Method for predicting damage scale of deep-sea pressure-resistant cylindrical shell structure

Abstract

The invention provides a deep-sea pressure-resistant cylindrical shell structure damage scale prediction method, and belongs to the field of service safety evaluation, and the method comprises the following steps: 1, constructing a failure mode of a deep-sea pressure-resistant cylindrical shell structure according to a strain expression; and 2, predicting the axial damage scale of the deep-sea pressure-resistant cylindrical shell structure according to the failure model. The method not only can be used for predicting the failure mode and the damage scale of the deep-sea large titanium alloy pressure-resistant structure, but also can be used for predicting the damage problem of other metal structures with lower moduli.

Description

Technical Field

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

[0002] The ring-ribbed cylindrical shell is a common pressure-resistant structure for large deep-sea equipment. In the structural design and safety evaluation of manned deep-sea equipment, failure analysis is an indispensable part in addition to determining the ultimate bearing capacity. At present, numerical simulation methods are basically used to predict failure modes. In terms of damage scale prediction, most of them are aimed at high-speed collisions (such as damage hole scale). For pressure-resistant structures under quasi-static pressure conditions, no reasonable prediction method has been established. Summary of the invention

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

[0004] The present invention is based on the classic Donnell shell deformation theory. Considering that in the process of nonlinear large deformation, the plastic strain of the shell mid-surface bending is much greater than the elastic strain, and because 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 is unstable, 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 when the material is damaged as the criterion, the expression of the maximum radial displacement when the structure is broken is derived. It can be seen that the maximum radial displacement when the structure is broken is closely related to the mode when the structure is unstable and damaged, and there is an extreme value in value. Take the function related to the modal number and find the partial derivative to obtain the relationship between the longitudinal and circumferential modal numbers. For overall modal instability damage, the lower the circumferential modal number (for example, 2), the lower the corresponding limit load, so the longitudinal modal number is obtained, and the corresponding geometric size is the structural damage scale; for local single-span instability damage, the longitudinal modal number is 1, the longitudinal scale is the span, and the modal number of the circumferential strain can also be obtained.

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

[0006] A method for predicting the damage scale of a deep-sea pressure cylindrical shell structure comprises the following steps:

[0007] Step 1: Based on the classic Donnell shell deformation theory, the expression of radial deflection after the main shell is unstable is introduced to obtain the strain components of the main shell, and then the expression of equivalent plastic strain is obtained, so as to construct the failure mode of the deep-sea pressure cylindrical shell structure according to the expression of equivalent plastic strain;

[0008] Step 2: According to the failure mode, the failure strain at the time of material damage is used as the criterion to derive the expression of the maximum radial displacement 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.

[0009] Furthermore, the non-mid-surface strain expression of the Donnell shell is constructed as:

[0010] (1)

[0011] (2)

[0012] (3)

[0013] 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, and R is the radius of the shell mid-surface.

[0014] Furthermore, the step 1 further comprises:

[0015] When the main shell of the deep-sea pressure cylindrical shell structure loses stability under load, the radial deflection It is expressed as:

[0016] (4)

[0017] 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 .

[0018] Furthermore, the step 1 further comprises:

[0019] Substitute (4) into (1) to (3) to calculate the equivalent plastic strain for:

[0020] (5)

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

[0022] (6)

[0023] in, It is the fracture strain obtained from the material performance test, and max represents the maximum value.

[0024] Furthermore, the step 1 further comprises:

[0025] Pick , the maximum radial displacement of the deep-sea pressure cylindrical shell structure when it breaks is obtained for:

[0026] (7)

[0027] Where h is the shell thickness.

[0028] Furthermore, the step 2 comprises:

[0029] For the overall instability of the deep-sea pressure cylindrical shell structure, the axial modal number m is calculated according to formula (7):

[0030] (8)

[0031] (9)

[0032] make get:

[0033] (10)

[0034] Let m and n be integers, and we get:

[0035] (11)

[0036] in, represents the function for calculating the axial mode number m in relation to m and n, [ ] indicates rounding operation.

[0037] Furthermore, the step 2 also includes:

[0038] The axial failure scale D of the deep-sea pressure cylindrical shell structure is calculated based on the axial modal number m:

[0039] (12).

[0040] Furthermore, the step 2 also includes:

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

[0042] (7) where m = 1, the local maximum radial displacement of the deep-sea pressure cylindrical shell structure is for:

[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, R is the shell mid-surface radius, and h is the shell thickness.

[0045] Furthermore, the step 2 also includes:

[0046] According to formula (14), the circumferential mode number n is determined as:

[0047] (14)

[0048] (15)

[0049] in, represents the function required to solve for the number of hoop modes n.

[0050] Furthermore, the step 2 also includes:

[0051] make get:

[0052] (16)

[0053] in, [ ] indicates rounding operation.

[0054] Beneficial effects:

[0055] The present invention proposes for the first time a calculation formula for the geometric range of the failure scale of deep-sea pressure-resistant reinforced cylindrical shell structures, and the theoretical analysis results, numerical simulation results and structural scale model test results are consistent. This method has not yet been reported in public data. The present invention can not only be used to predict the failure mode and failure scale of large-scale titanium alloy pressure-resistant structures in the deep sea, but also to predict the failure problems of other metal structures with lower modulus. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a schematic diagram of the reinforced cylindrical shell structure, and the dotted line is a local cross-sectional view;

[0057] Figure 2a This is the failure diagram of the reinforced cylindrical shell structure;

[0058] Figure 2b This is the equivalent strain distribution diagram when the reinforced cylindrical shell structure is destroyed;

[0059] Figure 2c is the failure diagram of the reinforced cylindrical shell structure (same as Figure 2a vertical direction);

[0060] Figure 2d The equivalent strain distribution diagram of the reinforced cylindrical shell structure when it is destroyed (similar to Figure 2b vertical direction);

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

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

[0063] Figure 3c The equivalent strain distribution diagram of the internal ribs when the structure is damaged (with Figure 3a vertical direction);

[0064] Figure 3d The equivalent strain distribution diagram of the internal ribs when the structure is damaged (with Figure 3b vertical direction);

[0065] Figure 4 is the circumferential mode of the main shell when the structure is destroyed; a is the main view and b is the edge view;

[0066] Figure 5 Schematic diagram of the maximum relative displacement in radial direction of structural damage corresponding to the fracture strain of different materials;

[0067] Figure 6 Schematic diagram of the relationship between the maximum radial relative displacement of local instability and the circumferential mode. DETAILED DESCRIPTION

[0068] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with 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 intended to limit the present invention. In addition, the technical features involved in each embodiment of the present invention described below can be combined with each other as long as they do not conflict with each other. An embodiment of the present invention provides a method for predicting the damage scale of a deep-sea pressure-resistant cylindrical shell structure, comprising the following steps:

[0069] Step 1: Based on the classic Donnell shell deformation theory, the expression of radial deflection after the main shell is unstable is introduced to obtain the strain components of the main shell, and then the expression of equivalent plastic strain is obtained, so as to construct the failure mode of the deep-sea pressure cylindrical shell structure according to the expression of equivalent plastic strain;

[0070] Step 2: According to the failure mode, the failure strain at the time of material damage is used as the criterion to derive the expression of the maximum radial displacement 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.

[0071] Specifically, the step 1 includes:

[0072] The strain expression of the non-mid-surface of the Donnell shell is:

[0073] (1)

[0074] (2)

[0075] (3)

[0076] Among them, x is the generatrix direction, θ is the circumferential direction, , and are the axial and annular normal strains and the shear strain parallel to the mid-surface at any position of the shell, , and are the axial, annular normal strain and shear strain of the shell mid-surface, z is the distance from the mid-surface, Represents radial deflection, and R is the radius of the shell mid-surface.

[0077] When the deep-sea pressure cylindrical shell structure is subjected to load, the radial deflection of the main shell of the deep-sea pressure cylindrical shell structure is unstable. It can be approximately expressed as:

[0078] (4)

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

[0080] Substitute (4) into (1) to (3) to calculate the equivalent plastic strain for:

[0081] (5)

[0082] The plastic strain of the material is used as the failure criterion, that is:

[0083] (6)

[0084] in, That is, the fracture strain obtained from the material performance test, and , the maximum radial displacement when the structure breaks is obtained for:

[0085] (7)

[0086] Where L is the longitudinal length of the cylindrical shell, h is the shell thickness, 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 cylindrical shell structure, the axial modal number m is calculated according to the following formula:

[0089] (8)

[0090] (9)

[0091] make We can get:

[0092] (10)

[0093] m and n are both integers, and we get:

[0094] (11)

[0095] in, represents the function for calculating the axial mode number m in relation to m and n, [ ] indicates rounding operation.

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

[0097] (12)

[0098] For local instability of deep-sea pressure cylindrical shell structure, the local maximum radial displacement of the deep-sea pressure cylindrical shell structure is It is rewritten from formula (7):

[0099] (13)

[0100] At this time, it is only necessary to determine the circumferential mode number n.

[0101] The calculation of n is introduced according to the following formula:

[0102] (14)

[0103] (15)

[0104] make We can get:

[0105] (16)

[0106] Where l is the rib span, represents the function required to solve for the number of hoop modes n.

[0107] Example:

[0108] like Figure 1 As shown in the figure, a deep-sea pressure cylindrical shell structure is analyzed. The structure has 22 ribs in total, and the rib span is l=0.16m. Considering the distance between the end and the rib, L=23×0.16=3.68m, R=0.65m. Figure 1 In, t s is the thickness of the cylindrical shell, t w is the rib web thickness, t f is the rib wing plate thickness, l w is the rib belly height, l t is the wing width.

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

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

[0111] For the local instability of the deep-sea pressure cylindrical shell structure (i.e., a 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 consistent.

[0112] like Figure 2a-Figure 3d The results of the experimental verification and numerical simulation are shown. Figure 2a This is the failure diagram of the reinforced cylindrical shell structure; Figure 2b This is the equivalent strain distribution diagram when the reinforced cylindrical shell structure is destroyed; Figure 2cis the failure diagram of the reinforced cylindrical shell structure (same as Figure 2a vertical direction); Figure 2d The equivalent strain distribution diagram of the reinforced cylindrical shell structure when it is destroyed (similar to Figure 2b vertical direction); Figure 3a This is the equivalent strain distribution diagram of the internal ribs when the structure is destroyed; Figure 3b This is the deformation diagram of the internal ribs when the structure is destroyed; Figure 3c The equivalent strain distribution diagram of the internal ribs when the structure is damaged (with Figure 3a vertical direction); Figure 3d The equivalent strain distribution diagram of the internal ribs when the structure is damaged (with Figure 3b vertical direction); Figure 4 is the annular mode of the main shell when the structure is destroyed, where Figure 4 a is the main view, Figure 4 b is the edge graph; Figure 5 Schematic diagram of the maximum relative displacement in radial direction of structural damage corresponding to the fracture strain of different materials; Figure 6 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 the main shell is unstable is introduced to obtain the strain components of the main shell, and then the expression of equivalent plastic strain is obtained, so as to construct the failure mode of the deep-sea pressure cylindrical shell structure according to the expression of equivalent plastic strain; Step 2: According to the failure mode, the failure strain at the time of material damage is used as the criterion to derive the expression of the maximum radial displacement 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.

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 1 comprises: 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, and R is the radius of the shell mid-surface.

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 1 also includes: 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 .

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 1 also includes: 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, It is the fracture strain obtained from the material performance test, and max represents the maximum value.

5. A method for predicting the damage scale of a deep-sea pressure cylindrical shell structure according to claim 4, characterized in that: The step 1 also includes: 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.

6. A method for predicting the damage scale of a deep-sea pressure cylindrical shell structure according to claim 5, characterized in that: The step 2 comprises: 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.

7. A method for predicting the damage scale of a deep-sea pressure cylindrical shell structure according to claim 6, characterized in that: The step 2 also includes: The axial failure scale D of the deep-sea pressure cylindrical shell structure is calculated based on the axial modal number m: （12）。 8. The 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.

9. A method for predicting the damage scale of a deep-sea pressure cylindrical shell structure according to claim 8, 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.

10. A method for predicting the damage scale of a deep-sea pressure cylindrical shell structure according to claim 9, characterized in that: The step 2 also includes: make get: （16） in, [ ] indicates rounding operation.

Images