Method for calculating sinking deformation of reinforced cylindrical shell structure under deepwater explosion

Abstract

The invention relates to a method for calculating sunken deformation of a reinforced cylindrical shell structure under deepwater explosion, and belongs to the technical field of underwater explosion. The method comprises the following steps: determining overall parameters of a model, determining boundary conditions according to reinforced structure characteristics, calculating deepwater explosion loads including shock waves and multiple bubble pulsation loads, establishing a shell plate motion differential equation to solve sunken deformation, and calculating final deformation according to hydrostatic pressure acting correction deformation deflection. Wherein the boundary processing is divided into three types of clamped boundaries, elastic supporting boundaries and mixed boundaries; the load treatment considers the coupling effect of shock wave load, multiple bubble pulsation load and hydrostatic pressure. According to the method, factors are comprehensively considered, deformation is rapidly evaluated, and important support is provided for follow-up evaluation of dynamic response of the reinforced cylindrical shell structure under deepwater explosion.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater explosion, and in particular to a method for calculating the depression deformation of a stiffened cylindrical shell structure under deep water explosion. Background Art

[0002] The stiffened cylindrical shell structure is a common structural type of marine equipment. In recent years, with the continuous attention to the deep sea, various deep sea equipment has emerged continuously. Studying the dynamic response of the stiffened cylindrical shell structure under deep water explosion is of great significance for improving the anti-explosion performance of various deep sea equipment. Compared with shallow water explosion, the dynamic response of the stiffened cylindrical shell model under deep water explosion is more complex. On the one hand, as the water depth increases, the constraint effect of the external hydrostatic pressure on the bubble during the underwater explosion process becomes stronger and stronger, the bubble pulsation period becomes extremely short, and multiple bubble pulsation loads will appear during the deep water explosion process; on the other hand, as the water depth increases, 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 the related technology, the strip beam calculation model is a commonly used simplified calculation model for the stiffened cylindrical shell model, and it is an important method for analyzing the strength of the stiffened cylindrical shell structure under high hydrostatic pressure. However, in the current analysis model of the strip beam, the boundary is usually regarded as a fixed support boundary, that is, the rib does not deform. In the actual structure, for ordinary ribs, especially under the action of explosion load, the shell usually deforms coordinately with the ribs connected to it, and the fixed support boundary is difficult to apply. Summary of the Invention

[0004] The applicant of the present invention aims at the above-mentioned disadvantages in the existing production technology, and provides a method for calculating the depression deformation of a stiffened cylindrical shell structure under deep water explosion, so as to be used for quickly evaluating the deformation calculation of the stiffened cylindrical shell model at different explosion point positions, and providing an important technical basis for the anti-explosion performance evaluation and optimal design of deep sea equipment.

[0005] The technical solution adopted by the present invention is as follows: A method for calculating the depression deformation of a stiffened cylindrical shell structure under deep water explosion, comprising the following steps:

[0006] Step 1, determining the overall parameters of the stiffened cylindrical shell model;

[0007] Step 2, determining the boundary conditions according to the stiffening structure characteristics at both ends of the shell plate:

[0008] When both ends are strongly stiffened, it is regarded as a fixed support boundary;

[0009] When both ends are commonly stiffened, it is regarded as an elastic support boundary;

[0010] When one end is strongly stiffened and the other end is commonly stiffened, it is regarded as a fixed support boundary at one end and an elastic support boundary at the other end;

[0011] Step 3: Calculate the deep - water explosion load, including the shock - wave load and multiple bubble - pulsation loads, based on the mass of the explosive package, the explosion distance, the depth, and the equivalent spherical radius.

[0012] Step 4: Based on the strip - beam mechanical model, establish the differential equations of the shell - plate motion under the action of the shock - wave load and multiple bubble - pulsation loads respectively. Combining with the boundary conditions determined in Step 2, assume the deformation mode and obtain the governing equations by the method of separation of variables, and solve them by numerical methods to get the depression deformation of the shell - plate under the action of the shock - wave load and the bubble - pulsation load.

[0013] Step 5: Correct the deformation deflection obtained in Step 4 according to the work done by the hydrostatic pressure on the deformed area of the shell - plate, and calculate the final deformation by balancing the work done by the hydrostatic pressure and the increment of the shell - plate deformation energy.

[0014] In one embodiment, the overall parameters in Step 1 at least include the shell - plate thickness, the stiffening size parameters, the stiffening spacing, and the material properties.

[0015] In one embodiment, the mathematical expressions for the both - ends clamped boundary in Step 2 are:

[0016] w(t, x)| x＝0 =0, w(t, x)| x＝L =0

[0017] The mathematical expressions for the both - ends elastically - supported boundary in Step 2 are:

[0018]

[0019] The mathematical expressions for the one - end clamped boundary and the other - end elastically - supported boundary in Step 2 are:

[0020] w(t, x)| x＝0 =0

[0021]

[0022] Where:

[0023] w(t, ) represents the shell - plate deformation function;

[0024] L is the length of the shell - plate;

[0025] E is the elastic modulus;

[0026] F is the cross - sectional area of the stiffening;

[0027] R is the radius of the shell;

[0028]

[0029] is the flexural rigidity of the shell - plate.

[0030] In one of the embodiments, the calculation formula in Step 3 is as follows:

[0031]

[0032] T 1 = b 1 (H 0 + 10.33) -56 W 13

[0033] T 2 = b 2 (H 0 + 10.33) -56 (W) 13

[0034] T 3 = b 3 (H 0 + 10.33) -56 (W) 13

[0035] In the formula, W is the mass of the explosive package, R 1 is the explosion distance, H 0 is the depth where the explosive package is located, R 0 is the equivalent spherical radius of the explosive package, θ is the shock wave attenuation time parameter, P 1 , a 1 , a 2 , a 3 , b 1 , b 2 , b 3 are parameters for different charges.

[0036] In one of the embodiments, the fluid-structure interaction effect between the shock wave load and the shell plate is considered in Step 4, and based on the strip beam mechanical model, the motion differential equation of the shell plate under the action of the shock wave load is obtained as follows:

[0037]

[0038] Among them, is the dynamic yield limit of the shell plate material; h is the thickness of the shell plate; m is the linear mass of the beam plate strip; P m is the peak pressure of the shock wave;

[0039] When the two ends are fixed boundaries, the deformation mode of w(t, x) is assumed to be:

[0040]

[0041] When the two ends are elastic support boundaries, the deformation mode of w(t, x) is assumed to be:

[0042]

[0043] When one end is a fixed boundary and the other end is an elastic support boundary, the deformation mode of w(t,x) is assumed as:

[0044]

[0045] Substitute the deformation function equation into the motion differential equation, and obtain the governing equation of w 1 (t) by the method of separation of variables;

[0046] When both ends are fixed boundaries, the governing equation is:

[0047]

[0048] When both ends are elastic support boundaries, the governing equation is:

[0049]

[0050] When one end is a fixed boundary and the other end is an elastic support boundary, the governing equation is:

[0051]

[0052] The governing equation is a typical second-order differential equation with constant coefficients. It is solved by numerical methods to obtain the depression deformation w of the shell plate under the shock wave load in deep water explosion shock .

[0053] In one embodiment, in the fifth step, the depression deformation w of the shell plate under the action of multiple bubble pulsation loads in deep water explosion is further calculated bubble ;

[0054] Based on the mechanics model of the strip beam, the motion differential equation of the shell plate under the shock wave load is obtained. According to the boundary conditions at both ends of the shell plate, different deformation modes are assumed. Substitute the deformation function equation into the motion differential equation, and obtain the main governing equation by the method of separation of variables. It is solved by numerical methods to obtain the depression deformation w of the shell plate under the action of three bubble pulsation loads in deep water explosion bubble ;

[0055] The calculation result of the depression deformation of the shell plate under the coupled action of the shock wave load and the three bubble pulsation loads is:

[0056] w 1max = w shock + w bubble

[0057] Calculate the final deformation of the shell plate under the action of external high hydrostatic pressure:

[0058] w 2max = w 1max + Δw

[0059] Under the action of the underwater explosion shock wave and bubble pulsation, the final deformation deflection of the strip beam is:

[0060]

[0061] After being corrected by the work done by hydrostatic pressure, the deflection becomes:

[0062]

[0063] When the two ends are fixed boundaries, the work done by the high hydrostatic pressure q on the concave deformation area is:

[0064]

[0065] The increment of the bending deformation energy of the shell plate is:

[0066]

[0067] The increment of the tensile deformation energy of the shell plate is:

[0068]

[0069] According to the work done by hydrostatic pressure being equal to the increment of the deformation energy of the strip beam, establish the equation W = ΔU 1 + ΔU 2 , and solve to obtain the final deformation of the shell plate;

[0070] When the two ends are elastic support boundaries, the work done by the high hydrostatic pressure q on the concave deformation area is:

[0071]

[0072] Calculate the increment of the bending deformation energy ΔU 1 of the shell plate, and the tensile deformation energy ΔU 2 ;

[0073] At the same time, the potential energy of the elastic fixed end is calculated as follows:

[0074]

[0075] At this time, according to the work done by hydrostatic pressure being equal to the increment of the deformation energy of the strip beam, establish the equation W = ΔU 1 + ΔU 2 + ΔU 3 , and solve to obtain the final deformation of the shell plate;

[0076] When one end is a fixed boundary and the other end is an elastic support boundary, the work done by the high hydrostatic pressure q on the concave deformation area is:

[0077]

[0078] Calculate the increment ΔU of the bending deformation energy of the shell plate 1 and the tensile deformation energy ΔU 2 and the potential energy ΔU of the elastic fixed end 3 , and establish the equation W = ΔU based on the work done by the hydrostatic pressure being equal to the increment of the deformation energy of the strip beam 1 +ΔU 2 +ΔU 3 , and solve to obtain the final deformation of the shell plate.

[0079] In one embodiment, the numerical method is one of the finite difference method, the finite element method, or the Runge - Kutta method.

[0080] The beneficial effects of the present invention are as follows:

[0081] The calculation process of the present invention is clear and reasonable. In terms of boundary treatment, according to the stiffening structure characteristics at both ends of the shell plate, it is divided into three types of boundaries for treatment. One type is strong stiffening at both ends, which is regarded as a fixed - support boundary at this time; one type is ordinary stiffening at both ends, and the boundary condition is an elastic - support boundary at this time; one type of boundary is strong stiffening at one end and ordinary stiffening at the other end, and the boundary condition is a fixed - support boundary at one end and an elastic - support boundary at the other end. At the same time, in terms of load treatment, the present invention can simultaneously consider the coupling effect of the shock wave load and the multiple - bubble pulsation load under deep - water explosion, and can also consider the coupling effect of the hydrostatic pressure. Therefore, a method for calculating the depression deformation of a stiffened cylindrical shell structure under deep - water explosion of the present invention can provide important support for subsequent evaluation of the dynamic response of the stiffened cylindrical shell structure under deep - water explosion. Description of the Drawings

[0082] Figure 1 is a schematic diagram of the calculation flow of the depression deformation of the stiffened cylindrical shell structure under deep - water explosion of the present invention.

[0083] Figure 2 is the calculation model of the strip beam of the present invention.

[0084] Figure 3 is a schematic diagram of the three types of boundary conditions of the present invention. Specific Embodiments

[0085] In order to make the above objects, features, and advantages of the present invention more obvious and understandable, the following provides a detailed description of the specific embodiments of the present invention with reference to the accompanying drawings. In the description of the present invention, it should be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", "axial", "radial", "circumferential", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings. These are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as a limitation on the present invention.

[0086] In addition, the terms "first" and "second" are only used for descriptive purposes and should not be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one of such features. In the description of the present invention, "a plurality" means at least two, such as two, three, etc., unless otherwise specifically and clearly defined.

[0087] In the present invention, unless otherwise clearly specified and defined, the terms "mounted", "connected", "coupled", "fixed", etc. should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or integrated; it may be a mechanical connection or an electrical connection; it may be directly connected or indirectly connected through an intermediate medium, and it may be the internal communication of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0088] In the present invention, unless otherwise clearly specified and defined, the first feature being "on" or "under" the second feature may be that the first and second features are in direct contact, or the first and second features are indirectly in contact through an intermediate medium. Moreover, the first feature being "above", "over", and "on top of" the second feature may mean that the first feature is directly above or obliquely above the second feature, or simply indicates that the first feature has a higher horizontal height than the second feature. The first feature being "below", "beneath", and "underneath" the second feature may be that the first feature is directly below or obliquely below the second feature, or simply indicates that the first feature has a lower horizontal height than the second feature.

[0089] It should be noted that when an element is referred to as "fixed to" or "disposed on" another element, it can be directly on the other element or there may also be an intermediate 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 intermediate element at the same time. The terms "vertical", "horizontal", "upper", "lower", "left", "right" and similar expressions used herein are only for the purpose of illustration and do not represent the only implementation.

[0090] As Figures 1 - 3 shown, the present invention provides a method for calculating the dent deformation of a stiffened cylindrical shell structure under deep - water explosion, including the following steps:

[0091] Step 1, determining the overall parameters of the stiffened cylindrical shell model;

[0092] Step 2, determining the boundary conditions according to the stiffening structure characteristics at both ends of the shell plate:

[0093] When both ends are strongly stiffened, it is regarded as a fixed - support boundary;

[0094] When both ends are commonly stiffened, it is regarded as an elastic - support boundary;

[0095] When one end is strongly stiffened and the other end is commonly stiffened, it is regarded as a fixed - support boundary at one end and an elastic - support boundary at the other end;

[0096] Step 3, calculating the deep - water explosion load based on the charge mass, explosion distance, depth and equivalent spherical radius, including the shock - wave load and multiple bubble - pulsation loads;

[0097] Step 4, based on the strip - beam mechanical model, respectively establishing the differential equations of motion of the shell plate under the action of the shock - wave load and multiple bubble - pulsation loads, combining with the boundary conditions determined in Step 2, assuming the deformation mode and obtaining the control equations through the method of separation of variables, and using numerical methods to solve to obtain the dent deformation of the shell plate under the action of the shock - wave load and the bubble - pulsation load;

[0098] Step 5, correcting the deformation deflection obtained in Step 4 according to the work done by the hydrostatic pressure on the deformed area of the shell plate, and calculating the final deformation by balancing the work done by the hydrostatic pressure and the increment of the deformation energy of the shell plate.

[0099] In this embodiment, the overall parameters in Step 1 at least include the shell - plate thickness, stiffening dimension parameters, stiffening spacing and material properties.

[0100] In this embodiment, the mathematical expression of the fixed - support boundary at both ends in Step 2 is:

[0101] w(t, x)| x＝0 =0, w(t, x)| x＝L =0

[0102] The mathematical expression of the elastic support boundaries at both ends in the second step is as follows:

[0103]

[0104] The mathematical expression of the fixed support boundary at one end and the elastic support boundary at the other end in the second step is as follows:

[0105] w(t, x)| x＝0 = 0

[0106]

[0107] Where:

[0108] w(t, ) represents the shell plate deformation function;

[0109] L is the length of the shell plate;

[0110] E is the elastic modulus;

[0111] F is the sectional area of the stiffener;

[0112] R is the radius of the shell;

[0113]

[0114] is the flexural rigidity of the shell plate.

[0115] In this embodiment, the calculation formula in the third step is as follows:

[0116]

[0117] T 1 = b 1 (H 0 + 10.33) -5 / 6 W 1 / 3

[0118] T 2 = b 2 (H 0 + 10.33) -5 / 6 (W) 1 / 3

[0119] T 3 = b 3 (H 0 + 10.33) -5 / 6 (W) 1 / 3

[0120] In the formula, W is the mass of the charge, R 1 is the detonation distance, H 0 is the depth where the charge is located, R 0is the equivalent spherical radius of the medicine package, θ is the shock wave attenuation time parameter, P 1 , a 1 , a 2 , a 3 , b 1 , b 2 , b 3 are the parameters of different charges.

[0121] In this embodiment, in step four, considering the fluid-structure interaction effect between the shock wave load and the shell plate, based on the strip beam mechanical model, the following differential equation of motion of the shell plate under the action of the shock wave load is obtained:

[0122]

[0123] Among them, is the dynamic yield limit of the shell plate material; h is the thickness of the shell plate; m is the linear mass of the beam plate strip; P m is the peak pressure of the shock wave;

[0124] When both ends are fixed boundaries, the deformation mode of w(t,x) is assumed to be:

[0125]

[0126] When both ends are elastic support boundaries, the deformation mode of w(t,x) is assumed to be:

[0127]

[0128] When one end is a fixed boundary and the other end is an elastic support boundary, the deformation mode of w(t,x) is assumed to be:

[0129]

[0130] Substitute the deformation function equation into the differential equation of motion, and through the method of separation of variables, obtain the control equation of w 1 (t);

[0131] When both ends are fixed boundaries, the control equation is:

[0132]

[0133] When both ends are elastic support boundaries, the control equation is:

[0134]

[0135] When one end is a fixed boundary and the other end is an elastic support boundary, the control equation is:

[0136]

[0137] The control equation is a typical second-order differential equation with constant coefficients, which is solved by numerical methods to obtain the depression deformation w of the shell plate under the shock wave load in deep water explosion. shock .

[0138] In this embodiment, in step five, the depression deformation w of the shell plate under the action of multiple bubble pulsation loads in deep water explosion is further calculated. bubble ;

[0139] Similar to the shock wave load, based on the strip beam mechanical model, the motion differential equation of the shell plate under the shock wave load is obtained. According to the boundary conditions at both ends of the shell plate, different deformation modes are assumed, and the deformation function equation is substituted into the motion differential equation. By the method of separating variables, the main control equation is obtained and solved by numerical methods to obtain the depression deformation w of the shell plate under the action of three bubble pulsation loads in deep water explosion. bubble ;

[0140] The calculation result of the depression deformation of the shell plate under the coupled action of the shock wave load and the three bubble pulsation loads is:

[0141] w 1max = w shock + w bubble

[0142] Calculate the final deformation of the shell plate under the action of external high hydrostatic pressure:

[0143] w 2max = w 1max + Δw

[0144] The final deformation deflection of the strip beam under the action of the underwater explosion shock wave and bubble pulsation is:

[0145]

[0146] After being corrected by the work done by the hydrostatic pressure, the deflection becomes:

[0147]

[0148] When the two ends are fixed boundaries, the work done by the high hydrostatic pressure q on the concave deformation region is:

[0149]

[0150] The increment of the bending deformation energy of the shell plate is:

[0151]

[0152] The increment of the tensile deformation energy of the shell plate is:

[0153]

[0154] An equation \(W = \Delta U\) is established based on the work done by hydrostatic pressure being equal to the increment of the deformation energy of the strip beam. 1 +\(\Delta U\) 2 , and solve to obtain the final deformation of the shell plate;

[0155] When the two ends are elastic support boundaries, the work done by the high hydrostatic pressure \(q\) on the concave deformation region is:

[0156]

[0157] Calculate the increment of the bending deformation energy \(\Delta U\) of the shell plate 1 、the tensile deformation energy \(\Delta U\) 2 , and the calculation method is the same as described above;

[0158] Meanwhile, the potential energy of the elastic fixed end is calculated as follows:

[0159]

[0160] At this time, an equation \(W = \Delta U\) is established based on the work done by hydrostatic pressure being equal to the increment of the deformation energy of the strip beam 1 +\(\Delta U\) 2 +\(\Delta U\) 3 , and solve to obtain the final deformation of the shell plate;

[0161] When one end is a fixed boundary and the other end is an elastic support boundary, the work done by the high hydrostatic pressure \(q\) on the concave deformation region is:

[0162]

[0163] Calculate the increment of the bending deformation energy \(\Delta U\) of the shell plate 1 、the tensile deformation energy \(\Delta U\) 2 、the potential energy of the elastic fixed end \(\Delta U\) 3 , and establish an equation \(W = \Delta U\) based on the work done by hydrostatic pressure being equal to the increment of the deformation energy of the strip beam 1 +\(\Delta U\) 2 +\(\Delta U\) 3 , and solve to obtain the final deformation of the shell plate.

[0164] In this embodiment, the numerical method is one of the finite difference method, the finite element method, or the Runge - Kutta method.

[0165] In a specific embodiment, taking the structural parameters of a typical cylindrical shell stiffened model as an example for calculation, the radius of the pressure - resistant shell is 3.5 m, the plate thickness is 30 mm, the rib pitch is 600 mm, and the yield strength is 690 MPa;

[0166] The dimensions of the ordinary stiffeners are:

[0167]

[0168] The dimensions of the strong stiffeners are:

[0169]

[0170] Change the drug dosage and hydrostatic pressure, and calculate the results of the final depression deformation of the shell plate under different explosion conditions when both ends are reinforced, both ends are commonly reinforced, and one end is reinforced and the other end is commonly reinforced, respectively.

[0171] The results are shown in Table 1 below:

[0172] Table 1 List of calculation results

[0173]

[0174] To sum up, the boundary treatment of the present invention is flexible. According to the reinforcement structure characteristics at both ends of the shell plate, it is divided into three types of treatment: fixed boundary, elastic support boundary, and one fixed end and one elastic support boundary, which improves the calculation accuracy; the load treatment is comprehensive, considering the coupling effects of shock wave load, multiple bubble pulsation loads, and hydrostatic pressure under deep water explosion, making the calculation results more in line with the actual situation; the calculation method is clear. Based on the strip beam mechanical model, the differential motion equation of the shell plate is established and solved by numerical methods, with clear steps and easy to implement; it provides an important technical basis for quickly evaluating the dynamic response of the reinforced cylindrical shell structure under deep water explosion, and helps to evaluate and optimize the anti-explosion performance of deep sea equipment.

[0175] The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity of description, 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, it should be considered as the scope described in this specification.

[0176] The above-described embodiments only express the implementation manners of the present invention, and the description is relatively specific and detailed, but it cannot be understood as a limitation on the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several deformations and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention patent shall be subject to the appended claims.

Claims

1. A method for calculating the concave deformation of a reinforced cylindrical shell structure under deep-water explosion, characterized in that: The following steps are involved: Step 1, determine the overall parameters of the stiffened cylindrical shell model; Step 2: Determine the boundary conditions based on the reinforcement structure characteristics at both ends of the shell plate: When both ends are strongly reinforced, they are regarded as fixed support boundaries; When both ends are reinforced with ordinary reinforcement, they are regarded as elastically supported boundaries; When one end is strongly reinforced and the other end is normally reinforced, it is regarded as a fixed support boundary at one end and an elastic support boundary at the other end; Step 3: Calculate the deepwater explosion load, including shock wave load and multiple bubble pulsation load, based on the charge mass, explosion distance, depth and equivalent spherical radius; Step 4: Based on the slat beam mechanics model, the differential equations of shell plate motion under the action of shock wave load and multiple bubble pulsation load are established respectively. Combined with the boundary conditions determined in step 2, the deformation mode is assumed and the control equation is obtained by separation of variables method. The numerical method is used to solve the shell plate concave deformation under the action of shock wave load and bubble pulsation load. Step 5: According to the work done by the hydrostatic pressure on the shell plate deformation area, the deformation deflection obtained in step 4 is corrected, and the final deformation is calculated by balancing the work done by the hydrostatic pressure and the shell plate deformation energy increment.

2. The method for calculating the concave deformation of a reinforced cylindrical shell structure under deep water explosion according to claim 1, characterized in that: The overall parameters in step 1 at least include shell thickness, reinforcement size parameters, reinforcement spacing and material properties.

3. The method for calculating the concave deformation of a reinforced cylindrical shell structure under deep water explosion according to claim 1, characterized in that: The mathematical expression of the fixed support boundaries at both ends in step 2 is: The mathematical expression of the elastic support boundaries at both ends in step 2 is: The mathematical expression of the fixed support boundary at one end and the elastic support boundary at the other end in step 2 is: w(t,x)| x＝0 =0 in: w(t, x) represents the shell deformation function; L is the length of the shell plate; E is the elastic modulus; F is the cross-sectional area of ​​reinforcement; R is the shell radius; is the flexural stiffness of the shell.

4. The method for calculating the concave deformation of a reinforced cylindrical shell structure under deep water explosion according to claim 1, characterized in that: The calculation formula in step 3 is: T1=b1(H0+10.33) -56 IN 13 <h2 style=";text-align:left;direction:ltr">T2 = b2(H0 + 10.33) - 56(W)<h2 style=";text-align:left;direction:ltr"> 13 <h2 style=";text-align:left;direction:ltr">T3 = b3(H0 + 10.33)<h2 style=";text-align:left;direction:ltr"> -56 <h2 style=";text-align:left;direction:ltr"> (W)<h2 style=";text-align:left;direction:ltr"> 13 Where W is the mass of the charge, R1 is the explosion distance, H0 is the depth of the charge, R0 is the equivalent spherical radius of the charge, θ is the shock wave attenuation time parameter, and P1, a1, a2, a3, b1, b2, and b3 are parameters of different charges.

5. The method for calculating the concave deformation of a reinforced cylindrical shell structure under deep water explosion as claimed in claim 1, wherein The method is characterized in that, in step 4, the fluid-solid coupling effect of the shock wave load and the shell plate is considered, and based on the slat beam mechanical model, the motion differential equation of the shell plate under the shock wave load is obtained as follows: in, is the dynamic yield limit of the shell material; h is the thickness of the shell; m is the linear mass of the beam strip; P m is the peak pressure of the shock wave; When both ends are fixed boundaries, the deformation mode of w(t,x) is assumed to be: When both ends are elastically supported boundaries, the deformation mode of w(t,x) is assumed to be: When one end is a fixed support boundary and the other end is an elastic support boundary, the deformation mode of w(t,x) is assumed to be: Substitute the deformation function equation into the differential equation of motion and obtain the control equation of w1(t) by separation of variables method; When both ends are fixed boundaries, the control equation is: When both ends are elastically supported boundaries, the governing equation is: When one end is a fixed support boundary and the other end is an elastic support boundary, the governing equation is: The control equation is a typical second-order differential equation with constant coefficients, which is solved by numerical method to obtain the concave deformation w of the shell plate under the shock wave load under deep-water explosion. shock .

6. The method for calculating the concave deformation of a reinforced cylindrical shell structure under deep water explosion according to claim 1, characterized in that: In step 5, the shell plate concave deformation w under the action of multiple bubble pulsation loads under deep water explosion is further calculated. bubble ; Based on the slat beam mechanics model, the motion differential equation of the shell plate under the shock wave load is obtained. According to the boundary conditions at both ends of the shell plate, different deformation modes are assumed, and the deformation function equation is brought into the motion differential equation. The main control equation is obtained by separation of variables method, and the numerical method is used to solve it to obtain the concave deformation w of the shell plate under the three-bubble pulsation load under deep-water explosion. bubble ; The calculation results of the shell plate concave deformation under the coupling of shock wave load and tertiary bubble pulsation load are as follows: In 1max =in shock +in bubble Calculate the final deformation of the shell plate under the external high hydrostatic pressure: In 2max =in 1max +Δw The final deformation deflection of the slat beam under the action of underwater explosion shock wave and bubble pulsation is: After correction for the work done by hydrostatic pressure, the deflection becomes: When both ends are fixed boundaries, the work done by the high hydrostatic pressure q on the concave deformation area is: The increment of shell bending deformation energy is: The increment of tensile deformation energy of shell plate is: According to the fact that the work done by the hydrostatic pressure is equal to the increment of the deformation energy of the slat beam, the equation W = ΔU1 + ΔU2 is established and solved to obtain the final deformation of the shell plate; When both ends are elastically supported boundaries, the work done by the high hydrostatic pressure q on the concave deformation area is: Calculate the increment of shell plate bending deformation energy ΔU1 and tensile deformation energy ΔU2; At the same time, the potential energy of the elastic fixed end is calculated as follows: At this time, the equation W = ΔU1 + ΔU2 + ΔU3 is established based on the fact that the work done by the hydrostatic pressure is equal to the increment of the deformation energy of the slat beam, and the final deformation of the shell plate is obtained by solving it; When one end is a fixed support boundary and the other end is an elastic support boundary, the work done by the high hydrostatic pressure q on the concave deformation area is: The increment of the shell plate bending deformation energy ΔU1, the tensile deformation energy ΔU2, and the potential energy ΔU3 of the elastic fixed end are calculated, and the equation W=ΔU1+ΔU2+ΔU3 is established based on the fact that the work done by the hydrostatic pressure is equal to the increment of the deformation energy of the slat beam, and the final deformation of the shell plate is obtained by solving it.

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

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