Prediction Method for Failure Scale of Deep-Sea Pressure-Resistant Cylindrical Shell Structure

Abstract

The present invention provides a method for predicting the failure scale of a deep-sea pressure-resistant cylindrical shell structure, belonging to the field of service safety evaluation, which includes the following steps: Step 1, construct the failure mode of the deep-sea pressure-resistant cylindrical shell structure according to the strain expression; Step 2, predict the axial failure scale of the deep-sea pressure-resistant cylindrical shell structure according to the failure model. The present invention can not only be used for predicting the failure mode and failure scale of large deep-sea titanium alloy pressure-resistant structures, but also for predicting the failure problems of other metal structures with lower moduli.

Description

Technical Field

[0001] The present invention belongs to the field of service safety evaluation, and particularly relates to a method for predicting the failure scale of a deep-sea pressure-resistant cylindrical shell structure. Background Art

[0002] The ring-stiffened cylindrical shell is a commonly used pressure-resistant structure form for large deep-sea equipment. In the structural design and safety evaluation of manned deep-diving equipment, in addition to determining the ultimate bearing capacity, failure analysis is an essential part. At present, numerical simulation methods are basically used to predict the failure mode. In terms of predicting the failure scale, most are for high-speed collisions (such as the scale of the damaged hole). For pressure-resistant structures under quasi-static pressure conditions, a reasonable prediction method has not been established yet. Summary of the Invention

[0003] Aiming at the instability failure problem of the deep-sea large titanium alloy stiffened cylindrical shell pressure-resistant structure under the ultimate load, the present invention provides a method for predicting the failure scale of the deep-sea pressure-resistant cylindrical shell structure, and gives an analytical expression (longitudinal and circumferential mode numbers) of the failure scale. Taking the main load-bearing structure of a certain large equipment as an example, the theoretical prediction results are highly consistent with the numerical simulation results and also in good agreement with the test results.

[0004] Based on the classical Donnell shell deformation theory, the present invention considers that in the process of nonlinear large deformation, the plastic strain of the mid-surface bending of the shell is much larger than the elastic strain, and since the shell thickness is much smaller than the shell radius, the difference in the bending plastic strain between the shell surface and the mid-surface can be ignored. By introducing the expression of the radial deflection after the main shell loses stability, the strain components of the shell can be obtained, and then the expression of the equivalent plastic strain can be obtained. Taking the failure strain at material failure as the criterion, the expression of the maximum radial displacement at the time of structural fracture is derived. It can be seen that the maximum radial displacement at the time of structural fracture is closely related to the mode at the time of structural instability failure, and there is an extreme value numerically. Taking the function related to the mode number and taking the partial derivative, the relationship between the longitudinal and circumferential mode numbers can be obtained. For the overall modal instability failure, the lower the circumferential mode number (for example, taking 2), the lower the corresponding ultimate load, so the longitudinal mode number is obtained, and the corresponding geometric dimension is the structural failure scale; for the local single-span instability failure, at this time the longitudinal mode number is taken as 1, the longitudinal scale is taken as the span, and the mode number of the circumferential strain can also be obtained.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for predicting the failure scale of a deep-sea pressure-resistant cylindrical shell structure, comprising the following steps:

[0007] Step 1: Based on the classical Donnell shell deformation theory, introduce the expression of the radial deflection after the instability of the main shell, obtain the strain components of the main shell, and then obtain the expression of the equivalent plastic strain. Thus, construct the failure mode of the deep-sea pressure-resistant cylindrical shell structure according to the expression of the equivalent plastic strain.

[0008] Step 2: According to the failure mode, taking the failure strain at material failure as the criterion, derive the expression of the maximum radial displacement at the fracture of the deep-sea pressure-resistant cylindrical shell structure. By taking the partial derivative of the function related to the maximum radial displacement and the modal number, obtain the relationship between the longitudinal modal number and the circumferential modal number, so as to predict the axial failure scale of the deep-sea pressure-resistant cylindrical shell structure.

[0009] Furthermore, construct the Donnell shell non-midplane strain expression as:

[0010] (1)

[0011] (2)

[0012] (3)

[0013] Wherein, is the generatrix direction, θ is the circumferential direction, , and are respectively the axial normal strain, circumferential normal strain and shear strain parallel to the midplane at any position of the shell, , and are respectively the axial normal strain, circumferential normal strain and shear strain of the shell midplane, z is the distance from the midplane, represents the radial deflection, and R is the radius of the shell midplane.

[0014] Furthermore, the said Step 1 also includes:

[0015] When bearing the load, after the instability of the main shell of the deep-sea pressure-resistant cylindrical shell structure, the radial deflection is expressed as:

[0016] (4)

[0017] Wherein, m and n are respectively the axial modal number and the circumferential modal number, is the longitudinal length of the cylindrical shell, is the deflection at both ends of the cylindrical shell, is the deflection corresponding to the axial modal number m, and the amplitude of the relative deflection curve corresponding to the axial modal number m is calculated .

[0018] Furthermore, the said Step 1 also includes:

[0019] Substitute equation (4) into equations (1) to (3) to calculate the equivalent plastic strain It is:

[0020] (5)

[0021] Taking the plastic strain of the material as the failure criterion, that is:

[0022] (6)

[0023] Among them, is the fracture strain obtained from the material performance test, and max represents taking the maximum value.

[0024] Furthermore, step 1 further includes:

[0025] Take , and obtain the maximum radial displacement at the fracture of the deep - sea pressure - resistant cylindrical shell structure It is:

[0026] (7)

[0027] Among them, h is the shell thickness.

[0028] Furthermore, step 2 includes:

[0029] For the overall instability of the deep - sea pressure - resistant cylindrical shell structure, calculate the axial mode number m according to equation (7):

[0030] (8)

[0031] (9)

[0032] Let We get:

[0033] (10)

[0034] Make both m and n integers, and we get:

[0035] (11)

[0036] Among them, represents a function related to m and n for calculating the axial mode number m, [ ] represents the rounding operation.

[0037] Furthermore, step 2 further includes:

[0038] Calculate the axial failure scale D of the deep - sea pressure - resistant cylindrical shell structure according to the axial mode number m as:

[0039] (12).

[0040] Furthermore, step 2 further includes:

[0041] For the local instability of the deep - sea pressure - resistant cylindrical shell structure, let:

[0042] In (7), let m = 1, then the circumferential local maximum radial displacement of the deep - sea pressure - resistant cylindrical shell structure is:

[0043] (13)

[0044] where l is the rib span, is the fracture strain obtained from the material performance test, m and n are the axial mode number and the circumferential mode number respectively, R is the radius of the middle surface of the shell, and h is the thickness of the shell.

[0045] Furthermore, step 2 further includes:

[0046] Determine the circumferential mode number n according to formula (14):

[0047] (14)

[0048] (15)

[0049] where, represents the function required to solve the circumferential mode number n.

[0050] Furthermore, step 2 further includes:

[0051] Let to obtain:

[0052] (16)

[0053] where, [ ] represents the rounding operation.

[0054] Advantageous effects:

[0055] The present invention firstly proposes a calculation formula for the geometric range of the failure scale of the deep - sea pressure - resistant stiffened cylindrical shell structure, and the theoretical analysis results, numerical simulation results and structural scale - down model test results are consistent. This method has not been reported in the public literature yet. The present invention can not only be used for predicting the failure mode and failure scale of large - scale deep - sea titanium alloy pressure - resistant structures, but also for predicting the failure problems of other metal structures with lower moduli. Description of the Drawings

[0056] Figure 1 It is a schematic diagram of a stiffened cylindrical shell structure, and the part surrounded by the dashed line is a local sectional view;

[0057] Figure 2a It is the failure diagram of the stiffened cylindrical shell structure;

[0058] Figure 2b It is the distribution diagram of equivalent strain when the stiffened cylindrical shell structure fails;

[0059] Figure 2c It is the failure diagram of the stiffened cylindrical shell structure (in the Figure 2a vertical direction);

[0060] Figure 2d It is the distribution diagram of equivalent strain when the stiffened cylindrical shell structure fails (in the Figure 2b vertical direction);

[0061] Figure 3a It is the distribution diagram of equivalent strain of the internal ribs when the structure fails;

[0062] Figure 3b It is the deformation diagram of the internal ribs when the structure fails;

[0063] Figure 3c It is the distribution diagram of equivalent strain of the internal ribs when the structure fails (in the Figure 3a vertical direction);

[0064] Figure 3d It is the distribution diagram of equivalent strain of the internal ribs when the structure fails (in the Figure 3b vertical direction);

[0065] Figure 4 It is the circumferential mode of the main shell when the structure fails; among them, a is the front view and b is the edge view;

[0066] Figure 5 It is the schematic diagram of the maximum relative radial displacement of the structure failure corresponding to the fracture strain of different materials;

[0067] Figure 6 It is the schematic diagram of the relationship between the maximum relative radial displacement of local instability and the circumferential mode. Specific implementation manners

[0068] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other. The embodiment of the present invention provides a method for predicting the failure scale of a deep-sea pressure-resistant cylindrical shell structure, including the following steps:

[0069] Step 1: Based on the classical Donnell shell deformation theory, introduce the expression of the radial deflection after the instability of the main shell, obtain the strain components of the main shell, and then obtain the expression of the equivalent plastic strain. Thus, construct the failure mode of the deep-sea pressure-resistant cylindrical shell structure according to the expression of the equivalent plastic strain.

[0070] Step 2: According to the failure mode, taking the failure strain at material failure as the criterion, derive the expression of the maximum radial displacement at the fracture of the deep-sea pressure-resistant cylindrical shell structure. By taking the partial derivative of the function related to the maximum radial displacement and the mode number, obtain the relationship between the longitudinal mode number and the circumferential mode number, so as to predict the axial failure scale of the deep-sea pressure-resistant cylindrical shell structure.

[0071] Specifically, Step 1 includes:

[0072] The Donnell shell non-middle-plane strain expression is:

[0073] (1)

[0074] (2)

[0075] (3)

[0076] where x is the generatrix direction, θ is the circumferential direction, , and are respectively the axial, circumferential normal strains and the shear strain parallel to the middle plane at any position of the shell, , and are respectively the axial, circumferential normal strains and the shear strain of the middle plane of the shell, z is the distance from the middle plane, represents the radial deflection, and R is the radius of the middle plane of the shell.

[0077] Under the load borne by the deep-sea pressure-resistant cylindrical shell structure, after the instability of the main shell of the deep-sea pressure-resistant cylindrical shell structure, the radial deflection can be approximately expressed as:

[0078] (4)

[0079] where m and n are respectively the axial and circumferential mode numbers, is the longitudinal length of the cylindrical shell, is the deflection at both ends of the cylindrical shell, is the deflection corresponding to the mode number m, and the amplitude of the relative deflection curve corresponding to the mode number m is calculated.

[0080] Substitute equation (4) into equations (1) to (3), and calculate the equivalent plastic strain as:

[0081] (5)

[0082] Taking the plastic strain of the material as the failure criterion, i.e.:

[0083] (6)

[0084] Wherein, That is, the fracture strain obtained from the material property test, and taking , the maximum radial displacement at the time of structural fracture is obtained as:

[0085] (7)

[0086] Wherein, L is the longitudinal length of the cylindrical shell, h is the thickness of the shell, is the material failure strain, m and n are the axial mode number and the circumferential mode number respectively.

[0087] Specifically, the step 2 includes:

[0088] For the overall instability of the deep-sea pressure-resistant cylindrical shell structure, the axial mode number m is calculated according to the following formula:

[0089] (8)

[0090] (9)

[0091] Let It can be obtained:

[0092] (10)

[0093] Both m and n are taken as integers, and it is obtained:

[0094] (11)

[0095] Wherein, represents a function for calculating the axial mode number m related to m and n, [ ] represents the rounding operation.

[0096] The axial failure scale D of the deep-sea pressure-resistant cylindrical shell structure is:

[0097] (12)

[0098] For the local instability of the deep-sea pressure-resistant cylindrical shell structure, the circumferential local maximum radial displacement of the deep-sea pressure-resistant cylindrical shell structure is formed by rewriting formula (7):

[0099] (13)

[0100] At this time, only the circumferential mode number n needs to be determined.

[0101] Introduce the calculation of n according to the following formula:

[0102] (14)

[0103] (15)

[0104] Let It can be obtained:

[0105] (16)

[0106] Among them, l is the rib span, represents the function required to solve the circumferential mode number n.

[0107] Example:

[0108] Such as Figure 1 As shown, analyze a deep-sea pressure-resistant cylindrical shell structure. The structure has a total of 22 ribs, the rib span l = 0.16 m, considering the distance between the ends and the ribs, L = 23×0.16 = 3.68 m, R = 0.65 m. Figure 1 In, t s is the thickness of the cylindrical shell, t w is the thickness of the rib web, t f is the thickness of the rib flange, l w is the height of the rib web, l t is the width of the flange.

[0109] For the overall instability of the deep-sea pressure-resistant cylindrical shell structure, according to the analysis of the structural instability mode, n = 2, m = 5 or 6.

[0110] Therefore, for the mode corresponding to m = 5, the axial failure scale D of the deep-sea pressure-resistant cylindrical shell structure is 0.73 m, corresponding to the scale between 5 ribs; it is consistent with the numerical simulation; for the mode corresponding to m = 6, the axial failure scale D of the deep-sea pressure-resistant cylindrical shell structure is 0.61 m, corresponding to the scale between 4 ribs.

[0111] For the local instability of the deep-sea pressure-resistant cylindrical shell structure (i.e., the single span between two adjacent ribs), for the calculated structure, the rib span l = 0.16 m, R = 0.65 m, n = 13, and the numerical simulation is 12, which is basically the same.

[0112] Such as Figures 2a - 3d As shown is the test verification result and the numerical simulation result, Figure 2a is the failure diagram of the stiffened cylindrical shell structure; Figure 2b is the equivalent strain distribution diagram when the stiffened cylindrical shell structure fails; Figure 2cis the failure diagram of the stiffened cylindrical shell structure (perpendicular to Figure 2a the vertical direction); Figure 2d is the equivalent strain distribution diagram of the stiffened cylindrical shell structure at the time of failure (perpendicular to Figure 2b the vertical direction); Figure 3a is the equivalent strain distribution diagram of the internal ribs at the time of structure failure; Figure 3b is the deformation diagram of the internal ribs at the time of structure failure; Figure 3c is the equivalent strain distribution diagram of the internal ribs at the time of structure failure (perpendicular to Figure 3a the vertical direction); Figure 3d is the equivalent strain distribution diagram of the internal ribs at the time of structure failure (perpendicular to Figure 3b the vertical direction); Figure 4 is the circumferential mode of the main shell at the time of structure failure, where Figure 4 a of Figure 4 is the front view, Figure 5 b of Figure 6 is the schematic diagram of the relationship between the maximum radial relative displacement of local instability and the circumferential mode.

Claims

1. A method for predicting the damage scale of a deep-sea pressure cylindrical shell structure, characterized in that: The steps include: Step 1: Based on the classic Donnell shell deformation theory, the expression of radial deflection after instability of the main shell is introduced to obtain the strain components of the main shell, and then the expression of equivalent plastic strain is obtained. According to the expression of equivalent plastic strain, the failure mode of deep-sea pressure cylindrical shell structure is constructed, including: The non-mid-surface strain expression of the Donnell shell is constructed as follows: （1） （2） （3） in, is the busbar direction, θ is the circumferential direction, , and are the axial normal strain, annular normal strain and shear strain parallel to the mid-plane at any position of the shell, , and are the axial normal strain, annular normal strain and shear strain of the shell mid-surface respectively, z is the distance from the mid-surface, represents radial deflection, R is the radius of the shell mid-surface; When the main shell of the deep-sea pressure cylindrical shell structure loses stability under load, the radial deflection It is expressed as: （4） Among them, m and n are the axial mode number and the circumferential mode number, respectively. is the longitudinal length of the cylindrical shell, is the deflection at both ends of the cylindrical shell, The relative deflection curve amplitude corresponding to the axial modal number m is calculated as ; Substitute (4) into (1) to (3) to calculate the equivalent plastic strain for: （5） The plastic strain of the material is used as the failure criterion, that is: （6） in, is the fracture strain obtained from the material performance test, and max represents the maximum value; Pick , the maximum radial displacement of the deep-sea pressure cylindrical shell structure when it breaks is obtained for: （7） Where, h is the shell thickness; Step 2: According to the failure mode, the failure strain at the time of material failure is used as the criterion to derive the maximum radial displacement expression when the deep-sea pressure cylindrical shell structure is broken. By taking the partial derivative of the function related to the maximum radial displacement and the modal number, the relationship between the longitudinal modal number and the circumferential modal number is obtained, thereby predicting the axial failure scale of the deep-sea pressure cylindrical shell structure, including: For the overall instability of the deep-sea pressure cylindrical shell structure, the axial modal number m is calculated according to formula (7): （8） （9） make get: （10） Let m and n be integers, and we get: （11） in, represents the function for calculating the axial mode number m in relation to m and n, [ ] indicates rounding operation; The axial failure scale D of the deep-sea pressure cylindrical shell structure is: （12）。 2. A method for predicting the damage scale of a deep-sea pressure cylindrical shell structure according to claim 1, characterized in that: The step 2 also includes: For the local instability of deep-sea pressure cylindrical shell structure, let: (7) where m = 1, the local maximum radial displacement of the deep-sea pressure cylindrical shell structure is for: （13） Where l is the rib span, is the fracture strain obtained from the material performance test, m and n are the axial mode number and the circumferential mode number, R is the shell mid-surface radius, and h is the shell thickness.

3. A method for predicting the damage scale of a deep-sea pressure cylindrical shell structure according to claim 2, characterized in that: The step 2 also includes: According to formula (14), the circumferential mode number n is determined as: （14） （15） in, represents the function required to solve for the number of hoop modes n.

4. A method for predicting the damage scale of a deep-sea pressure cylindrical shell structure according to claim 3, characterized in that: The step 2 also includes: make get: （16） in, [ ] indicates rounding operation.

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