Calculation method of indentation deformation of stiffened cylindrical shell under deep water explosion

Abstract

The application relates to a kind of deep water explosion under reinforced cylindrical shell structure indentation deformation calculation method, belong to the technical field of underwater explosion.It is determined by model overall parameter, boundary condition is determined according to the characteristics of reinforced structure, the calculation of deep water explosion load, including shock wave, multiple bubble pulsation load, the differential equation of shell plate motion is established to solve indentation deformation and the final deformation is calculated according to the static water pressure work correction deformation deflection;Among them, boundary treatment is divided into three types of fixed boundary, elastic support boundary and mixed boundary;Load processing considers the coupling effect of shock wave load, multiple bubble pulsation load and static water pressure.The application considers comprehensive factors, quickly evaluates deformation, and provides important support for subsequent evaluation of the dynamic response of reinforced cylindrical shell structure under deep water explosion.

Description

Technical Field

[0001] This invention relates to the field of underwater explosion technology, and in particular to a method for calculating the indentation deformation of a reinforced cylindrical shell structure under deep-water explosion. Background Technology

[0002] Stiffened cylindrical shell structures are a common structural type in marine equipment. In recent years, with increasing emphasis on the deep sea, various deep-sea equipment has emerged. Studying the dynamic response of stiffened cylindrical shell structures under deep-water explosions is of great significance for improving the explosion resistance of various deep-sea equipment. Compared with shallow-water explosions, the dynamic response of stiffened cylindrical shell models under deep-water explosions is more complex. On the one hand, with the increase of water depth, the constraint of the bubbles on the external hydrostatic pressure becomes stronger during the underwater explosion, and the bubble pulsation period becomes drastically shorter, resulting in multiple bubble pulsation loads during deep-water explosions. On the other hand, with the increase of water depth, the work done by the hydrostatic pressure on the structure cannot be ignored, and there is a strong coupling effect on the deformation of the structure.

[0003] In related technologies, the lath beam calculation model is a commonly used simplified calculation model for stiffened cylindrical shell models, and it is an important method for analyzing the strength of stiffened cylindrical shell structures under high hydrostatic pressure. However, current lath beam analysis models usually treat the boundaries as fixed boundaries, meaning the ribs do not deform. In actual structures, for ordinary ribs, especially under explosive loads, the shell and the connected ribs usually deform simultaneously and in coordination, making the fixed boundary model difficult to apply. Summary of the Invention

[0004] To address the shortcomings of existing production technologies, the applicant provides a method for calculating the indentation deformation of a reinforced cylindrical shell structure under deep-sea blasting conditions. This method can be used to quickly evaluate the deformation of reinforced cylindrical shell models at different blast point locations, providing important technical support for the evaluation and optimization design of the blast resistance performance of deep-sea equipment.

[0005] The technical solution adopted in this invention is as follows: A method for calculating the indentation deformation of a reinforced cylindrical shell structure under deep-water blasting, comprising the following steps:

[0006] Step 1: Determine the overall parameters of the stiffened cylindrical shell model;

[0007] Step 2: Determine the boundary conditions based on the stiffening structural features at both ends of the shell plate:

[0008] When both ends are reinforced, it is considered a fixed boundary;

[0009] When both ends are ordinary reinforced, they are considered as elastic support boundaries;

[0010] When one end is strongly reinforced and the other end is normally reinforced, it is considered as a fixed boundary at one end and an elastically supported boundary at the other end.

[0011] Step 3: Based on the mass of the explosive charge, detonation distance, depth, and equivalent sphere radius, calculate the deep-water explosion load, including the shock wave load and the load from multiple bubble pulsations.

[0012] Step 4: Based on the lath beam mechanical model, establish the differential equations of shell plate motion under shock wave load and multiple bubble pulsation load respectively. Combined with the boundary conditions determined in Step 2, assume the deformation mode and obtain the control equations through the separation of variables method. Solve the equations using numerical methods to obtain the shell plate concave deformation under shock wave load and bubble pulsation load.

[0013] Step 5: Based on the work done by the hydrostatic pressure on the deformed area of ​​the shell plate, correct the deformation deflection obtained in Step 4, and calculate the final deformation by balancing the work done by the hydrostatic pressure and the increase in the deformation energy of the shell plate.

[0014] In one embodiment, the overall parameters in step one include at least the shell thickness, stiffening dimensions, stiffening spacing, and material properties.

[0015] In one embodiment, the mathematical expression for the two fixed-end boundaries in step two is:

[0016]

[0017] The mathematical expression for the two elastic support boundaries in step two is:

[0018]

[0019] The mathematical expression for the boundary with one fixed end and the boundary with elastic support at the other end in step two is:

[0020]

[0021] in:

[0022] Represents the shell deformation function;

[0023] The length of the shell plate;

[0024] It is the elastic modulus;

[0025] The cross-sectional area of ​​the reinforcement;

[0026] Where is the shell radius;

[0027] This represents the bending stiffness of the shell plate.

[0028] In one embodiment, the calculation formula in step three is:

[0029] In the formula, For the quality of the medicine package, For the distance of the explosion, This indicates the depth of the medicine pack. Let the radius of the equivalent sphere of the medicine pack be denoted as . The parameters are the shock wave decay time and P1, a1, a2, a3, b1, b2, and b3, which are parameters for different charges.

[0030] In one embodiment, step four considers the fluid-structure interaction effect between the shock wave load and the shell plate. Based on the lath beam mechanical model, the differential equation of motion of the shell plate under the shock wave load is obtained as follows:

[0031]

[0032] in, The dynamic yield limit of the shell material; The thickness of the shell plate; For the linear mass of the beam-slab strip; This refers to the peak pressure of the shock wave.

[0033] When both ends are fixed boundaries The deformation mode is assumed to be:

[0034]

[0035] When both ends are elastically supported boundaries The deformation mode is assumed to be:

[0036]

[0037] When one end is a fixed support boundary and the other end is an elastically supported boundary. The deformation mode is assumed to be:

[0038]

[0039] Substituting the equation of the deformable function into the equation of motion, and using the method of separation of variables, we obtain... The governing equations;

[0040] When both ends are fixed boundaries, the governing equations are:

[0041]

[0042] When both ends are elastically supported boundaries, the governing equation is:

[0043]

[0044] When one end is a fixed boundary and the other end is an elastically supported boundary, the governing equation is:

[0045]

[0046] The governing equations are typical second-order differential equations with constant coefficients, which are solved numerically to obtain the indentation deformation of the shell plate under shock wave loads during deep-water blasting. .

[0047] In one embodiment, step five further calculates the indentation deformation of the shell plate under multiple bubble pulsation loads during deep-water explosion. ;

[0048] Based on the lath beam mechanical model, the differential equations of motion for the shell plate under shock wave load are obtained. According to the boundary conditions at both ends of the shell plate, different deformation modes are assumed, and the deformation function equations are substituted into the differential equations of motion. The main governing equations are obtained through the method of separation of variables, and numerical methods are used to solve them, obtaining the indentation deformation of the shell plate under three bubble pulsation loads during deep-water explosion. ;

[0049] The calculation results of the indentation deformation of the shell plate under the coupled action of shock wave load and three-stage bubble pulsation load are as follows:

[0050]

[0051] Calculate the final deformation of the shell plate under external high hydrostatic pressure:

[0052]

[0053] The final deformation deflection of the lath beam under the action of underwater explosion shock wave and bubble pulsation is:

[0054]

[0055] After correction by hydrostatic pressure, the deflection becomes:

[0056]

[0057] When both ends are fixed boundaries, high hydrostatic pressure The work done on the concave deformation region is:

[0058]

[0059] The increment of the shell plate's bending deformation energy is:

[0060]

[0061] The increment of the tensile deformation energy of the shell plate is:

[0062]

[0063] An equation is established based on the fact that the work done by hydrostatic pressure equals the increase in the deformation energy of the lathe beam. Solve to obtain the final deformation of the shell plate;

[0064] When both ends are elastically supported boundaries, high hydrostatic pressure The work done on the concave deformation region is:

[0065]

[0066] Calculate the increment of the bending deformation energy of the shell plate , tensile deformation energy ;

[0067] Meanwhile, the potential energy at the elastic fixed end is calculated as follows:

[0068]

[0069] At this point, an equation is established based on the principle that the work done by the hydrostatic pressure equals the increase in the deformation energy of the lathe beam. Solve to obtain the final deformation of the shell plate;

[0070] When one end is a fixed support boundary and the other end is an elastic support boundary, high hydrostatic pressure The work done on the concave deformation region is:

[0071]

[0072] Calculate the increment of the bending deformation energy of the shell plate , tensile deformation energy Potential energy at the elastic fixed end And based on the fact that the work done by hydrostatic pressure is equal to the increase in the deformation energy of the lath beam, an equation is established. Solve to obtain the final deformation of the shell plate.

[0073] In one embodiment, the numerical method is one of the finite difference method, the finite element method, or the Runge-Kutta method.

[0074] The beneficial effects of this invention are as follows:

[0075] The calculation process of this invention is clear and reasonable. Regarding boundary treatment, based on the stiffening structural characteristics at both ends of the shell plate, three types of boundaries are treated: one type has strong stiffening at both ends, which is treated as a fixed boundary; another type has ordinary stiffening at both ends, in which case the boundary condition is an elastically supported boundary; and the third type has strong stiffening at one end and ordinary stiffening at the other end, in which case the boundary condition is a fixed boundary at one end and an elastically supported boundary at the other. Simultaneously, in terms of load treatment, this invention can simultaneously consider the coupled effects of shock wave loads and multiple bubble pulsation loads under deep-water blasting, and also the coupling effect of hydrostatic pressure. Therefore, this invention's method for calculating the concave deformation of a stiffened cylindrical shell structure under deep-water blasting can provide important support for subsequent evaluation of the dynamic response of stiffened cylindrical shell structures under deep-water blasting. Attached Figure Description

[0076] Figure 1 This is a schematic diagram illustrating the calculation process for the concave deformation of a reinforced cylindrical shell structure under deep-water explosion conditions, as described in this invention.

[0077] Figure 2 This is the calculation model for the lath beam of the present invention.

[0078] Figure 3 This is a schematic diagram of the three types of boundary conditions of the present invention. Detailed Implementation

[0079] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. In the description of the present invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the present invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention.

[0080] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0081] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0082] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "over," and "on top" of the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0083] It should be noted that when an element is referred to as being "fixed to" or "set on" another element, it can be directly on the other element or there may be an intervening element. When an element is considered to be "connected to" another element, it can be directly connected to the other element or there may be an intervening element. The terms "vertical," "horizontal," "upper," "lower," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible implementation.

[0084] like Figures 1-3 As shown, this invention provides a method for calculating the indentation deformation of a reinforced cylindrical shell structure under deep-water blasting conditions, comprising the following steps:

[0085] Step 1: Determine the overall parameters of the stiffened cylindrical shell model;

[0086] Step 2: Determine the boundary conditions based on the stiffening structural features at both ends of the shell plate:

[0087] When both ends are reinforced, it is considered a fixed boundary;

[0088] When both ends are ordinary reinforced, they are considered as elastic support boundaries;

[0089] When one end is strongly reinforced and the other end is normally reinforced, it is considered as a fixed boundary at one end and an elastically supported boundary at the other end.

[0090] Step 3: Based on the mass of the explosive charge, detonation distance, depth, and equivalent sphere radius, calculate the deep-water explosion load, including the shock wave load and multiple bubble pulsation loads.

[0091] Step 4: Based on the lath beam mechanical model, establish the differential equations of shell plate motion under shock wave load and multiple bubble pulsation load respectively. Combined with the boundary conditions determined in Step 2, assume the deformation mode and obtain the control equations through the separation of variables method. Solve the equations using numerical methods to obtain the shell plate concave deformation under shock wave load and bubble pulsation load.

[0092] Step 5: Based on the work done by the hydrostatic pressure on the deformed area of ​​the shell plate, correct the deformation deflection obtained in Step 4, and calculate the final deformation by balancing the work done by the hydrostatic pressure and the increase in the deformation energy of the shell plate.

[0093] In this embodiment, the overall parameters in step one include at least the shell thickness, stiffening dimensions, stiffening spacing, and material properties.

[0094] In this embodiment, the mathematical expression for the two fixed-end boundaries in step two is:

[0095]

[0096] The mathematical expression for the two elastic support boundaries in step two is:

[0097]

[0098] The mathematical expression for the boundary with one fixed end and the boundary with elastic support at the other end in step two is:

[0099]

[0100] in:

[0101] Represents the shell deformation function;

[0102] The length of the shell plate;

[0103] It is the elastic modulus;

[0104] The cross-sectional area of ​​the reinforcement;

[0105] Where is the shell radius;

[0106] This represents the bending stiffness of the shell plate.

[0107] In this embodiment, the calculation formula in step three is:

[0108] In the formula, For the quality of the medicine package, For the distance of the explosion, This refers to the depth of the medicine pack. Let the radius of the equivalent sphere of the medicine pack be denoted as . The parameters are the shock wave decay time and P1, a1, a2, a3, b1, b2, and b3, which are parameters for different charges.

[0109] In this embodiment, step four considers the fluid-structure interaction effect between the shock wave load and the shell plate. Based on the lath beam mechanical model, the differential equation of motion of the shell plate under the shock wave load is obtained as follows:

[0110]

[0111] in, The dynamic yield limit of the shell material; The thickness of the shell plate; For the linear mass of the beam strip; The peak pressure of the shock wave;

[0112] When both ends are fixed boundaries The deformation mode is assumed to be:

[0113]

[0114] When both ends are elastically supported boundaries The deformation mode is assumed to be:

[0115]

[0116] When one end is a fixed support boundary and the other end is an elastically supported boundary. The deformation mode is assumed to be:

[0117]

[0118] Substituting the equation of the deformable function into the equation of motion, and using the method of separation of variables, we obtain... The governing equations;

[0119] When both ends are fixed boundaries, the governing equations are:

[0120]

[0121] When both ends are elastically supported boundaries, the governing equation is:

[0122]

[0123] When one end is a fixed boundary and the other end is an elastically supported boundary, the governing equation is:

[0124]

[0125] The governing equations are typical second-order differential equations with constant coefficients, which are solved numerically to obtain the indentation deformation of the shell plate under shock wave loads during deep-water blasting. .

[0126] In this embodiment, step five further calculates the indentation deformation of the shell plate under multiple bubble pulsation loads during deep-water explosion. ;

[0127] Similar to shock wave loads, based on the lath beam mechanical model, the differential equations of motion for the shell plate under shock wave loads are obtained. According to the boundary conditions at both ends of the shell plate, different deformation modes are assumed, and the deformation function equations are substituted into the differential equations of motion. The main governing equations are obtained through the method of separation of variables, and numerical methods are used to solve them, obtaining the indentation deformation of the shell plate under three bubble pulsation loads during deep-water explosions. ;

[0128] The calculation results of the indentation deformation of the shell plate under the coupled action of shock wave load and three-stage bubble pulsation load are as follows:

[0129]

[0130] Calculate the final deformation of the shell plate under external high hydrostatic pressure:

[0131]

[0132] The final deformation deflection of the lath beam under the action of underwater explosion shock wave and bubble pulsation is:

[0133]

[0134] After correction by hydrostatic pressure, the deflection becomes:

[0135]

[0136] When both ends are fixed boundaries, high hydrostatic pressure The work done on the concave deformation region is:

[0137]

[0138] The increment of the shell plate's bending deformation energy is:

[0139]

[0140] The increment of the tensile deformation energy of the shell plate is:

[0141]

[0142] An equation is established based on the fact that the work done by hydrostatic pressure equals the increase in the deformation energy of the lathe beam. Solve to obtain the final deformation of the shell plate;

[0143] When both ends are elastically supported boundaries, high hydrostatic pressure The work done on the concave deformation region is:

[0144]

[0145] Calculate the increment of the bending deformation energy of the shell plate , tensile deformation energy The calculation method is the same as described above;

[0146] Meanwhile, the potential energy at the elastic fixed end is calculated as follows:

[0147]

[0148] At this point, an equation is established based on the principle that the work done by the hydrostatic pressure equals the increase in the deformation energy of the lathe beam. Solve to obtain the final deformation of the shell plate;

[0149] When one end is a fixed support boundary and the other end is an elastic support boundary, high hydrostatic pressure The work done on the concave deformation region is:

[0150]

[0151] Calculate the increment of the bending deformation energy of the shell plate , tensile deformation energy Potential energy at the elastic fixed end And based on the fact that the work done by hydrostatic pressure is equal to the increase in the deformation energy of the lath beam, an equation is established. Solve to obtain the final deformation of the shell plate.

[0152] In this embodiment, the numerical method is one of the finite difference method, the finite element method, or the Runge-Kutta method.

[0153] In one specific embodiment, the structural parameters of a typical reinforced cylindrical shell model are used as an example for calculation. The pressure shell has a radius of 3.5m, a plate thickness of 30mm, a rib spacing of 600mm, and a yield strength of 690MPa.

[0154] The standard reinforced dimensions are:

[0155]

[0156] The dimensions of the reinforcing ribs are as follows:

[0157]

[0158] By changing the charge and hydrostatic pressure, the final indentation deformation of the shell plate was calculated under different explosion conditions: both ends were reinforced, both ends were simply reinforced, one end was reinforced, and one end was simply reinforced.

[0159] The results are shown in Table 1 below:

[0160] Table 1 Calculation Results List

[0161]

[0162] In summary, the boundary treatment of this invention is flexible, and based on the stiffening structural characteristics at both ends of the shell plate, it is divided into three categories: fixed-support boundary, elastic-support boundary, and boundary with one end fixed and the other end elastically supported, which improves the accuracy of the calculation. The load treatment is comprehensive, taking into account the coupling effect of shock wave load, multiple bubble pulsation load, and hydrostatic pressure under deep-water explosion, making the calculation results more consistent with the actual situation. The calculation method is clear, based on the plate beam mechanical model, establishing the differential equation of shell plate motion, and solving it using numerical methods. The steps are clear and easy to implement. It provides important technical basis for rapidly evaluating the dynamic response of stiffened cylindrical shell structures under deep-water explosion, which is helpful for the evaluation and optimization design of the explosion-proof performance of deep-sea equipment.

[0163] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0164] The embodiments described above are merely illustrative of implementation methods of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for calculating the concave deformation of a reinforced cylindrical shell structure under deep-water blasting, characterized in that, Includes the following steps: Step 1: Determine the overall parameters of the stiffened cylindrical shell model; Step 2: Determine the boundary conditions based on the stiffening structural features at both ends of the shell plate: When both ends are reinforced, it is considered a fixed boundary; When both ends are ordinary reinforced, they are considered as elastic support boundaries; When one end is strongly reinforced and the other end is normally reinforced, it is considered as a fixed boundary at one end and an elastically supported boundary at the other end. The mathematical expression for the two fixed-end boundaries in step two is: The mathematical expression for the two elastic support boundaries in step two is: The mathematical expression for the boundary with one fixed end and the boundary with elastic support at the other end in step two is: in: Represents the shell deformation function; The length of the shell plate; It is the elastic modulus; The cross-sectional area of ​​the reinforcement; Where is the shell radius; The bending stiffness of the shell plate; Step 3: Based on the mass of the explosive charge, detonation distance, depth, and equivalent sphere radius, calculate the deep-water explosion load, including the shock wave load and the load from multiple bubble pulsations. Step 4: Based on the lath beam mechanical model, establish the differential equations of shell plate motion under shock wave load and multiple bubble pulsation load respectively. Combined with the boundary conditions determined in Step 2, assume the deformation mode and obtain the control equations through the separation of variables method. Solve the equations using numerical methods to obtain the shell plate concave deformation under shock wave load and bubble pulsation load. Step 5: Based on the work done by the hydrostatic pressure on the deformed area of ​​the shell plate, correct the deformation deflection obtained in Step 4, and calculate the final deformation by balancing the work done by the hydrostatic pressure and the increase in the deformation energy of the shell plate.

2. The method for calculating the concave deformation of a reinforced cylindrical shell structure under deep-water blasting as described in claim 1, characterized in that, The overall parameters in step one include at least the shell thickness, stiffening dimensions, stiffening spacing, and material properties.

3. The method for calculating the concave deformation of a reinforced cylindrical shell structure under deep-water blasting as described in claim 1, characterized in that, The calculation formula in step three is as follows: In the formula, For the quality of the medicine package, For the distance of the explosion, This indicates the depth of the medicine pack. Let the radius of the equivalent sphere of the medicine pack be denoted as . The parameters are the shock wave decay time and P1, a1, a2, a3, b1, b2, and b3, which are parameters for different charges.

4. The method for calculating the concave deformation of a reinforced cylindrical shell structure under deep-water blasting as described in claim 1, characterized in that, In step four, considering the fluid-structure interaction effect between the shock wave load and the shell plate, based on the lath beam mechanical model, the differential equation of motion of the shell plate under the shock wave load is obtained as follows: in, The dynamic yield limit of the shell material; The thickness of the shell plate; For the linear mass of the beam-slab strip; This refers to the peak pressure of the shock wave. When both ends are fixed boundaries The deformation mode is assumed to be: When both ends are elastically supported boundaries The deformation mode is assumed to be: When one end is a fixed support boundary and the other end is an elastically supported boundary. The deformation mode is assumed to be: Substituting the equation of the deformable function into the equation of motion, and using the method of separation of variables, we obtain... The governing equations; When both ends are fixed boundaries, the governing equations are: When both ends are elastically supported boundaries, the governing equation is: When one end is a fixed boundary and the other end is an elastically supported boundary, the governing equation is: The governing equations are typical second-order differential equations with constant coefficients, which are solved numerically to obtain the indentation deformation of the shell plate under shock wave loads during deep-water blasting. .

5. The method for calculating the concave deformation of a reinforced cylindrical shell structure under deep-water blasting as described in claim 1, characterized in that, Step five further calculates the indentation deformation of the shell plate under multiple bubble pulsation loads during deep-water explosion. ; Based on the lath beam mechanical model, the differential equations of motion for the shell plate under shock wave load are obtained. According to the boundary conditions at both ends of the shell plate, different deformation modes are assumed, and the deformation function equations are substituted into the differential equations of motion. The main governing equations are obtained through the method of separation of variables, and numerical methods are used to solve them, obtaining the indentation deformation of the shell plate under three bubble pulsation loads during deep-water explosion. ; The calculation results of the indentation deformation of the shell plate under the coupled action of shock wave load and three-stage bubble pulsation load are as follows: Calculate the final deformation of the shell plate under external high hydrostatic pressure: The final deformation deflection of the lath beam under the action of underwater explosion shock wave and bubble pulsation is: After correction by hydrostatic pressure, the deflection becomes: When both ends are fixed boundaries, high hydrostatic pressure The work done on the concave deformation region is: The increment of the shell plate's bending deformation energy is: The increment of the tensile deformation energy of the shell plate is: An equation is established based on the fact that the work done by hydrostatic pressure equals the increase in the deformation energy of the lathe beam. Solve to obtain the final deformation of the shell plate; When both ends are elastically supported boundaries, high hydrostatic pressure The work done on the concave deformation region is: Calculate the increment of the bending deformation energy of the shell plate , tensile deformation energy ; Meanwhile, the potential energy at the elastic fixed end is calculated as follows: At this point, an equation is established based on the principle that the work done by the hydrostatic pressure equals the increase in the deformation energy of the lathe beam. Solve to obtain the final deformation of the shell plate; When one end is a fixed support boundary and the other end is an elastic support boundary, high hydrostatic pressure The work done on the concave deformation region is: Calculate the increment of the bending deformation energy of the shell plate , tensile deformation energy Potential energy at the elastic fixed end And based on the fact that the work done by hydrostatic pressure is equal to the increase in the deformation energy of the lath beam, an equation is established. Solve to obtain the final deformation of the shell plate.

6. The method for calculating the concave deformation of a reinforced cylindrical shell structure under deep-water blasting as described in any one of claims 1 to 5, characterized in that, The numerical method is one of the following: finite difference method, finite element method, or Runge-Kutta method.

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