Finite element model establishment method of pressure-bearing equipment with connecting pipe based on non-uniform spring

Abstract

The invention discloses a finite element model establishment method of pressure-bearing equipment with a connecting pipe based on a non-uniform spring. According to the technical scheme, the method comprises the steps of parametric modeling of the pressure-bearing equipment with the end socket, division of a structural grid and a swept grid, inner and outer face recognition based on an undirected graph, surface node bias based on node projection, analysis area limitation and shrinkage based on the undirected graph, solving of the minimum potential energy problem of a non-uniform spring system based on a gradient descent method and node updating. And adjusting the spring stiffness and generating a final finite element grid. The method mainly aims at solving the problems that when finite element grid division is carried out on a fillet detail structure with a welding seam, the fillet structure with the welding seam remarkably changes the geometric topological relation of a model, manual subdivision is needed, and efficient automation cannot be achieved. According to the method, the function of generating the finite element mesh with weld seam rounding details can be realized only by dividing the mesh for the reference model without weld seam rounding and without manually dividing the target model with the weld seam fillet, and the method has an application value for improving the efficiency of 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 device with a pipe, and in particular to the technical field of a method for establishing a finite element mesh model of a pressure-bearing device with a pipe based on a non-uniform spring. Background Art

[0002] In the field of special equipment, the cylinder, head and pipe are conventional components of pressure equipment, which are usually designed and manufactured according to the conventional design standard GB-150 or the analysis and design standard GB / T-4732. During the design process, finite element analysis verification is usually required. Finite element analysis verification requires a series of steps such as establishing a geometric model, dividing the mesh, performing calculations, extracting stress data, and evaluating according to standards. Among them, the establishment of the geometric model and mesh division are complicated and time-consuming, which significantly limits the efficiency of the relevant verification. In terms of mesh division, since the connection between the pipe and the cylinder and the head is a welded structure, in order to avoid stress singularity, especially in fatigue analysis, it is necessary to divide the fillet of a certain radius. For example, it is stipulated in the boiler standard GB / T-16508: When applying the finite element analysis verification method, all corners of the component should have appropriate fillets, and the fillet radius should not be less than the smaller value of 10mm and 1 / 4 of the thickness of the thicker part. However, the filleting significantly changes the geometric topological structure of the takeover area. The existing technology generally simplifies the topological structure through complex manual segmentation. The related operations have high requirements on personnel and the process is complicated. It usually requires special meshing software (such as Hypermesh software). Different segmentation methods are usually used according to different fillet conditions. Therefore, it is difficult to achieve programming and automation, which significantly limits the efficiency of related work. Summary of the invention

[0003] The purpose of the present invention is to solve the problems in the prior art and propose a finite element model establishment method for pressure-bearing equipment with pipes based on non-uniform springs. The method can realize the function of generating a regular grid of a target model from an easily divided reference geometric model mesh without chamfering through node projection offset and non-uniform stiffness spring analysis. It does not require manual subdivision, which significantly reduces the difficulty of grid division of the chamfered model and has certain reference value to related fields.

[0004] To achieve the above object, the present invention proposes a method for establishing a finite element model of a pressure-bearing device with a pipe based on a non-uniform spring, comprising the following steps: 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; rigidly rotate and translate the nozzle model and the cylinder model based on the center point parameters of the cross sections at both ends; rigidly rotate and translate the head based on the end center point coordinates and the top direction vector; perform Boolean merging on 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 of the tube is used to cut the cylinder body to form an annular area around the tube; for each tube, two auxiliary planes are made through the center points of the cross sections at both ends of the tube and are perpendicular to each other, and the tube and the annular area of ​​the tube 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 can be 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; Among them, the mesh nodes of the outer surface and inner surface of the reference geometric model are obtained based on the mesh node offset of the node projection; the association between the reference geometric model mesh and the reference geometric model is deleted to generate an isolated mesh; the inner and outer geometric surfaces of the target geometric model are imported, and the outer surface nodes and the inner surface nodes are projected onto the outer surface and inner surface of the target geometry respectively according to the shortest distance method; the coordinates of the outer surface and inner surface nodes after projection are recorded; 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 The nodes s greater than eps are 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 P that belong to the manifold surface in the reference geometric model, and record them as P'; take the set of nodes in P' but not in S as P'', and record them as ; 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; as a preferred option, it is recommended to initially take ; 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 node coordinates, based on the mesh quality of the node index, correct The final smoothed mesh is obtained by repeated iterations.

[0005] Preferably, 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.

[0006] Preferably, the internal boundary faces should be retained during the Boolean merging in step 101 - 1 , and for each take-over tube, the additional faces contained in the take-over tube should be deleted.

[0007] Preferably, in step 104-1, The value shall not exceed mm.

[0008] Preferably, in step 104-1, N is an integer between 6 and 10.

[0009] The beneficial effects of the method for establishing a finite element model of a pressure-bearing equipment with a pipe connection based on a non-uniform spring of the present invention are as follows: the present invention aims at the problem that when the finite element mesh is divided for the structure with weld fillet details, the structure with weld fillet significantly changes the geometric topological relationship of the model, requires manual segmentation, and cannot achieve efficient automation. The present invention only needs to mesh the reference geometric model without the weld fillet details of the pipe connection, and the final target geometric model with fillet is automatically obtained by the program by solving a minimum potential energy problem based on the non-uniform spring, thereby avoiding the manual segmentation of the target geometric model with fillet, significantly improving the automation and programming level of the generation of the finite element mesh model of the pressure-bearing equipment with the pipe connection, and improving the 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 in the present invention is convenient for secondary development platforms such as Abaqus The development and software packaging are completed in Python, etc., which is convenient for direct calling later; the inner and outer surface recognition method based on undirected graph proposed in the present invention can realize automatic recognition of the inner and outer surfaces of the reference geometric model and the target geometric model without manual operation; the solution method of the minimum potential energy problem of the non-uniform spring system based on the gradient descent method proposed in the present invention avoids the solution of matrix equations, and can be conveniently compiled and implemented in the form of C language dynamic link library, etc., with fast calculation speed; the analysis area reduction method proposed in the present invention reduces the area that requires mesh smoothing, and only needs to carry out mesh smoothing calculations on the areas near the significant deformation nodes, which further improves the calculation efficiency.

[0010] The features and advantages of the present invention will be described in detail through embodiments in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a general step flowchart of the method for establishing a finite element model of a pressure-bearing device with a pipe connection based on a non-uniform spring of the present invention.

[0012] Figure 2 It is a framework diagram for automatic identification of inner and outer surfaces of the present invention.

[0013] Figure 3 It is a step diagram of the analysis area narrowing method based on the undirected graph BFS of the present invention.

[0014] Figure 4 It is a schematic diagram of the overall dimensions of an engineering example diagram of pressure-bearing equipment including pipe connections.

[0015] Figure 5 It is a schematic diagram of the local dimensions of the pipe in an engineering example drawing of a pipe-bearing pressure equipment.

[0016] Figure 6 It is a component 3D modeling structure diagram.

[0017] Figure 7 It is the overall three-dimensional modeling structure diagram.

[0018] Figure 8 It is a three-dimensional schematic diagram of the segmentation method of taking over the local area.

[0019] Fig. 9 It is a plan view of the segmentation method for taking over the local area.

[0020] Fig.10 It is a structured mesh in the local area of ​​the nozzle and a swept mesh in the area outside the nozzle.

[0021] Fig.11 It is the mesh division diagram near the nozzle intersection area.

[0022] Fig.12 is an undirected graph and a connected branch in this case.

[0023] Fig.13 It is a schematic diagram of the inner and outer surfaces in the automatic recognition effect.

[0024] Fig.14 It is a schematic diagram of the inner surface in the automatic recognition effect of the inner and outer surfaces.

[0025] Fig.15 It is a rounded geometry model with an external 7.5mm taper.

[0026] Fig.16 is the mesh of the intersecting region before projection.

[0027] Fig.17 is the mesh after projection of the intersecting area.

[0028] Fig.18 is the set of significant deformation nodes Schematic diagram.

[0029] Fig.19 It is a schematic diagram of the grid unit E′ to be smoothed.

[0030] Fig. 20 It is a schematic diagram of the boundary unit set E′′.

[0031] Fig.21 This is the mesh division effect diagram of the area near the intersection of nozzle 1 (the influence of the original length of the spring on the initial stiffness is not considered).

[0032] Fig. 22 This is the mesh division effect diagram of the area near the intersection of nozzle 2 (the influence of the original length of the spring on the initial stiffness is not considered).

[0033] Fig.23This is the mesh division effect diagram of the area near the intersection of nozzle 1 (the initial stiffness is inversely proportional to the original length of the spring).

[0034] Fig.24 This is the mesh division effect diagram of the area near the intersection of nozzle 2 (the initial stiffness is inversely proportional to the original length of the spring).

[0035] Fig.25 is based on the stiffness gain factor The grid situation in the area near the intersection of pipe 1.

[0036] Fig.26 is based on the stiffness gain factor The grid situation in the area near the intersection of pipe 2.

[0037] Fig. 27 is based on the stiffness gain factor The grid situation in the area near the intersection of pipe 1.

[0038] Fig.28 is based on the stiffness gain factor The grid situation in the area near the intersection of pipe 2.

[0039] Fig.29 is based on the stiffness gain factor The grid situation in the area near the intersection of pipe 1.

[0040] Fig.30 is based on the stiffness gain factor The grid situation in the area near the intersection of pipe 2.

[0041] Fig.31 This is a partial dimension diagram of the connecting pipe of Example 3.

[0042] Fig.32 This is a diagram of the mesh situation in the vicinity of the intersection with internal and external rounded structures, and the mesh situation before projection.

[0043] Fig.33 This is a diagram of the mesh condition in the vicinity of the intersection with internal and external rounded structures, and the mesh condition before smoothing after projection.

[0044] Fig.34 This is a grid diagram of the intersecting area with internal and external rounded structures. Grid conditions under parameters.

[0045] Fig.35 This is a grid diagram of the intersecting area with internal and external rounded structures. Grid conditions under parameters.

[0046] Fig.36 This is a grid diagram of the intersecting area with internal and external rounded structures. Grid conditions under parameters. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is further described in detail below through 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 intended to limit the scope of the present invention. In addition, in the following description, the description of known structures and technologies is omitted to avoid unnecessary confusion of the concept of the present invention.

[0048] 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 may 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 may be directly connected to the other element or indirectly connected to the other element.

[0049] In the description of the present invention, it should be noted that the terms "center", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, or the positions or positional relationships in which the invention product is usually placed when in use, and are 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 therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", "third" and the like are only used to distinguish descriptions, and cannot be understood as indicating or implying relative importance. Thus, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, "multiple" means two or more, unless otherwise clearly and specifically defined. "Several" means one or more, unless otherwise clearly and specifically defined.

[0050] In the description of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, the terms "set", "install", "connect", and "connect" 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 a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances. Embodiment 1:

[0051] See also Figure 1-Figure 5 The finite element modeling method of the pressure-bearing equipment with a pipe connected to a non-uniform spring according to the present invention includes the following four main steps: Step 101, geometric parameterization and automatic generation of a reference geometric model of a pressure-bearing device with a nozzle; Step 102, automatically identifying the inner and outer surfaces of the reference geometric model and meshing the reference geometric model; Step 103, importing the target geometric model with welding fillet details and automatically identifying the inner and outer surfaces of the target geometric model; Step 104 , mesh node offset based on node projection and mesh smoothing based on the non-uniform spring minimum potential energy principle.

[0052] Among them, in step 101, the 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. The three-dimensional modeling software is called through the API, and the three-dimensional geometric models of the pipe and the main cylinder are generated through the stretching command, and the three-dimensional geometric model of the head is generated through the rotation command, and a separate component model is generated.

[0053] Since the component model is generated in the component's own coordinate system, it is necessary to rotate and translate each component later. The specific method is as follows: The connecting pipe and the cylinder are based on the coordinates of the center points of the two end faces (denoted as ,remember ), determine the direction vector of the center line , the head is based on the coordinates of the end face center point and the top facing direction vector (denoted as ).

[0054] When the component is generated, the center point of the end face of the nozzle and the cylinder and the stretching direction vector are and , Similarly, when the component is generated, the center point of the end face of the head and the top direction vector are recorded as and . Take two vectors , The angle bisector direction vector , first use vector Translation component, then vector Rotate 180 degrees, and finally, with 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.

[0055] 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 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.

[0056] 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.

[0057] 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.

[0058] The mesh smoothing based on the non-uniform spring minimum potential energy principle in step 104 is the core content of the present invention, which realizes the generation of a finite element mesh model with chamfered details without artificial segmentation. The specific implementation steps are as follows: Step 104-1, shrinking the analysis area. Calculate the coordinate difference of all the nodes s on the outer and inner surfaces before and after the projection. , set the threshold , the Euclidean norm Greater than The node s is defined as the set of significant deformation nodes As a preferred option, The value shall not exceed 0.1 mm.

[0059] Define two nodes contained in the same grid unit as adjacent nodes, and construct an undirected graph G of all nodes.

[0060] Specify a positive integer N, As the starting point, a breadth-first search BFS is carried out on G to obtain the set of nodes with significant deformations. For all nodes within and exactly at distance N (respectively denoted as S′ and S′′), the relevant unit sets of S′ and S′′ are obtained as E′ and E′′, respectively. The relevant step diagram is as follows: Figure 3 As shown, it can be seen that through BFS, the final analysis area only contains the grid cells E′ close to S, which reduces the amount of calculation and improves the calculation efficiency.

[0061] In the assessment of conventional pressure-bearing equipment (see GB / T-4732 or ASME standard BPVC Ⅷ.2), not only the average stress on the wall thickness section but also the bending stress that varies linearly along the wall thickness is required. Pressure-bearing equipment and nozzles usually need to be divided into at least 4 layers of grids in the wall thickness direction to accurately capture the bending stress. Therefore, it is appropriate for N to be an integer between 6 and 10. On the one hand, all the grids in the wall thickness direction of the local area can be included in the calculation. On the other hand, it can avoid taking too large a value and increasing the amount of calculation.

[0062] Take all the nodes in E′ and E′′ as , let all the related nodes of E'' be S''', take The nodes in the reference geometric model that belong to the manifold surface are denoted as P′; the set of nodes in P′ but not in S is denoted as P′′. The main purpose is to determine different boundary conditions, where the nodes of the non-significantly deformed nodes and the surface nodes (H) are set to zero displacement boundaries, while the nodes of the significantly deformed nodes are set to zero displacement boundaries. The projected coordinate values ​​need to be maintained.

[0063] 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, ,in, The restriction is to ensure that only one spring is added to a pair of nodes. M is the number of nodes contained in the unit. The two nodes in the reference geometry model are obtained. The distance between , at the node Between, add the initial stiffness as Linear spring.

[0064] It should be pointed out that Is the first source of the non-uniformity of the stiffness of the spring of the present invention, taking The value is to ensure that the spring force is proportional to the extension or compression rate of the spring.

[0065] Step 104-3, optimization calculation based on the minimum potential energy principle. The nodes involved in the calculation are , assume 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 , the specific method is as follows: For a single spring, the potential energy is , respectively and Take the derivatives of each component of :

[0066] 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 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 ,in for The number of nodes in express Middle The three-dimensional gradient components of the nodes (corresponding to In three directions), in order to meet the boundary conditions, if , get the number of s ,Will Set to 0, and obtain the modified gradient vector that is coordinated with the boundary conditions, denoted as ( dimensional vector). In order to control the size of each iteration step, Carry out normalization, the specific method is as follows: Similarly, let , take the maximum value , and obtain the normalized .

[0067] Set the number of iterations and the step size of each iteration ,set up for The three-dimensional coordinate value of the midpoint is calculated iteratively as follows: Each iteration first calculates the normalized gradient vector ,according to renew , , Indicates The three-dimensional component of the node; when the number of iterations reaches the set number When , exit the iteration and return the current The 3D coordinate values ​​of the midside nodes. Can be set manually, larger setting When , each iteration results in a large change in the coordinate value, which can reduce the number of iterations and is recommended for initial fast calculations. When , the coordinate value changes caused by each iteration are small, which is recommended for fine-tuning the grid units.

[0068] Step 104-4, adding the non-uniform stiffness gain coefficient. Based on the topological characteristics of the region near the nozzle intersection, the grid unit of the region where the nozzle and the main body intersect in step 101 is taken as , take the set of significant deformation units The relevant units are , take the set intersection , denoted as the key grid unit set ; Define two mesh cells that share a mesh surface as adjacent cells.

[0069] Pick The set of adjacent cells ,Pick ,in, Performs the difference operation on a set.

[0070] Similarly, take The set of adjacent cells ,Pick .

[0071] 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 .

[0072] 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:

[0073] 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.

[0074] 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.

[0075] The parametric three-dimensional modeling of the reference geometric model is used as an example of parameterization. According to the parameterization method of the pipe and the pressure-bearing equipment, the structure is divided into the main component (motherComponents) and the pipe (pipes). Since the python secondary development platform of the Abaqus software provides a python language interpreter, the parameterization method of this embodiment is represented by a Python list as follows: (1) Parameterization scheme of the main component (represented by a Python list, each component is represented by a Python dictionary): motherComponents=[ {'motherType':'mainPipe','parameters':{'point1':(0,0,0),'point2':(0,0,1000), 'thickness':5, 'outerDiameter':1000}}, {'motherType':'cap','parameters':{'capType':'elliptic','diameter':1000, 'thickness':5, 'orientationUp':[0,0,1], 'center'(0,0,1000), 'type':'outerBased','h':10, 'Height':250}},] As can be seen, the main component contains two Python dictionaries: the first dictionary is about the pipe, where the motherType attribute indicates the type of component (mainPipe represents the main pipe), the parameters attribute gives the geometric parameters of the pipe, and point1 and point2 specify the coordinates of the centers of the two ends of the pipe. Figure 4 The values ​​are (0,0,0) and (0,0,1000mm) respectively. The thickness attribute gives the wall thickness of the cylinder, which is 5mm. The second dictionary is about the head. The motherType attribute indicates that the component type is a head (cap). The parameters parameter gives the geometric parameters of the head, where capType indicates the type of head (here it is an elliptical head). According to the standard "GB / T-25198 Pressure Equipment Head", the elliptical head can be divided into two types: internal reference head and external reference head. For the internal reference head, 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 inner wall height. For the external reference head, the type parameter is set to outerBased, the diameter parameter diameter is the outer diameter, and the height parameter Height is the outer wall height. Figure 4 The head is an external reference head with an outer diameter of 1000mm, a height of 250mm, a wall thickness of 5mm, an end face center coordinate of (0,0,1000mm), a straight edge length of h=10mm, and a top direction vector orientationUp of (0,0,1), which represents the direction vector of the line connecting the top of the head and the end face center point.

[0076] (2) Parameterization scheme of pipes (represented by a Python list pipes, each pipe is represented by a Python dictionary): pipes=[{'point1':(-600,0,500),'point2':(-400,0,500),'thickness':5,'outerDiameter':200}, {'point1':(600,0,500),'point2':(400,0,500),'thickness':5,'outerDiameter':200}].

[0077] Here, the pipes list contains two connecting pipes, both with a thickness of 5 mm and an outer diameter of 200 mm. The positions of the connecting pipes are determined by the center points of the two ends, point1 and point2.

[0078] The tensile modeling command of Abaqus software is used to build the connecting pipe and main cylinder, and the rotation modeling command is used to build the head.

[0079] (3) Rigid rotation, translation, and Boolean merging of components Figure 6 , Figure 7 The 3D modeling results of the single nozzle assembly on the left and the 3D modeling results of the overall pressure-bearing equipment with nozzles are given. It can be seen that after the component is modeled by stretching, The axis is the coordinate system when modeling the component. Since the nozzle is generated by the extrusion feature, the length direction of the component and The axis is consistent, but the length direction of the nozzle in the overall model is The axis direction still needs to be rotated and translated to ensure the coordinate values ​​of point1 and point2. The general method is as follows: The pipe and the cylinder are based on the coordinates of the two end faces (remember ,remember ), determine the direction vector of the center line , the head is based on the coordinates of the end face center point and the top facing direction vector (denoted as ), it is clear that this takeover , , , .

[0080] When the component is generated, the center point of the end face of the nozzle and the cylinder and the stretching direction vector are , , this takeover , , take two vectors , The angle bisector direction vector , here are , first use vector Translation component (here, Panning does not work, for general , the translation cannot be ignored), and then the unit vector Rotate 180 degrees, and finally, with vector By translating the component, the pipe can be moved to a position consistent with the parameters. The rotation and translation operations of other components are similar.

[0081] After all components are moved to the specified position by rigid rotation and translation, the Boolean merge operation is used to generate the overall three-dimensional model. For subsequent meshing, the internal interface needs to be retained during merging, and the cylinder area contained in the inner wall of the nozzle is removed by stretching and deletion to generate the final three-dimensional model (such as Figure 7 ).

[0082] (4) Cutting of the local area.

[0083] 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 , Fig. 9 shown.

[0084] (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. Fig.10 He Ru Fig.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.

[0085] Automatic identification of internal and external surfaces based on undirected graphs. 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.

[0086] 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: Fig.12 As shown: Fig.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. Fig.13 , 14 The effects of automatic recognition and classification of inner and outer surfaces are given, and it can be seen that the method of the present invention can accurately identify inner and outer surfaces. Since inner and outer surfaces are surfaces that require subsequent node projection offset, accurate recognition of inner and outer surfaces is one of the key contents of the present invention.

[0087] The fillet generates the target geometric model and identifies the inner and outer surfaces.

[0088] like Figure 5 As shown, there is a fillet with a radius of 7.5 mm between the connecting pipe and the cylinder. The feature of the present invention is that the fillet details make the topology of the connecting pipe and the cylinder complex in the relevant area. The prior art requires manual segmentation, which is not conducive to automation and programming. The present invention only needs to generate a fillet geometry model without considering mesh division, which greatly reduces manual operation. In this example, the same parameterization method and modeling method as the above steps (1), (2), and (3) are used to generate a reference geometry model, and then a 7.5 mm fillet is set on the outside of the intersection position. The effect is as follows: Fig.15 The inner and outer surfaces can be automatically identified in the same way as in step (6) above.

[0089] Projection-based node offsets for inner and outer surfaces.

[0090] Assume that the outer surface of the reference geometry model is Surf-1, the inner surface is Surf-2, and the outer surface of the target geometry model with rounded corners is S-1, the inner surface is S-2. Since the reference geometry model is meshed, all mesh nodes on Surf-1 and Surf-2 can be taken, recorded as Node-1 set and Node-2 set respectively, and all nodes of Node-1 and Node-2 are projected onto the S-1 and S-2 surfaces respectively according to the shortest distance. In this example, the projectNode command of the Abaqus software platform is used to implement the projection operation.

[0091] Fig.16 , Fig.17 The mesh conditions before and after projection are given. Fig.16 is the mesh condition of the reference geometry model before projection, Fig.17 This is the case of the target geometry model after projection (with external fillet). It can be seen that the projection offsets the outer surface nodes of the reference geometry mesh to the outer surface of the target geometry model. However, the mesh shape is severely distorted after the projection offset and cannot be used directly for calculation. A subsequent mesh smoothing step is required.

[0092] Analysis region reduction based on undirected graphs.

[0093] Depend on Fig.16 , Fig.17 It 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 (In this case, 0.1 mm is used), and 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.

[0094] 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, . Fig.18 , Fig.19 , Fig. 20 In this example, of Set, E′ set and boundary cell set E′′.

[0095] Solving the minimum potential energy problem based on non-uniform springs.

[0096] 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.

[0097] Specific implementation effects.

[0098] The spring stiffness is the inverse of the length Necessity: If the length of the spring is not taken into account , that is, the initial stiffness of all springs is uniformly set to 1, and the gain coefficient , the grid results near the nozzle intersection area are as follows Fig.21 , Fig. 22 As shown. Fig.21 It can be seen that the mesh distortion in the intersection area of ​​pipe 1 is serious. The initial stiffness is set to , the gain factor remains unchanged , the mesh division results are as follows Fig.23 , Fig.24 As shown by Fig.23 , Fig.24 It can be seen that considering the initial stiffness The mesh distortion of takeover 1 is alleviated.

[0099] all Example of the process to obtain a smoothed mesh: To illustrate the gain factor in non-uniform spring stiffness The initial stiffness is set to Then set the gain factor , re-solve the minimum potential energy problem, and the obtained grid is as follows Fig.25 , Fig.26 As shown. And Fig.23 , Fig.24 compared to, Fig.23 , Fig.24 The sharpness of the grid in the area with severe distortion is Fig.25 , Fig.26 The gain factor is adjusted to The grid situation is as follows Fig. 27 , Fig.28 As shown, the gain factor is adjusted to The resulting grid is as follows Fig.29 , Fig.30 As shown. Fig.29 , Fig.30 It can be seen that the mesh shape is regular, the quality is high, and there are no obvious and severe sharp points. This example illustrates how to gradually change the mesh by adjusting the gain factor. Embodiment three:

[0100] See also Fig.31 On the basis of the second embodiment, in order to further illustrate the applicability of the present invention, the overall structure and Figure 4 , Figure 5 Same as above, add a fillet with a radius of 5mm, and take over the local diagram as shown below Fig.31 .

[0101] Since the steps are the same as those in Example 2, Example 3 will only describe the final mesh situation. Figure 32-Figure 36 Shown: before smoothing and after projection ( Fig.33 ) The mesh is severely distorted. Adjust the parameters ( Fig.34 )、 ( Fig.35 )and ( Fig.36 ), it can be seen that the distortion of the mesh is significantly reduced before smoothing. Fig.36 There are no obviously irregular grid units in the figure, which illustrates the effectiveness of the parameter adjustment method proposed in the present invention.

[0102] It should be noted that, although the above embodiments have been described in this article, the scope of patent protection of the present invention is not limited thereby. Therefore, based on the innovative concept of the present invention, changes and modifications made to the embodiments described herein, or equivalent structures or equivalent process changes made using the contents of the present specification and drawings, directly or indirectly applying the above technical solutions to other related technical fields are all included in the scope of protection of the patent of the present invention.

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 can be 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; as a preferred option, it is recommended to initially take ; 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 node coordinates, based on the mesh quality of the node index, 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 1, 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 1, characterized in that: In step 104-1, N is an integer between 6 and 10.

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