the target geometric model with fillets be S-1, and the inner surface be S-2. Since the reference geometric model is meshed, all mesh nodes on Surf-1 and Surf-2 can be taken, denoted as the Node-1 set and the Node-2 set respectively. All nodes of Node-1 and Node-2 are projected onto the S-1 and S-2 surfaces according to the shortest distance. In this example, the projectNode command of the Abaqus software platform is used to implement the projection operation.

[0121] Figure 16 、 Figure 17 show the mesh conditions before and after projection. Figure 16 is the mesh condition of the reference geometric model before projection. Figure 17 is the situation of the target geometric model after projection (with external fillets). It can be seen that the projection offsets the outer surface nodes of the reference geometric mesh to the outer surface of the target geometric model. However, after the projection offset, the mesh shape is severely distorted and cannot be directly used for calculation, and subsequent mesh smoothing steps are required.

[0122] Analysis region reduction based on undirected graph.

[0123] From Figure 16 、 Figure 17It can be seen that the node offset only moves the outer nodes to the target position, but the inner nodes do not move, resulting in serious unit distortion and cannot be applied to subsequent calculations. Therefore, on the one hand, it is necessary to smooth the mesh to reduce mesh distortion. On the other hand, since only a small number of nodes move during the node projection process, only the mesh near the few mobile nodes needs to be analyzed and smoothed. Therefore, limiting the analysis area is of great value in reducing the amount of calculation and improving efficiency. The present invention proposes an undirected graph method based on mesh connectivity to limit the analysis area. The specific steps include: first calculating the inner and outer surface nodes before and after the projection s The coordinate difference of , then set the threshold (0.1mm in this example), we get The Euclidean norm of The nodes are recorded as a set If there is a grid unit that contains two nodes at the same time, the two nodes are called adjacent, and the undirected graph G of all nodes is constructed by the adjacent relationship.

[0124] Set a positive integer N, Set as the starting point, carry out depth-first search BFS in G, and obtain The nodes within the distance of N are recorded as S′, and the The node with a distance of exactly N is recorded as S''; the unit set related to the node S' is recorded as E', and the unit set related to the node S'' is recorded as E''. According to this method, only the mesh units in E' need to be smoothed in the future. As a preferred method, since the wall thickness of the pressure-bearing equipment pipe and the cylinder usually requires at least 5 layers of mesh (6 layers of mesh in the wall thickness direction in this example) to capture the stress distribution in the wall thickness direction, N can be a positive integer between 6 and 10. In this example, . Figure 18 , Figure 19 , Figure 20 In this example, of Set, E′ set and boundary cell set E′′.

[0125] Solving the minimum potential energy problem based on non-uniform springs.

[0126] This embodiment is based on the Python secondary development platform of Abaqus. However, since Python is an interpreted language, it is not suitable for situations with large amounts of calculations. The amount of calculation required to solve the minimum potential energy problem is large. Therefore, Python's ctypes library is used to compile and generate a dynamic link library in C language for solving the minimum potential energy problem. Python imports the dynamic link library through the CDLL command.

[0127] Specific implementation effects.

[0128] The spring stiffness takes the reciprocal of the length Necessity:

[0129] If the length of the spring is not considered , that is, if the initial stiffness of all springs is uniformly set to 1, the gain coefficient , the mesh results near the intersection area of the nozzle are as Figure 21 , Figure 22 shown. It can be seen from Figure 21 that the mesh distortion in the intersection area of nozzle 1 is severe. By considering effect, the initial stiffness is set to , and the gain coefficient remains unchanged , the divided mesh results are as Figure 23 , Figure 24 shown. It can be seen from Figure 23 , Figure 24 that considering the influence of in the initial stiffness, the mesh distortion of nozzle 1 is alleviated.

[0130] Example of the process of obtaining a smoothed mesh:

[0131] To illustrate the effectiveness of the gain coefficient in the non-uniform spring stiffness, after the initial stiffness is set to , the gain coefficient is set to , and the minimum potential energy problem is solved again. The obtained mesh conditions are as Figure 25 , Figure 26 shown. Compared with Figure 23 , Figure 24 , the sharpness of the mesh at the severely distorted areas in Figure 23 , Figure 24 is significantly alleviated in Figure 25 , Figure 26 . When the gain coefficient is adjusted to , the obtained mesh conditions are as Figure 27 , Figure 28 shown. When the gain coefficient is adjusted to , the obtained mesh conditions are as Figure 29 , Figure 30 shown. It can be seen from Figure 29 , Figure 30 that the mesh shape is regular, the quality is high, and there are no obvious severe sharp points. This example illustrates that by adjusting the gain coefficient, the mesh conditions can be gradually changed. Example 3:

[0132] Referring to Figure 31 , on the basis of Example 2, to further illustrate the applicability of the present invention, the overall structure and Figure 4 , Figure 5 ​Consistent, add an internal fillet with a radius of 5 mm. The partial view of the nozzle is as shown in Figure 31 .

[0133] Since the steps are the same as those in the second embodiment, therefore, the third embodiment only describes the final mesh situation. The mesh element situation in the area near the nozzle before projection, after projection offset, and after mesh fairing is as shown in Figures 32-36 : After projection before fairing ( Figure 33 ), there are serious distortions in the mesh. The parameters ( Figure 34 ) ( Figure 35 ) ( Figure 36 ) are adjusted in sequence. It can be seen that compared with before fairing, the distortion of the mesh is significantly reduced. Figure 36 There are no obvious irregular mesh elements, which demonstrates the effectiveness of the parameter adjustment method proposed by the present invention.

[0134] It should be noted that although the above embodiments have been described in this article, the patent protection scope of the present invention is not limited thereby. Therefore, based on the innovative concept of the present invention, any changes and modifications made to the embodiments described in this article, or equivalent structural or equivalent process transformations made using the content of the specification and drawings of the present invention, directly or indirectly applying the above technical solutions to other related technical fields, are all included in the protection scope of the present invention patent.

Claims

1. A finite element modeling method for pressure-bearing equipment with a pipe connection based on a non-uniform spring, characterized in that: The following steps are involved: Step 101, geometric parameterization and automatic generation of a reference geometric model of a pressure-bearing device with a nozzle; the following steps are automatically implemented by a program; Step 101-1, component modeling and assembly, first generate the nozzle, cylinder and head components in sequence according to the parametric modeling method; based on the center point parameters of the cross sections at both ends, rigidly rotate and translate the nozzle model and the cylinder model; based on the end center point coordinates and the top direction vector, rigidly rotate and translate the head; Boolean merge of all rigidly rotated and translated components; Step 101-2, cutting of the local area of ​​the pipe, for each pipe, based on the outer diameter of the pipe , set the scale factor , as the diameter The auxiliary cylindrical surface cuts the cylinder body to form an annular area around the tube; For each pipe, two auxiliary planes are made through the center points of the cross sections at both ends of the pipe and are perpendicular to each other, and the pipe and the pipe annular area are cut based on the auxiliary planes; Step 102, automatically identifying the inner and outer surfaces of the reference geometric model and meshing the reference geometric model, extracting all geometric faces of the reference geometric model, obtaining the number of entities corresponding to each face, that is, counting the number of entities with the face as the boundary, and calling the face with a number of 1 as a manifold face; eliminating all manifold faces that are planes, and forming an undirected graph for the remaining manifold faces according to the adjacent relationship; obtaining the connected branches of the undirected graph, after removing the connected branches corresponding to the inner wall surface of each nozzle, the remaining two connected branches are the inner surface and the outer surface, and the inner and outer surfaces are distinguished by the relationship of area size; dividing the structural grid in the nozzle and the annular area, and generating a swept grid along the wall thickness in the remaining area; Step 103, importing the target geometric model with welding chamfer details and automatically identifying the inner and outer surfaces of the target geometric model; the target geometric model with welding chamfer details is different from the reference geometric model only in the welding chamfer area and does not need to be meshed, and is obtained by adding chamfer features to the reference geometric model generated in step 101; The method for automatically identifying the inner and outer surfaces of the target geometric model is the same as that for automatically identifying the inner and outer surfaces of the reference geometric model; Step 104 , mesh node offset based on node projection and mesh smoothing based on the non-uniform spring minimum potential energy principle.

2. The method for establishing a finite element model of a pressure-bearing device with a pipe connection based on a non-uniform spring according to claim 1, characterized in that: The mesh nodes of the outer surface and the inner surface of the reference geometric model are obtained respectively by mesh node offset based on node projection; Deleting the association between the reference geometry model mesh and the reference geometry model to generate an isolated mesh; Import the inner and outer geometric surfaces of the target geometric model, project the outer surface nodes and inner surface nodes onto the outer and inner surfaces of the target geometry respectively according to the shortest distance method; and record the coordinates of the outer and inner surface nodes after projection.

3. The method for establishing a finite element model of a pressure-bearing device with a pipe connection based on a non-uniform spring according to claim 1, characterized in that: Mesh smoothing based on the non-uniform spring minimum potential energy principle includes: Step 104-1, the analysis area is narrowed down, and the coordinate difference of all the nodes s on the outer and inner surfaces before and after the projection is calculated. , set the threshold , the Euclidean norm Greater than The node s is defined as the set of significant deformation nodes ; Define two nodes contained in the same grid unit as adjacent nodes, and construct an undirected graph G of all nodes; specify a positive integer N, with As the starting point, a breadth-first search BFS is carried out on G to obtain the set of nodes with significant deformations. All nodes within and exactly at distance N are denoted as S′ and S′′, respectively. The relevant unit sets of S′ and S′′ are obtained as E′ and E′′ respectively. All nodes in E′ and E′′ are denoted as , let all the related nodes of E'' be S''', take The nodes in the reference geometry model that belong to the manifold surface are denoted as P′; the nodes in P′ but not in The node set in is P′′, let ; Step 104-2, construct the initial spring system, traverse the units in E′, and set the internal node number of each unit to , for any pair of nodes ,in, , M is the number of nodes contained in the unit, and the two nodes in the reference geometric model are obtained. The distance between , at the node Between, add the initial stiffness as Linear spring; Step 104-3, based on the optimization calculation of the minimum potential energy principle, assume that the linear spring The stiffness is , let the total potential energy be ,in, represents the sum of all springs, is the spring in the iteration step The current length of The spring in the initial reference geometry model The original length of Number the nodes at both ends of the spring. is the current three-dimensional coordinate of the node to be optimized, is the 3D coordinate of the node in the reference geometry model. Set the boundary conditions: , set zero boundary conditions, , for the node ,set up Based on the gradient descent method, the iterative calculation satisfies the boundary conditions. Smallest ; Step 104-4, adding the non-uniform stiffness gain coefficient, based on the topological characteristics of the pipe intersection area, the grid unit of the intersection area body in step 101-1 is taken as , take the relevant unit of the significant deformation unit set S as , take the set intersection , denoted as the key grid unit set ; Define two grid cells that share a grid surface as adjacent cells; Take The set of adjacent cells ,Pick ,in Perform the difference operation on the set; similarly, take The set of adjacent cells ,Pick ; respectively set The stiffness gain coefficient is , replace the The stiffness of the linear spring generated by the element in the middle, the gain is the initial stiffness times; initial ; Step 104-5, adjust the gain coefficient to optimize the grid quality, set value, and calculate using the method in step 104-3 to obtain the optimal value under the current stiffness distribution. Value, with Update the node coordinates, based on the mesh quality at the node coordinates, correct Numerical,iteration, to obtain the final smoothed mesh.

4. The method for establishing a finite element model of a pressure-bearing device with a pipe connection based on a non-uniform spring according to claim 1, characterized in that: In step 101, the connecting pipe is parameterized by the three-dimensional coordinates of the center points of the cross sections at both ends, the wall thickness, and the outer diameter; the cylinder is parameterized by the three-dimensional coordinates of the center points of the cross sections at both ends, the wall thickness, and the outer diameter; the elliptical head is parameterized by the straight edge height, wall thickness, top direction vector, end center point coordinates, head height, and head diameter; the hemispherical head is parameterized by the inner diameter, wall thickness, top direction vector, and end face center point three-dimensional coordinates.

5. The method for establishing a finite element model of a pressure-bearing device with a pipe connection based on a non-uniform spring according to claim 1, characterized in that: In step 101 - 1 , the internal boundary faces should be retained during the Boolean merging, and for each take-over tube, the additional faces contained in the take-over tube should be deleted.

6. The method for establishing a finite element model of a pressure-bearing device with a pipe connection based on a non-uniform spring according to claim 3, characterized in that: In step 104-1 The value shall not exceed 0.1mm.

7. The method for establishing a finite element model of a pressure-bearing device with a pipe connection based on a non-uniform spring according to claim 3, characterized in that: In step 104-1, N is an integer between 6 and 10.

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