CN110334394B - Method for constructing damage structure finite element model based on actual measurement pitting data - Google Patents
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Abstract
The invention discloses a method for constructing a finite element model of a damaged structure based on actually measured pitting data, which is suitable for various structures such as flat plates, cylindrical shells and the like. Firstly, a group of pseudo-random cylindrical pitting pits which accord with the actually measured statistical characteristics are generated by a random number method according to pitting statistical data, and random numbers representing shapes are randomly given to the cylindrical pitting pits. Secondly, establishing a geometric model of the structure, and arranging pitting pits; before the pit is arranged, the pit shape is transformed according to the shape random number. And then, performing Boolean operation on the pitting pit model and the structural geometric model, and constructing a geometric form of random pitting in the structural geometric model. And finally, carrying out finite element meshing to obtain a finite element model of the damage structure. The invention provides a method for simulating random pitting corrosion in a random pitting corrosion damage structure, which is used for constructing a finite element analysis model of the structure based on the statistical data of the actually measured pitting corrosion and accurately evaluating the structure performance.
Description
Technical Field
The invention belongs to the technical field of numerical model construction, and particularly relates to a method for constructing a finite element model of a damaged structure based on statistical data of actual measurement pitting corrosion, which is suitable for various structures such as flat plates, cylindrical shells and the like. The method is characterized in that the random state of the size, shape and distribution position of the pitting pits can be simulated according to the statistical data of the actually measured random pitting. The method can be used for accurately evaluating the performance degradation of the pitting damage structure and can also be used for other research works related to the pitting influence.
Background
The occurrence of pitting corrosion is mainly caused by the presence of defects, impurities, solutes, and the like in the metal material. Although the pitting corrosion causes little volume loss of metal, the corrosion rate is high, and in severe cases, equipment can be perforated, so that a large amount of oil, water and gas can be leaked, and even serious accidents such as fire, explosion and the like can be caused, and the risk is high.
Although the adverse effect of the pitting corrosion on the structure is widely concerned, a plurality of difficulties still exist in the simulation of the pitting corrosion, and a perfect pitting corrosion simulation method is urgently required to be explored. For round tubes damaged by random pitting, patent CN104484489B proposes an automatic generation method of quadrilateral finite element mesh based on shell units, but the method simplifies pitting pits into uniformly distributed cylinders with the same shape and size, which is far from the random pitting damage in the actual structure. Patent CN104834783B proposes a parameterization construction method of a cylindrical shell numerical model based on shell unit pitting random distribution, which better simulates random pitting but does not realize the simulation of pit shape randomness by equally dividing a structure surface into geometric grids with uniform size and randomly arranging pitting pits with random size at corner points of the grids. Patent CN109002592a discloses a finite element model modeling method based on a solid unit random pitting flat plate, similar to patent CN104834783B, by dividing the flat plate into geometric grids and randomly arranging cylindrical pits at the grids, also, this patent fails to simulate well the random state of pitting in the shape, size and distribution pattern in the actual structure.
Due to the non-uniformity of the material in the component and the complex influence of the surrounding environment, there is a significant uncertainty about the generation position of the pitting corrosion. Meanwhile, the evolution of the size and the shape of the etching pit is influenced by the complicated electrochemical behavior of pitting corrosion, and the strong randomness is realized. For extensive engineering structural performance evaluation, it is costly, and sometimes even impossible, to accurately describe pitting damage of a structure. Therefore, the performance evaluation of the damaged structure according to the current specifications also mainly depends on the statistical data of the pitting damage provided by the thickness measuring company. Therefore, according to the statistical data of the actually measured pitting corrosion, a set of random pitting corrosion damages meeting the actually measured statistical characteristics are generated to construct a finite element model of a damaged structure, and the finite element model has practical significance and engineering application value when used for evaluating the performance of the in-service structure.
Disclosure of Invention
The invention aims to overcome the technical defects of the prior patents, and provides a modeling method for simulating the random state of the size, the shape and the distribution form of pits in a pitting damage structure.
In order to achieve the purpose, the invention is realized by adopting the following technical scheme:
a method for constructing a finite element model of a damaged structure based on actually measured pitting data is suitable for various structures such as flat plates, cylindrical shells and the like, and comprises the following steps:
1. generating a group of depth data and radius data of a pseudo-random cylindrical pitting pit according with the actual measurement statistical characteristics by using a random number method according to the actual measurement pitting statistical data provided by a thickness measuring company, judging whether the generated data are usable or not, if not, re-generating the pitting data until the data are usable, if so, generating position data of the pitting pit by using the random number method, and giving a random number representing the shape to the cylindrical pitting pit;
2. establishing a geometric model of the structure, converting all the pitting pits generated in the step (1) into corresponding shapes according to shape random numbers, determining the position of each pitting pit in the geometric model of the structure, establishing a geometric model of the pitting pits, enabling the pitting pit model and the geometric model of the structure to perform Boolean operation, and constructing a geometric form of random pitting in the geometric model of the structure;
3. and 3, carrying out finite element meshing on the geometric model obtained by the Boolean operation in the step 2 to obtain a finite element model of the damage structure.
Further preferably, the statistical data of pitting corrosion are as follows: number N of pit, average radius mu of pit r Average pit depth [ mu ] of the pit d Maximum radius r max And minimum radius r min Maximum depth d max And a minimum depth d min 。
Further preferably, the random numbers representing the shape are cylindrical =1, semi-ellipsoidal =2, conical =3.
Further preferably, the specific content and method for generating a set of depth and radius data of the pseudo-random cylindrical pitting which meet the measured statistical characteristics by using the random number method is as follows:
1) Generating a set of random depth data using a probability distribution function based on the provided measured pitting data, such as: normal distribution function, lognormal distribution function, etc., the specific generation method is as follows:
(a) Random depth d for generating nth spot etch pit i N starts from 1, i = n;
(b) Judgment of d i Whether or not it is greater than d max If greater, take d i ＝d max Otherwise, keeping the original value; judgment of d i Whether or not it is less than d min If less than d, then take i ＝d min Otherwise, keeping the original value;
(c) Repeating (a) to (b) until N depth values meeting the requirements are generated;
2) According to the rule between the depth and the radius of the pitting and the actually measured pitting data, the generated depth data is used for generating the random radius, and the specific generation method comprises the following steps:
(d) Random radius r for generating nth spot etch pit i N starts from 1, i = n;
(e) Judgment of r i Whether or not greater than r max If it is greater than this, then r is taken i ＝r max Otherwise, keeping the original value; judgment of r i Whether or not less than r min If it is smaller than the value, then r is taken i ＝r min Otherwise, keeping the original value;
(f) And (e) repeating the steps (d) to (e) until N radius values meeting the requirements are generated.
Further preferably, the specific content and method for determining whether the generated data is available are:
two groups of samples with different volumes are extracted from all generated random data, the average pit volumes of the two groups of samples are compared, when the two groups of samples are close to each other, the samples are available, and when the two groups of samples are far away from each other, the samples are unavailable, and the specific method is as follows:
randomly taking j points to etch pit, and calculating its total volume V j And the calculation mode is as follows:
wherein->
And calculating the average value of the values j And the calculation mode is as follows: μ V j ＝V j And j, randomly taking j-1 point etching pits, and calculating the total volume V j-1 And the calculation mode is as follows: />
Wherein->
And calculating the average value of the values j-1 And the calculation mode is as follows: μ V j-1 ＝V j-1 (j-1); comparison of μ V j And μ V j-1 Whether it is close enough, if it is close enough, random data of the pit is available; if not close enough, the point isRandom data of pits is not available.
Further preferably, the random number method generates position data of the pit, and gives a random number representing a shape to the cylindrical pit, and the specific content and method are as follows:
defining an array pitData (N, 5), an array with N rows and 5 columns, recording the information of the pit, a third column recording the radius of the pit, and a fourth column recording the depth of the pit; generating a set of coordinates for the center of each pit, requiring no overlapping between pits, placing the first two columns of pitData (N, 5), the first column being X coordinates, the second column being Y coordinates, giving a random number representing the shape to each pit randomly, and storing in the fifth column of pitData (N, 5); the specific method comprises the following steps:
randomly generating a first pit coordinate in a generation mode: unfolding a surface of the structure containing the pitting corrosion into a plane, defining a rectangular coordinate system at any position, randomly taking values of an X coordinate and a Y coordinate in the plane, and respectively storing the values in the first two columns of the pitData (N, 5);
(II) generating an nth point etching pit coordinate, wherein n starts from 2, the mode is the same as that of the first point etching pit coordinate, whether the nth point etching pit coordinate is overlapped with the first n-1 point etching pits or not is judged, and when the nth point etching pit coordinate is overlapped with at least one point etching pit, the nth point etching pit coordinate is regenerated until the nth point etching pit coordinate is not overlapped with the first n-1 point etching pits; the comparison method comprises the following steps: the distance of a straight line between two coordinates, i.e.
Whether or not it is larger than the sum of the radii of the two pitting pits, i.e. r i +r j If the difference is larger than the preset value, the overlapping is not performed, and if the difference is smaller than the preset value, the overlapping is performed;
(III) randomly generating any number in 1,2,3 with equal probability to determine the random shape of the pitting and storing the random shape in the fifth column of pitData (N, 5); when the number is 1, the pit shape is a cylinder; when the pit shape is 2, the pit shape is a semi-ellipsoid; if the number is 3, the pit shape is conical;
and (IV) repeating the steps (II) to (III) until the coordinates of the N point etching pits are completely generated and meet the requirements.
Further preferably, the specific steps for constructing the geometric form of the pitting structure are as follows:
the method comprises the following steps that (I) because initial random pit data generated according to actual measurement data are cylindrical, when a geometric pit model of a pit structure is constructed, the cylindrical pit data are converted according to the shape of a randomly generated pit; when pitData (N, 5) =1, pitData [ N ] with radius is generated][3]Depth of pitData [ n ]][4]A cylinder of (a); when pitData (N, 5) =2, the generated radius is
Depth of pitData [ n ]][4]A semi-ellipsoid of (a); when pitData (N, 5) =3, a radius of ^ based on/in is generated>
Depth of pitData [ n ]][4]The cone of (a);
(II) converting the positions represented by the plane coordinates (pitData [ n ] [1], pitData [ n ] [2], pitData [ n ] [4 ]) to the surface of the structure, generating corresponding entities at the positions according to the shapes of the pitting pits, and performing Boolean operation on the entities and the geometric model of the structure to form the geometric model of the pitting structure;
and (III) repeating the steps (I) to (II) until all N etching pits are generated.
The invention provides a method for simulating random pitting corrosion in a random pitting corrosion damage structure, which is used for constructing a finite element analysis model of the structure based on the statistical data of the actually measured pitting corrosion and accurately evaluating the structure performance.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. statistical data of actually measured radius and depth of the pitting pits in the structure are utilized to generate randomly distributed and randomly shaped pitting pits, the pit depth can obey the probability distribution of the actually measured data, and the pitting damage structure finite element model constructed by the method is more universal and truer.
2. The shape of the random pits in the structural finite element model is arbitrary and generally includes mainly cylindrical, semi-ellipsoidal and conical shapes. The occurrence probability of the pits of various shapes obeys uniform distribution, and is close to the pitting morphology observed in the actual structure.
Drawings
FIG. 1 is a schematic diagram of a pit position in an embodiment of the invention.
FIG. 2 is a schematic diagram of the structure and geometry of an embodiment of the present invention.
FIG. 3 is a detailed view of the pitting damage structure model and the pitting pit according to the embodiment of the present invention. The figure a shows a pitting damage structure model, the figure b shows details of a cylindrical pitting pit, the figure c shows details of a hemispherical pitting pit, and the figure d shows details of a conical pitting pit.
FIG. 4 is a schematic diagram of a finite element model of a pitting damage structure according to an embodiment of the invention.
Description of reference numerals: l-structure length; w-structure width; d-structure thickness.
The specific implementation mode is as follows:
the invention will be further described in detail below with reference to the drawings by taking a simple pitting damage plate as an example and using ANSYS as the finite element software.
A method for constructing a damage structure finite element model based on actually measured pitting data specifically comprises the following steps:
the first step is as follows: according to the measured number of the pitting pits 82, the average radius of the pitting pits 20.1mm, the average depth of the pitting pits 9.62mm, the maximum and minimum radii of 44.03mm and 8.64mm, and the maximum and minimum depths of 10.77mm and 6.66mm, a group of depth data (average value of 9.62mm and standard deviation of 0.5, function used: NORMINV (RAND ()), 9.62,0.5)) conforming to random normal distribution is generated in EXCEL in a specific generation mode as follows:
(1) Generating a random depth d of the nth (n starting from 1) pit i (i＝n)。
(2) Judgment of d i Whether it is greater than 10.77, if so, take d i =10.77, otherwise the original value is maintained; judgment of d i Whether it is less than 6.66, if so, take d i =6.66, otherwise the original value is maintained.
(3) And (3) repeating the steps (1) to (2) until 82 depth values meeting the requirements are generated.
Then, generating random radius according to the existing depth data, that is, the radius of each etch pit will randomly appear between 4 times and 5 times of the depth (r = d (4 + rand ())), specifically generating the following way:
(1) Random radius r for generating the nth (n starting from 1) dot pit i (i＝n)。
(2) Judgment of r i Whether it is greater than 44.03, if so, r is taken i =44.03, otherwise keep original value; judgment of r i Whether it is less than 8.64, if it is less than r i =8.64, otherwise the original value is maintained.
(3) Repeating (1) to (2) until 82 radius values meeting the requirement are generated.
Randomly taking 60 pits and calculating the total volume V j Is 828998.1mm 3 (
Wherein->
) And calculating the average value of the values j Is 13816.63mm 3 (μV j ＝V j /j), then randomly taking 59 point pits and calculating the total volume V j-1 Is 823897.3mm 3 (/>
Wherein->
) And calculating the average value of the values j-1 Is 13964.36mm 3 (μV j-1 ＝V j-1 /(j-1))。μV j And μ V j-1 Close enough, random data of the pit is available.
The data set pitData (82,5) (array 82 rows and 5 columns) defined in the APDL (ANSYS parametric design language) records the information of the generated pit, the third column records the pit radius, and the fourth column records the pit depth. And generating a set of coordinates for the center of each etch pit, requiring no overlap between etch pits, and placing the first two columns of pitData (82,5), the first column being X coordinates, the second column being Y coordinates, as shown in FIG. 1, while randomly assigning a random number representing the shape to each pit, and storing in the fifth column of pitData (N, 5). The X coordinate is the structure length (L) direction and the Y coordinate is the structure width (W) direction. The specific mode is as follows:
(1) Randomly generating a first dot and pit coordinate, wherein the generation mode is as follows: the X coordinate is RAND (0,800) and the Y coordinate is RAND (0,800).
(2) Generating the nth (n is from 2) etching pit coordinate in the same way as the first etching pit coordinate, judging whether the first etching pit coordinate is overlapped with the first n-1 etching pits, and if the first etching pit coordinate is overlapped with at least one etching pit, regenerating the nth etching pit coordinate until the first etching pit coordinate is not overlapped with the first n-1 etching pits. The comparison method comprises the following steps: linear distance between two coordinates
Whether or not it is larger than the sum of the radii of the two pits (r) i +r j ) And when the ratio is larger than the above range, the layers are not overlapped, and if the sum is less than or equal to the preset value, overlapping. />
(3) An NINT (RAND (1,4) -MOD (RAND (1,4), 1)) is generated with equal probability to determine the random shape of the pit and stored in pitData (82,5). When the etching depth is 1, the etching pit is cylindrical; when the etching depth is 2, the etching pit shape is a semi-ellipsoid; when the etching depth is 3, the etching pit shape is a cone.
(4) And (4) repeating the steps (2) to (3) until all the coordinates of the 82 point pits are generated and meet the requirement.
The second step: eight angular points are generated by the plate length 800, the plate width 800 and the plate thickness 15 respectively: (0,0,0), (800,0,0), (800,800,0), (0,800,0), (0,0,15), (800,0,15), (800,800,15), (0,800,15), and a model of the panel is generated from eight corner points, which is defined as a plate, as shown in fig. 2.
Boolean calculation is performed on the flat plate geometric model and the pitting model according to the existing pitData (82,5) data to construct the geometric form of the pitting structure, as shown in FIG. 3. The method comprises the following specific steps:
(1) Because the initial random pit data generated according to the actual measurement data is cylindrical, when a geometric pit model of the pit structure is constructed, the cylindrical pit data is converted according to the randomly generated pit shape. When pitData (82,5) =1, pitData [ n ] with radius is generated][3]depth-pitData [ n][4]A cylinder of (a); when pitData (82,5) =2, the generated radius is
The ball is proportioned in the Z direction
Becoming an ellipsoid; when pitData (82,5) =3, the generated radius is
depth-pitData [ n ]][4]The cone of (a).
(2) And moving the coordinate system of the working plane to the coordinates (pitData [ n ] [1], pitData [ n ] [2], pitData [ n ] [4 ]), generating corresponding entities according to the pit shapes of the pits, and performing Boolean operation on the entities and the geometric model of the structure to form the geometric model of the pit structure.
(3) Repeating the steps (1) to (2) until all 82 etching pits are generated.
The third step: solid187 units are selected and the finite element mesh of the geometric model is divided. In the gridding, the grid size is 15, and the etch pit portion is intelligently gridded using SMRT,4 command, as shown in fig. 4.
Claims (7)
1. A method for constructing a finite element model of a damaged structure based on actually measured random pitting data is suitable for various structures of flat plates and cylindrical shells, and is characterized by comprising the following steps:
(1) Generating a group of depth data and radius data of a pseudo-random cylindrical pitting pit according with the actual measurement statistical characteristics by using a random number method according to the actual measurement pitting statistical data provided by a thickness measuring company, judging whether the generated data are usable or not, if not, regenerating pitting pit data until the generated data are usable, if so, generating position data of the pitting pit by using the random number method, and endowing the cylindrical pitting pit with a random number representing the shape;
(2) Establishing a geometric model of the structure, converting all the pitting pits generated in the step (1) into corresponding shapes according to shape random numbers, determining the position of each pitting pit in the geometric model of the structure, establishing a geometric model of the pitting pits, enabling the model of the pitting pits and the geometric model of the structure to perform Boolean operation, and constructing a geometric form of random pitting in the geometric model of the structure;
(3) And (3) carrying out finite element meshing on the geometric model obtained by the Boolean operation in the step (2) to obtain a finite element model of the damage structure.
2. The method for constructing a finite element model of a damaged structure based on measured random pitting data according to claim 1, wherein the pitting statistical data are: number N of pit, average radius mu of pit r Average pit depth [ mu ] d Maximum radius r max And minimum radius r min Maximum depth d max And a minimum depth d min 。
3. The method for constructing a finite element model of a lesion structure based on measured random pitting data of claim 1, wherein the random numbers representing the shape are cylinder =1, semi-ellipsoid =2, and cone =3.
4. The method for constructing a finite element model of a damaged structure based on measured random pitting data according to claim 1, wherein the specific contents and methods for generating a set of depth and radius data of pseudo-random cylindrical pitting pits conforming to the measured statistical characteristics using a random number method are:
1) According to the provided actually measured pitting corrosion data, a group of random depth data, namely a normal distribution function and a lognormal distribution function, is generated by using a probability distribution function, and the specific generation method comprises the following steps:
(a) Random depth d for generating nth spot etch pit i N starts at 1, i = n;
(b) Judgment of d i Whether or not it is greater than d max If greater, take d i ＝d max Otherwise, keeping the original value; judgment of d i Whether or not it is less than d min If less than d, then take i ＝d min Otherwise, keeping the original value;
(c) Repeating (a) to (b) until N depth values meeting the requirements are generated;
2) According to the rule between the depth and the radius of the pitting and the actually measured pitting data, the generated depth data is used for generating the random radius, and the specific generation method comprises the following steps:
(d) Random radius r to generate nth spot etch pit i N starts from 1, i = n;
(e) Judgment of r i Whether or not greater than r max If it is greater than the above value, then r is taken i ＝r max Otherwise, keeping the original value; judgment of r i Whether or not less than r min If it is smaller than the value, then r is taken i ＝r min Otherwise, keeping the original value;
(f) And (e) repeating the steps (d) to (e) until N radius values meeting the requirements are generated.
5. The method for constructing a finite element model of a damage structure based on measured random pitting data as claimed in claim 1, wherein the specific contents and methods for judging whether the generated data is available are:
two groups of samples with different volumes are extracted from all generated random data, the average pit volumes of the two groups of samples are compared, when the two groups of samples are close to each other, the samples are available, and when the two groups of samples are far away from each other, the samples are unavailable, and the specific method is as follows:
randomly taking j points to etch pits and calculating the total volume V j And the calculation mode is as follows:
wherein +>
And calculating the average value of the values j And the calculation mode is as follows: μ V j ＝V j And/j, randomly taking j-1 point etching pits, and calculating the total volume V j-1 And the calculation mode is as follows:
wherein->
And calculating the average value of the values j-1 And the calculation mode is as follows: μ V j-1 ＝V j-1 (j-1); comparison of μ V j And μ V j-1 Whether it is close enough, if it is close enough, random data of the pit is available; if not close enough, the random data of the pit is not available.
6. The method for constructing a finite element model of a damage structure based on the actually measured random pitting data of claim 1, wherein the random number method generates the position data of the pitting pits, and gives the cylindrical pitting pits the specific contents and methods of the random numbers representing the shape are as follows:
defining an array pitData (N, 5), an array with N rows and 5 columns, recording the information of the pit, a third column recording the radius of the pit, and a fourth column recording the depth of the pit; generating a set of coordinates for the center of each pit, requiring no overlapping between pits, placing the first two columns of pitData (N, 5), the first column being X coordinates, the second column being Y coordinates, giving a random number representing the shape to each pit randomly, and storing in the fifth column of pitData (N, 5); the specific method comprises the following steps:
randomly generating a first pit coordinate in a generation mode: unfolding a surface with pitting corrosion into a plane, defining a rectangular coordinate system at any position, randomly taking values of an X coordinate and a Y coordinate in the plane, and respectively storing the values in the first two columns of pitData (N, 5);
(II) generating an nth point etching pit coordinate, wherein n starts from 2, the mode is the same as that of the first point etching pit coordinate, whether the nth point etching pit coordinate is overlapped with the first n-1 point etching pits or not is judged, and when the nth point etching pit coordinate is overlapped with at least one point etching pit, the nth point etching pit coordinate is regenerated until the nth point etching pit coordinate is not overlapped with the first n-1 point etching pits; the comparison method comprises the following steps: the linear distance between two coordinates, i.e.
Whether or not it is larger than the sum of the radii of the two pitting pits, i.e. r i +r j If the difference is larger than the preset value, the overlapping is not performed, and if the difference is smaller than the preset value, the overlapping is performed;
(III) randomly generating any number in 1,2,3 with equal probability to determine the random shape of the pitting and storing the random shape in the fifth column of pitData (N, 5); when the number is 1, the pit shape is a cylinder; when the pit shape is 2, the pit shape is a semi-ellipsoid; if the number is 3, the pit shape is a cone;
and (IV) repeating the steps (II) to (III) until the coordinates of the N point etching pits are completely generated and meet the requirements.
7. The method for constructing a finite element model of a damaged structure based on measured random pitting data according to claim 1, wherein the specific steps of constructing the geometric form of the random pitting are as follows:
the method comprises the following steps that (I) because initial random pit data generated according to actual measurement data are cylindrical, when a geometric pit model of a pit structure is constructed, the cylindrical pit data are converted according to the shape of a randomly generated pit; when pitData (N, 5) =1, a radius of pitData [ N ] is generated][3]Depth of pitData [ n ]][4]A cylinder of (a); when pitData (N, 5) =2, the generated radius is
Depth of pitData [ n ]][4]A semi-ellipsoid of (a); when pitData (N, 5) =3, a radius ^ is generated>
Depth of pitData [ n ]][4]The cone of (a);
(II) converting the positions represented by the plane coordinates (pitData [ n ] [1], pitData [ n ] [2], pitData [ n ] [4 ]) to the surface of the structure, generating corresponding entities at the positions according to the shapes of the pitting pits, and performing Boolean operation on the entities and the geometric model of the structure to form the geometric model of the pitting structure;
and (III) repeating the steps (I) to (II) until all N etching pits are generated.
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| CN104484489A (en) * | 2014-07-24 | 2015-04-01 | 江苏科技大学 | Automatic generation method for quadrilateral finite element mesh of pitting corrosion damage cylindrical shell |
| CN104834783A (en) * | 2015-05-12 | 2015-08-12 | 江苏科技大学 | Parameterized construction method of numerical model of pit-corrosion-randomly-distributed cylindrical shell |
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| CN104484489A (en) * | 2014-07-24 | 2015-04-01 | 江苏科技大学 | Automatic generation method for quadrilateral finite element mesh of pitting corrosion damage cylindrical shell |
| CN104834783A (en) * | 2015-05-12 | 2015-08-12 | 江苏科技大学 | Parameterized construction method of numerical model of pit-corrosion-randomly-distributed cylindrical shell |
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