Modeling of random pitting in arbitrary shaped hull structures

Abstract

The application discloses a modeling method of random pitting in an arbitrary shape shell structure, randomly generates a pitting and a pitting radius, randomly selects a grid node and judges whether the position of the grid node has the pitting, if not, temporarily assigns the position of the randomly selected grid node and the pitting radius information to the pitting, compares the generated temporary pitting with the existing pitting generated before one by one, if the distance satisfies the condition of not overlapping, generates the pitting at the randomly selected grid node; establishes a cylinder with the radius of the pitting radius and the height capable of penetrating through the thickness of the shell, carries out a Boolean operation between the cylindrical surface of each cylinder and the shell surface of the pitting area to obtain a pitting area; changes the thickness of all units in the pitting area, sets the offset direction of the pitting, and obtains a finite element analysis model; the application truly simulates the random state of the pitting by randomly determining the coordinates of the pitting distribution, randomly arranging the pitting, and randomly determining the pitting radius, thickness and offset mode.

Description

Technical Field

[0001] This invention relates to the field of finite element analysis model construction technology for random pitting structures, and in particular to a parametric modeling method for constructing random pitting damage on the surface of shell structures of arbitrary shapes, applicable to finite element analysis models constructed using SHELL or SOLID elements. Background Technology

[0002] Hollow spheres, steel pipes, and flat plates are widely used in marine engineering, industrial construction, deep-sea exploration, and aerospace engineering. During their service life, these structures inevitably suffer from environmental corrosion, which over time alters their performance and condition, affecting their safety in normal operation. Pitting corrosion is a common type of corrosion damage, with its geometric parameters exhibiting spatiotemporal random variations. Accurately describing the randomness of pitting damage is a prerequisite for assessing the true load-bearing capacity of corrosion-damaged structures, enabling timely maintenance measures to ensure safe operation and maximize their service life.

[0003] Current numerical modeling methods for pitting damage structures are only applicable to structures with single, regular shapes such as flat plates, cylindrical shells, and spherical shells. In the modeling process, solid elements are often used to simulate the structure and pits, with the internal shape of the pits obtained through Boolean operations between the sphere, cylinder, or cone and the structure. For example, Chinese Patent Publication No. CN112417738A, entitled "A Numerical Calculation Method for a Spherical Pressure Shell with Random Pitting Defects," discloses a modeling method for establishing randomly distributed spherical pits on the outer surface of a three-dimensional spherical pressure shell. However, it does not consider the randomness of pit size and internal corrosion depth, and is only applicable to spherical shells, not to engineering structures with irregular shapes. Similarly, the parametric modeling method for constructing random ellipsoidal pits on the surface of a circular tube, proposed in Chinese Patent Publication No. CN112668132A, aims to simulate the random distribution of ellipsoidal pitting, but it does not consider other shell structures in real engineering structures that cannot be represented by sphere center coordinates, and is also unsuitable for irregularly shaped structures. A fully automated modeling method for constructing random pitting in a plate solid structure is proposed in Chinese Patent Publication No. CN109002592A. The method randomly determines the pitting location by limiting the size of the plate structure in Cartesian coordinate system. All generated pits have the same depth. It aims to simulate the random distribution of cylindrical pitting on a plate structure. However, it is not suitable for structures with curved surfaces, and solid modeling increases the number of structural elements and computational cost. Summary of the Invention

[0004] The purpose of this invention is to solve the problems of existing random pitting structure modeling techniques, which cannot realistically simulate pitting damage in actual structures and are not applicable to irregularly shaped structures. The invention proposes a modeling method for random pitting in shell structures of arbitrary shapes, which can more realistically simulate pitting damage in actual structures.

[0005] To achieve the above objectives, the modeling method for random pitting corrosion in shell structures of arbitrary shapes in this invention adopts the following technical solution: including the following steps:

[0006] S1. Using the centroid of the arbitrary-shaped shell structure as the origin of the global coordinate system, establish the geometric model of the structure, and set the pitting area, number of pits, pit radius range, and pit thickness range of the shell structure.

[0007] S2. Divide the pitting area into finite element meshes, record the positions of the mesh nodes in the global coordinate system and whether there are pits, and then delete the finite element mesh.

[0008] S3. Randomly generate a pit and its radius. Randomly select a grid node and determine if there is a pit at its location. If there is a pit, reselect the grid node and re-determine. If there is no pit, temporarily assign the location of the randomly selected grid node and the pit radius information to the pit to generate a temporary pit.

[0009] S4. Compare the generated temporary pits with the previously generated existing pits one by one. If the distance between the temporary pit and the existing pits satisfies the condition that the two do not overlap, then generate a pit at a randomly selected grid node.

[0010] S5. Repeat steps S3-S4 until all pits are generated. Using the origin of the global coordinate system as the origin of the local cylindrical coordinate system, and the line connecting the origin and the location of the pit as the normal of the local coordinate system, establish a cylinder with a radius equal to the radius of the pit and a height that can penetrate the thickness of the shell. Generate the geometric model of each pit. Perform Boolean operation between the cylindrical surface of each cylinder and the shell surface of the pitting area to obtain the pit area.

[0011] S6. Freely generate the finite element mesh for the entire shell structure;

[0012] S7. Change the thickness of all units within the pitted area to simulate a corrosion region of random thickness; set the offset direction of the pits to simulate corrosion on the inner or outer surface of the shell structure, obtain the finite element analysis model of the randomly pitted shell, and complete the construction of the random pitting model in the shell structure of arbitrary shape.

[0013] Furthermore, in S2, a two-dimensional array PitPool(N,4) is defined to record the mesh nodes of the finite element mesh. The X, Y, and Z coordinates of mesh node j in the global coordinate system are stored in PitPool(j,1) = X j PitPool(j,2) = Y j PitPool(j,3) = Z j PitPool(j,4)=0 indicates that there is no pit at the grid node j, and PitPool(j,4)=1 indicates that pits have been placed at the grid node j; 1≤j≤N, where N is the number of finite element grid nodes;

[0014] Furthermore, in S3, a two-dimensional array Pit(M,5) is defined to record the position and radius of the pit in the global coordinate system. M is the number of pits. Pit(k,1), Pit(k,2), and Pit(k,3) represent the X, Y, and Z coordinates of the pit, respectively. Pit(k,4) represents the radius of the pit. Pit(k,5) indicates whether the pit is located on the inner or outer surface of the spherical shell. Pit(k,5) = 1 or 2, where 1 represents the outer surface and 2 represents the inner surface, and 1 ≤ k ≤ M.

[0015] The present invention has the following beneficial effects:

[0016] 1. This invention, based on a parametric programming language, implements a finite element modeling method for pitting corrosion structures with random distribution, shape, and thickness. By randomly determining the coordinates of the pitting corrosion distribution, randomly arranging pits in different regions of the pitting corrosion structure, and randomly determining the radius, thickness, and offset of the pits, a finite element analysis model of any shape can be constructed, exhibiting universality and realism.

[0017] 2. This invention can simulate different corrosion conditions of damaged structures and can simulate random corrosion of thin-walled shell structures, including the local distribution of pitting pits, the random number of pits, and the random characteristics of pit area, shape and thickness. It can effectively construct a finite element analysis model of damaged structures in harsh environments and has practical application value for performance evaluation of in-service structures.

[0018] 3. This invention can realistically simulate the random state of the distribution, shape and thickness of pitting, accurately analyze the stress concentration behavior of pitting damage structures, and reveal the law of pitting damage affecting the structural bearing capacity. Attached Figure Description

[0019] Figure 1 This is a flowchart of the modeling method for random pitting in shell structures of arbitrary shapes according to the present invention;

[0020] Figure 2 This is a geometric model diagram of a spherical shell structure.

[0021] Figure 3 for Figure 2 A schematic diagram of the finite element model of the spherical shell structure;

[0022] Figure 4 A diagram illustrating the process of creating the first cylindrical pit in a spherical shell structure;

[0023] Figure 5 A schematic diagram of the finite element model of erosion pits in a spherical shell structure;

[0024] Figure 6 A schematic diagram of a global surface random pitting model;

[0025] Figure 7 for Figure 6 A magnified view of a section of the medium-sized erosion pit region I;

[0026] Figure 8 A schematic diagram showing the structure of the pitting area and the improved area;

[0027] Figure 9 A schematic diagram showing random pitting corrosion occurring in a portion of the surface of a spherical shell;

[0028] Figure 10 This is a schematic diagram illustrating the random pitting corrosion that occurs in the column shell according to the present invention;

[0029] Figure 11 This is a schematic diagram illustrating the random pitting corrosion that occurs on a shell of arbitrary shape according to the present invention. Detailed Implementation

[0030] The technical solutions in the embodiments of the present invention will be clearly and completely described below, so that those skilled in the art can better understand the advantages and features of the present invention, thereby making a clearer definition of the scope of protection of the present invention. The embodiments described in this invention are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] The specific steps of this invention are as follows:

[0032] S1, see also Figure 1 The parameters such as pit size, pitting area, and number of pits M are set for the shell structure. The pit size includes the pit radius range [r] L ,r U ] and the thickness range of the erosion pit area [d L ,d U For shell structures of arbitrary shapes, based on the structure's geometric dimensions, including thickness t, the origin of the global coordinate system XYZ is taken as the centroid of the structure. Figure 2As shown in the coordinate system, a complete geometric model of the structure is established in the software.

[0033] When pitting corrosion is limited to a localized area on the structural surface, the pitted area is separated from the geometric model and defined as the pitted region. The remaining areas are designated as intact regions. Figure 8 As shown.

[0034] S2. Divide the pitting corrosion zone into finite element meshes and record the finite element mesh node information, the coordinate information of the global coordinate system XYZ, and whether pitting is arranged. Use the location of the finite element mesh node as the possible distribution location of pitting corrosion.

[0035] When dividing the finite element mesh for pitting corrosion, the radius range of the pits [r] is considered. L ,r U ], take the radius range [r L ,r U The average value of ] is used as the control size for mesh generation, and the number N of finite element mesh nodes is obtained.

[0036] Based on the number of finite element mesh nodes N, a two-dimensional array PitPool(N,4) is defined to record the position information of each mesh node and whether erosion pits have been placed. The position information of each mesh node is stored in the two-dimensional array PitPool(N,4). For example, the X, Y, and Z coordinates of mesh node j are stored in PitPool(j,1) = X j PitPool(j,2) = Y j PitPool(j,3) = Z j Where 1≤j≤N. The fourth parameter PitPool(j,4) of the two-dimensional array PitPool(N,4) is initially set to 0. It is used to indicate whether pits have been placed at the position of the grid node. PitPool(j,4)=0 indicates that there are no pits at the position of grid node j, and PitPool(j,4)=1 indicates that pits have been placed at the position of grid node j.

[0037] Then, the finite element mesh was deleted.

[0038] S3. Define a two-dimensional array Pit(M,5) to record the position and radius information of the pit to be generated in the global coordinate system XYZ. Pit(k,1), Pit(k,2), and Pit(k,3) represent the X, Y, and Z coordinate positions of the pit k, respectively, and Pit(k,4) represents the radius r of the pit. k Pit(k,5) indicates that the pit is located on the inner or outer surface of the spherical shell, and 1≤k≤M.

[0039] Randomly select grid nodes recorded in the two-dimensional array PitPool(N,4) as possible distribution locations of the pits, that is, generate pits by randomly selecting grid nodes in the two-dimensional array PitPool(N,4), and randomly generate the pit radius. Record this random pit information in the two-dimensional array Pit(M,5). When randomly generating the pit radius, it is necessary to ensure that the pit radius is within the range [r...]. L ,r U The radius r of the randomly generated erosion pit k within the [inner] area k .

[0040] Randomly select a finite element mesh node j from N nodes, where 1 ≤ j ≤ N. Check if the 2D array PitPool(j,4) is 1. If it is 1, it indicates that there is already a pit at this mesh node location, and a new node must be selected. If PitPool(j,4) is 0, it indicates that there is no pit at this mesh node location, and the pit radius r is set accordingly. k The X, Y, and Z coordinates of node j are temporarily assigned to pit k.

[0041] S4. Compare the information of the temporary pit k generated in step S3 with the previously generated existing pits one by one to ensure that the new pit to be generated at point j does not overlap with the existing pits, and record the location and radius information of the pit.

[0042] Calculate the distance between the temporary pit k and the k-1 pits generated before it, ensuring that the distance between them is greater than the sum of the radii of the two pits, i.e.: l = 1, 2, ..., k-1, SUM represents the summation formula, x k y k , z k The x represents the coordinates of the temporary pit k in the global coordinate system. l y l , z l This represents the coordinates of the previously generated pit l in the global coordinate system, preventing overlap between pits. When the condition is met, it indicates that pit k can be placed on node j. At this time, pit k is generated at point j, and the corresponding array value of node j is modified: PitPool(j,4)=1; at the same time, the information of the newly generated pit k is recorded: Pit(k,1)=PitPool(j,1), Pit(k,2)=PitPool(j,2), Pit(k,3)=PitPool(j,3), Pit(k,4)=r k If the distance condition is not met, delete the temporary pit k and then reselect a node as the pit center.

[0043] A random number 1 or 2 is randomly generated between [1,2] to determine whether the pits are distributed on the outer or inner surface of the shell, i.e.: Pit(k,5)=1 or 2; 1 represents the outer surface and 2 represents the inner surface.

[0044] S5. Repeat steps S3 and S4 until all random pits are generated, and record the location, radius, and surface information of each pit. Generate cylinders based on the pit locations and radii to construct the pit geometry model.

[0045] When generating the geometric model of each erosion pit, a local cylindrical coordinate system (u, v, w) needs to be established (u is the radius, v is the azimuth, and w is the height), such as... Figure 4 As shown in the coordinate system, the origin (0,0,0) of the global coordinate system (X,Y,Z) is taken as the origin of the local cylindrical coordinate system. The line connecting the origin O(0,0,0) and the location of pit k (Pit(k,1),Pit(k,2),Pit(k,3)) is taken as the normal of the local coordinate system. This direction is the height direction of the cylindrical coordinate system. In the local cylindrical coordinate system, a system with radius r is established. k A cylinder whose height can penetrate the thickness of the shell.

[0046] By performing Boolean operations on the cylindrical surfaces of the generated M cylinders and the structural shell surface of the pitted area, a geometric model of the pitted shell is constructed, thus obtaining the pitted area.

[0047] S6. Set the mesh control size for the improved area to the shell thickness t, and the mesh control size for the pitting area to r. L / 2, set the element thickness to t, and freely divide the finite element mesh of the entire shell structure.

[0048] S7. For a shell structure with a freely divided finite element mesh, modify the element thickness at all pits within the pitting region to simulate a corrosion region of random thickness, and obtain a finite element analysis model of the randomly pitted shell.

[0049] Similar to the method for constructing the cylindrical geometric model in step S5, a local cylindrical coordinate system u,v,w corresponding to the pit k is established. For the finite element mesh described in S6, the node coordinates are taken to be smaller than the pit radius r. k All nodes are the nodes within the erosion pit k, and the elements connected to the nodes are the erosion pit elements.

[0050] Within the thickness range of the erosion pit area [d] L ,d U A random thickness is generated within the pit, and the shell thickness of the element within the pit is modified. By changing the shell thickness of the pit element, the plate thickness of the pitting area can be simulated. By setting the offset direction of the pit, Pit(k,5), the corrosion of the inner or outer surface of the shell structure can be simulated, ultimately achieving both the change of the element thickness and the change of the offset direction in the pitting area.

[0051] At this point, the random pitting corrosion model in an arbitrary-shaped shell structure has been completed.

[0052] The following provides three embodiments of the present invention, taking spherical, cylindrical and arbitrary shaped surfaces with random pitting damage as examples, respectively, and using ANSYS finite element software to further illustrate the technical solution of the present invention.

[0053] Example 1

[0054] See Figure 2-9 The specific steps for modeling a spherical shell structure with random pitting corrosion are as follows:

[0055] Step 1: The geometric dimensions of the spherical shell structure are: radius R = 100mm, thickness t = 5mm. The center of the spherical shell is taken as the origin of the global coordinate system (X,Y,Z), with the origin O coordinates (0,0,0). Figure 2 The geometric model of a sphere with radius R is shown. In the finite element software parameterization program APDL, the number of pitting corrosions on the spherical shell is set to M = 25, and the radius of the pits is [r]. L ,r U ]=[5,15]、Pit thickness range [d L ,d U ] = [1,3].

[0056] See Figure 6 If 25 pitting corrosions are distributed across the entire sphere, then the pitting area is the entire sphere. Figure 7 for Figure 6 A magnified view of the marked pitted unit; if the pitting area exists only in a local area of ​​the sphere, then the corresponding pitting area needs to be segmented on the sphere, and the segmented pitting area is denoted as the pitting region, such as... Figure 8 As shown, the finite element model of a spherical shell with localized pitting corrosion is as follows: Figure 9 As shown.

[0057] The second step is to set the mesh control size to 0.5*(r). L +r U =10mm, divide the pitting corrosion area into finite element meshes, forming Figure 3 The finite element model shown is used to obtain the number of mesh nodes for the pitting corrosion region in the finite element model, which is 1538.

[0058] Define a two-dimensional array PitPool(1538,4) to store grid nodes. Each row and four columns of this array store the X, Y, and Z coordinates of the grid node and whether a pit exists. Initially, set PitPool(j,4) = 0, indicating no pits, and 1 ≤ j ≤ 1538. For example, PitPool(1,1), PitPool(1,2), and PitPool(1,3) correspond to the X, Y, and Z coordinates of the first node, which are [-2.6615, -2.6683, 99.9289], respectively. PitPool(1,4) = 0, indicating no pits.

[0059] Then, the finite element mesh is deleted.

[0060] The third step is to define another two-dimensional array Pit(25,5) to record the location and size information of the randomly generated pits. The location of the randomly generated pits is generated by randomly selecting grid nodes in the PitPool(1538,4) array.

[0061] Specifically, the radius r of the k-th erosion pit is first randomly generated within the radius range [5, 15]. k =Random(5,15)=10.8199,1≤k≤25. Then, randomly select grid node 1192 in the two-dimensional array PitPool(1538,4), and determine whether the two-dimensional array PitPool(1192,4) storing grid node 1192 is 1. If it is 1, it means that there is already a pit here, and the next grid node must be selected again; if it is 0, it means that there is no pit here, and the position and pit radius information of node 1192 can be temporarily assigned to pit k as the position and radius information of the kth pit.

[0062] The fourth step is to compare the kth temporary pit generated in the third step with each of the previously generated pits, that is, to compare the kth pit with each of the 1st to (k-1th)th pits, ensuring that the distance between the two pits meets the following condition: Where l = 1, 2, ..., k-1, SUM represents the summation formula, x k y k , z k The coordinates of pit k, x l y l , z l The coordinates of pit l are represented. When the condition is met, pit k can be placed on node 1192. Modify the corresponding element value of node 1192 in the two-dimensional array PitPool to: PitPool(1192,4)=1, indicating that a pit has been placed at this position.

[0063] Finally, the location information of grid node 1192 and the radius of the generated pit are assigned to pit k: Pit(k,1)=PitPool(1192,1), Pit(k,2)=PitPool(1192,2), Pit(k,3)=PitPool(1192,3), Pit(k,4)=10.8199.

[0064] Then, a random number 1 or 2 is randomly generated within [1,2] to determine whether pitting occurs on the outer or inner surface of the shell, i.e.: Pit(k,5)=1 or 2; 1 represents the outer surface and 2 represents the inner surface.

[0065] If the distance condition is not met, delete the temporary pit k and re-select the grid node to generate the pit location and pit information.

[0066] Step 5: Repeat steps 3 and 4 until 25 random pit information Pit(25,5) are generated, recording the location, radius, and surface of each pit. Establish a local cylindrical coordinate system (u,v,w), with the sphere center coordinates (0,0,0) as the origin. The line connecting pit k (X=Pit(k,1),Y=Pit(k,2),Z=Pit(k,3)) to the origin O(0,0,0), i.e., the line connecting the center of the kth pit to the sphere center coordinates (0,0,0), is used as the normal direction of the local cylindrical coordinate system (the height direction w of the cylindrical coordinate system). Create a cylinder with radius Pit(k,4) and height 40mm, capable of penetrating the shell thickness. Figure 4 As shown, by performing Boolean operations on the cylindrical surface of the generated cylinder and the surface of the spherical shell, a structure like the one shown can be constructed. Figure 5 The geometric model of the pitted shell structure shown is shown, where the small circular surfaces of different radii on the spherical shell are all pitted areas.

[0067] Step 6: Set the mesh control size of the perfect zone to 5mm, the mesh control size of the pitting zone to 4mm, and the shell thickness to t=5mm, then freely divide the finite element mesh of the entire shell structure.

[0068] Step 7: Select the product generated in step 6. Figure 5 The thickness of the pitted area is changed by altering the thickness of all elements within the pitted area.

[0069] Specifically, similar to the method used in step five for establishing the local cylindrical coordinate system, for the 25 pits, the origin of the local cylindrical coordinate system is set at the sphere center coordinates (0,0,0). The lines connecting Pit(k,1), Pit(k,2), and Pit(k,3) to the origin (0,0,0) are used as the normal directions of the cylindrical coordinates, thus establishing a local cylindrical coordinate system (u,v,w). In this cylindrical coordinate system, all nodes inside Pit(k,4), whose radius in the w direction is equal to the radius of the spherical shell (100mm) and whose radius in the u direction is smaller than the pit radius, are selected as the internal nodes of the pits on the surface of the spherical shell. The elements connected to these nodes are the pit elements. This operation achieves... Figure 5 All elements in the pitted region are selected, and a random thickness d is generated within the plate thickness range [1,3] of the pitted region. k Modify the shell thickness of the selected pitted area unit to d. k This achieves random thickness of the erosion pits.

[0070] The offset direction of the pitting elements is determined based on Pit(k,5) to simulate corrosion on the inner or outer surface of the shell structure. This process continues until the element properties at all 25 pit locations are modified, resulting in random thicknesses for all pitting elements.

[0071] At this point, the model of random pitting corrosion on the spherical shell surface is complete. See [link / reference]. Figure 6 (pitting corrosion distributed throughout the entire spherical shell) and Figure 9 (Pit corrosion in a certain area).

[0072] Example 2

[0073] The modeling steps for a randomly pitted cylindrical shell structure are as follows:

[0074] Step 1: In the finite element software parameterization program APDL, set the radius R = 100mm, thickness t = 8mm, cylinder height H = 280mm, and pitting quantity M = 30 for the cylindrical shell. Using the centroid of the cylinder as the origin O(0,0,0) of the global coordinate system (X,Y,Z), create a cylindrical surface with radius R and height H; set the pit radius range [r]. L ,r U ]=[5,15]、Pit thickness range [d L ,d U ] = [2,5].

[0075] The second step is to set the mesh control size to 0.5*(r). L +r U=10mm, the finite element mesh for the pitting corrosion region was divided, resulting in 1834 mesh nodes. A two-dimensional array PitPool(1834,4) was defined, where each row and four columns store the X, Y, and Z coordinates of the node and whether a pit exists. Initially, PitPool(j,4) = 0, indicating no pits. For example, PitPool(1,1), PitPool(1,2), and PitPool(1,3) correspond to the X, Y, and Z coordinates of the first node, respectively, which are [-100, 1.2246, 20]. PitPool(1,4) = 0, indicating no pits. Then, all finite element meshes were deleted.

[0076] The third step is to define a two-dimensional array Pit(30,5) to record the location and size information of the randomly generated pits. The pit locations are generated by randomly selecting nodes in the PitPool array. Specifically, the radius r of the k-th pit is randomly generated within the range [5,15]. k =Random(5,15)=5.9286, then randomly select node 1403 in the PitPool array, and check whether PitPool(1403,4) is 1. If it is 1, it means that there is already a pit here, and a new node must be selected; if it is 0, it means that there is no pit here, and the above node position and pit radius information can be temporarily regarded as the position and radius information of the kth pit.

[0077] The fourth step is to compare the pit k generated in the third step with all the previously generated k-1 pits one by one, ensuring that the distance between two pits meets the following condition: (l = 1, 2, ..., k-1), SUM represents the summation formula, x k y k , z k The coordinates of pit k, x l y l , z l This represents the coordinates of pit l. If the condition is met, it indicates that pit k can be placed on node 1403, and the corresponding element value of node 1403 in the PitPool array is modified: PitPool(1403,4) = 1. Finally, the position information of this node and the radius of the generated pit are assigned to pit k: Pit(k,1) = PitPool(1403,1), Pit(k,2) = PitPool(1403,2), Pit(k,3) = PitPool(1403,3), Pit(k,4) = 5.9286. Then, a random number 1 or 2 is randomly generated within [1,2] to determine whether the pitting occurs on the outer or inner surface of the shell, i.e.: Pit(k,5) = 1 or 2; 1 represents the outer surface, and 2 represents the inner surface. If the distance condition is not met, a new node needs to be selected to generate the pit location and pit information.

[0078] Fifth, repeat steps three and four until 30 random pits are generated, recording the location, radius, and surface of each pit. Establish a local cylindrical coordinate system (u,v,w), with (0,0,0) in the global coordinate system as the origin and the line connecting pits k (Pit(k,1), Pit(k,2), Pit(k,3)) to the origin (0,0,0) as the axis (w direction of the cylindrical coordinate system). Create a cylinder with radius Pit(k,4) and height 40mm that can penetrate the surface of the cylindrical shell. Perform Boolean operations on the cylindrical surface of the generated cylinder and the surface of the cylindrical shell until the Boolean operations for the 30 pit locations are completed, thus constructing the geometric model of the pitted shell structure.

[0079] Step 6: Set the mesh control size of the perfect zone to 8mm, the mesh control size of the pitting zone to 3mm, and the shell thickness to t=8mm, then freely generate the finite element mesh of the shell structure.

[0080] Step 7: Select all elements within the pitted area generated in Step 6, and change the element thickness of the pitted area by altering the thickness of these elements. Specific steps: Similar to the method for establishing the local cylindrical coordinate system in Step 5, use the coordinates (0,0,0) of the global coordinate system as the origin, and the lines connecting Pit(k,1), Pit(k,2), and Pit(k,3) to the origin as the height direction of the cylindrical coordinates to establish a local cylindrical coordinate system (u,v,w). Select a w direction equal to the radius of the cylindrical shell (100mm), and a u direction radius smaller than the pit radius Pit(k,4). All nodes within this direction are considered internal nodes of the pitted area, and the elements connected to these nodes are the pitted elements. Generate a random thickness d within the plate thickness range [2,5] of the pitted area. k Modify the shell thickness of the selected pitting element to d. k This process achieves random thickness for the pits; the offset direction of the pit elements is determined based on Pit(k,5), simulating corrosion on the inner or outer surface of the shell structure. This process continues until the element thicknesses at 30 pit locations are modified, thus completing the random thickness of the shell in the pitted area.

[0081] At this point, the model of random pitting corrosion on the surface of the cylindrical shell is complete. See below. Figure 10 .

[0082] Example 3

[0083] Figure 1 The method for modeling random pitting corrosion in an arbitrary-shaped shell structure is shown below. The modeling steps for the arbitrary-shaped shell structure are as follows:

[0084] Step 1: Set the pit radius range [r] in the parameterization program of the finite element software. L ,r U]=[5,15]、Pit thickness range [d L ,d U = [2,5], set the radius R = 100mm, thickness t = 8mm, height H = 200mm, and pitting number M = 50 for the irregular shell structure. Using the centroid of the structure as the origin O(0,0,0) of the global coordinate system (X,Y,Z), create a shell structure with a columnar middle and frustum-shaped ends.

[0085] The second step is to set the mesh control size to 0.5*(r). L +r U =10mm, the finite element mesh for the pitting corrosion region is divided, resulting in 3635 mesh nodes. A two-dimensional array PitPool(3635,4) is defined, where each row and four columns store the X, Y, and Z coordinates of the node and whether a pit exists. Initially, PitPool(j,4) = 0, indicating no pits. For example, PitPool(1,1), PitPool(1,2), and PitPool(1,3) correspond to the X, Y, and Z coordinates of the first node, i.e., [41.8655, 13.8272, -190.3129], and PitPool(1,4) = 0, indicating no pits. Then, all finite element meshes are deleted.

[0086] The third step is to define a two-dimensional array Pit(50,5) to record the location and size information of the randomly generated pits. The pit locations are generated by randomly selecting nodes in the PitPool array. Specifically, the pit radius r is first randomly generated within the range [5,15]. k =Random(5,15)=12.3673, then randomly select node 2802 in the PitPool array, and check whether PitPool(2802,4) is 1. If it is 1, it means that there is already a pit here, and a new node must be selected; if it is 0, it means that there is no pit here, and the above node position and pit radius information can be temporarily regarded as the position and radius information of the kth pit.

[0087] The fourth step is to compare the pit k generated in the third step with all the previously generated k-1 pits one by one, ensuring that the distance between two pits meets the following condition: (l = 1, 2, ..., k-1), SUM represents the summation formula, x k y k , z k The coordinates of pit k, x l y l , z lThis represents the coordinates of pit l. If the condition is met, it indicates that pit k can be placed on node 2802, and the corresponding element value of node 2802 in the PitPool array is modified: PitPool(2802,4)=1. Finally, the position information of this node and the radius of the generated pit are assigned to pit k: Pit(k,1)=PitPool(2802,1), Pit(k,2)=PitPool(2802,2), Pit(k,3)=PitPool(2802,3), Pit(k,4)=12.3673. Then, a random number 1 or 2 is randomly generated within [1,2] to determine whether the pitting occurs on the outer or inner surface of the shell, i.e.: Pit(k,5)=1or 2; 1 represents the outer surface, and 2 represents the inner surface. If the distance condition is not met, a new node needs to be selected to generate the pit location and pit information.

[0088] Fifth, repeat steps three and four until 50 random pits are generated, recording the location, radius, and surface of each pit. Establish a local cylindrical coordinate system (u,v,w). With (0,0,0) of the global coordinate system as the origin and the line connecting pits k (Pit(k,1), Pit(k,2), Pit(k,3)) to the origin as the axis (i.e., the height direction w of the cylindrical coordinate system), create a cylinder with radius Pit(k,4) and height 40mm. Perform Boolean operations on the cylindrical surface of the generated cylinder and the irregular structural surface until Boolean operations are completed for 50 pit locations, thus constructing the geometric model of the pitted shell structure.

[0089] Step 6: Set the mesh control size of the perfect zone to 7mm, the mesh control size of the pitting zone to 4mm, and the shell thickness to t=8mm, then freely generate the finite element mesh of the shell structure.

[0090] Step 7: Select all elements within the pitted area generated in Step 6, and change the element thickness of the pitted area by altering the thickness of these elements. Specific steps: Similar to the method for establishing the local cylindrical coordinate system in Step 5, for 50 pitted areas, with the global coordinate system (0,0,0) as the origin, and the line connecting pits k(Pit(k,1), Pit(k,2), Pit(k,3)) and (0,0,0) as the normal direction of the cylindrical coordinate system (i.e., the height direction w of the cylindrical coordinate system), establish a local cylindrical coordinate system. Select all nodes within Pit(k,4) whose w direction is equal to the radius R of the frustum and whose u direction radius is less than the pit radius, as nodes within the pitted area. Elements connected to these nodes are pitted elements. Generate random thicknesses d within the plate thickness range [2,5] of the pitted area. k Modify the shell thickness of the selected pitting element to d. kThis process achieved random thickness for the corrosion pits; the element cross-section offset direction was determined based on Pit(k,5) to simulate corrosion on the inner or outer surface of the shell structure. The random thickness of the corrosion pits was achieved after modifying the element properties at 50 pit locations.

[0091] At this point, the model of random pitting on the surface of an arbitrary-shaped shell is complete. See [link / reference]. Figure 11 .

[0092] Finally, after the parametric model that meets all the conditions is constructed, numerical simulation calculation and analysis of the spherical shell structure containing random pitting is performed in finite element software.

[0093] In summary, this invention uses pitting corrosion occurring on spherical shells, cylindrical shells, and shells of arbitrary shapes as examples. Through the meshing operations inherent in the finite element method, the center of the pit is defined based on the node position. The number, radius, thickness, and offset of pits are randomly generated, realizing the random characteristics of corrosion occurring on the inner / outer surface of the shell, the number, area, shape, and thickness of pits, thus simulating real pitting corrosion. Furthermore, the construction of the pitting geometry model in this invention is universal and practical, not limited to thin-walled spherical shell structures, but can also be extended to other structural surfaces such as ellipsoids, cylinders, rings, and eggs. (See reference...) Figure 6 and Figure 7 For partially corroded shell surfaces, initial mesh generation and node recording can be performed only within the corroded area. See the corrosion finite element model for details. Figure 5 As shown.

[0094] The descriptions and practices disclosed in this invention are readily apparent and understandable to those skilled in the art, and various modifications and refinements can be made without departing from the principles of this invention. Therefore, any modifications or improvements made without departing from the spirit of this invention should also be considered within the scope of protection of this invention.

Claims

1. A method of modeling random pitting in an arbitrarily shaped shell structure, characterized by The method comprises the following steps: S1, taking the centroid position of the arbitrary-shaped shell structure as the origin of the global coordinate system, establishing a geometric model of the structure, and setting the pitting area of the shell structure, the number of pits, the radius range of the pits, and the thickness range of the pit area plate; S2, dividing the finite element grid of the pitting area, and defining a two-dimensional array to record the position of the grid node of the finite element grid in the global coordinate system and whether there is a pit, and then deleting the finite element grid; S3, randomly generating a pit and a pit radius, randomly selecting a finite element grid node and judging whether its position has a pit, if there is a pit, reselecting the grid node and rejudging, if there is no pit, temporarily assigning the randomly selected grid node position and the pit radius information to the pit to generate a temporary pit; S4, comparing the generated temporary pit with the existing pits generated before one by one, if the distance between the temporary pit and the existing pit meets the condition of not overlapping, a pit is generated at the randomly selected grid node; S5, repeating steps S3-S4 until all pits are generated, taking the origin of the global coordinate system as the origin of the local cylindrical coordinate system, taking the line connecting the origin and the position of the pit as the normal line of the local coordinate system, establishing a cylinder with a radius of the pit radius and a height capable of penetrating the thickness of the shell, generating a geometric model of each pit, and performing a Boolean operation between the cylindrical surface of each cylinder and the shell surface of the pitting area to obtain a pit area; S6, freely dividing the finite element grid of the entire shell structure; S7, changing the thickness of all elements in the pit area to simulate a corrosion area with random thickness, setting the offset direction of the pit to simulate the corrosion of the inner or outer surface of the shell structure, obtaining a finite element analysis model of the random pitting shell, and completing the construction of the random pitting model of the arbitrary-shaped shell structure.

2. The method of claim 1, wherein S2 In the middle, define two-dimensional array PitPool(N,4) to record the grid nodes of the finite element grid, and the X, Y, Z coordinates of the grid node j in the global coordinate system are stored in PitPool(j,1)=X j , PitPool(j,2)=Y j , PitPool(j,3)=Z j , PitPool(j,4)=0, indicating that there is no etch pit at the position of the grid node j, PitPool(j,4)=1, indicating that an etch pit has been arranged at the position of the grid node j; 1≤j≤N, N is the number of finite element grid nodes.

3. The method of claim 1, further comprising: S3 In the method, a two-dimensional array Pit(M,5) is defined to record the position and radius of the pit in the global coordinate system, M is the number of pits, Pit(k,1), Pit(k,2), and Pit(k,3) represent the X, Y, and Z coordinates of the pit respectively, Pit(k,4) represents the pit radius, and Pit(k,5) represents whether the pit is located on the inner surface or the outer surface of the spherical shell, Pit(k,5) = 1 or 2; 1 represents the outer surface, and 2 represents the inner surface, 1≤k≤M.

4. The method of claim 1, wherein: In S3, the pit is generated by randomly selecting a grid node.

5. The modeling method of random pitting in an arbitrary-shaped shell structure according to claim 1, wherein in S3, the pit radius is randomly generated within the pit radius range.

6. The method of claim 1, wherein in S4, the condition that the distance between the temporary pit and the existing pit is satisfied so that they do not overlap is satisfied by: ###0003### k is the temporary pit, SUM represents a summation formula, x k , y k , z k are coordinates of the temporary pit k in a global coordinate system, x l , y l , z l represent coordinates of the existing pit 1 in the global coordinate system, r k is a radius of the temporary pit k, r l is a radius of the existing pit 1.​​​​​​​​​ 7. The method of modeling random pitting in an arbitrarily shaped shell structure according to claim 1, wherein in S6, the grid control size of the perfect zone outside the pitting zone is set to the thickness of the shell, and the grid control size of the pitting zone is set to r L / 2, r L is the lower limit value of the range of the pit radius.​ 8. The method of claim 1, wherein: In S7, for all elements in the pit area with changed thickness, a local cylindrical coordinate system corresponding to the pit is established, all nodes with a radius smaller than the corresponding pit radius are selected, and the elements connected to the nodes are the corresponding pit elements.

9. The method of claim 1, wherein: In S7, when changing the thickness, a random thickness is generated within the thickness range of the pit area.

10. The method of claim 1, wherein: In S1, when the pitting corrosion is only distributed in the local area of the surface of the shell structure, the pitting corrosion area is segmented from the geometric model, and the area is defined as the pitting corrosion area, and the other area outside the pitting corrosion area is defined as the perfect area. ​

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