A theoretical calculation method for the load-bearing safety of an underwater superstructure pressure-resistant body

Abstract

The present invention discloses a theoretical calculation method for the load-bearing safety of an underwater superstructure pressure-resistant body, which determines the geometric parameters of the superstructure pressure-resistant body; the superstructure pressure-resistant body includes an inner panel and an outer panel that form a cylindrical shell structure, and a core layer structure located between the inner panel and the outer panel, and the core layer structure is a simple cubic cell lattice structure arranged periodically; determines the allowable stresses of the panel and the core layer structure; determines the hydrostatic pressure load received by the superstructure pressure-resistant body; S4. Calculates the maximum principal stress on the panel of the cylindrical shell structure under the action of the hydrostatic pressure load; S5. Calculates the axial force and the maximum normal stress of the radial rod elements of the lattice structure; S6. Calculates the critical buckling load of the radial rod elements of the lattice structure; S7. Compares and verifies the load-bearing safety of the superstructure pressure-resistant body. The present invention can quickly calculate the load-bearing safety of the superstructure pressure-resistant body under known materials and geometric dimensions, can shorten the calculation time, reduce the calculation resources, and consider the influence of the axial load of the shell in the deep-water environment.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater pressure-resistant load-bearing structures, and particularly to a theoretical calculation method for the load-bearing safety of an underwater superstructure pressure-resistant body. Background Art

[0002] With the continuous development of the ocean, underwater superstructure pressure-resistant bodies are increasingly used in the exploration and development of ocean resources and are important components of equipment such as deep submersibles, underwater vehicles, and underwater space stations. The load-bearing capacity of the pressure-resistant body determines whether the deep-sea equipment can work safely and normally under high hydrostatic pressure.

[0003] At present, the load-bearing capacity of underwater superstructure pressure-resistant bodies is mainly tested through experiments and finite element simulations. The credibility of the experiments is relatively high, but they often face problems such as high costs and long cycles. Currently, most finite element simulations of high hydrostatic pressure are limited to the analysis of the buckling behavior of deep-water pressure-resistant shells, and the influence of axial loads on the shells is rarely considered. There is a lack of a method for quickly and accurately calculating the safety of underwater superstructure pressure-resistant bodies through theoretical calculations. Summary of the Invention

[0004] The main purpose of the present invention is to propose a theoretical calculation method for the load-bearing safety of an underwater superstructure pressure-resistant body, which can quickly calculate the load-bearing safety of the superstructure pressure-resistant body under known materials and geometric dimensions.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A theoretical calculation method for the load-bearing safety of an underwater superstructure pressure-resistant body, comprising the following steps:

[0007] S1. Determine the geometric parameters of the superstructure pressure-resistant body

[0008] The superstructure pressure-resistant body includes an inner panel and an outer panel that form a cylindrical shell structure, and a core layer structure located between the inner panel and the outer panel. The core layer structure is a periodically arranged simple cubic cell lattice structure, and the inside of the simple cubic cell is filled with a polymer material; the geometric parameters include the inner radius a, the outer radius b, the thickness c of the core layer structure, the thickness d of the inner and outer panels, the side length e of a single simple cubic cell bar, and the horizontal span f of the bar.

[0009] S2. Determine the allowable stresses [σ f , [σ c of the panel and the core layer structure;

[0010] S3. Determine the hydrostatic pressure load p received by the superstructure pressure-resistant body;

[0011] S4. Calculate the maximum principal stress on the panel of the cylindrical shell structure under the action of the hydrostatic pressure load p;

[0012] S5. Calculate the axial force F of the radial rod elements of the lattice structure Ng and the maximum normal stress σ Ng ;

[0013] S6. Calculate the critical buckling load F of the radial rod elements of the lattice structure cr ;

[0014] S7. Compare and verify the load-bearing safety of the superstructure pressure hull, including:

[0015] Compare the maximum principal stresses when the radius r of the cylindrical shell structure takes r = a and r = b respectively, extract the larger value and compare it with the allowable stress [σ f to verify the load-bearing safety of the panel;

[0016] Compare the maximum principal stress σ Ng of the radial rod elements of the lattice structure with the allowable stress [σ c of the core layer structure to verify the load-bearing safety of the lattice structure;

[0017] Compare the axial force F Ng of the radial rod elements of the lattice structure and the critical buckling load F cr to verify the stability of the lattice structure.

[0018] For further optimization, in step S4, calculating the maximum principal stress on the panel includes the following steps:

[0019] S41. Calculate the cross-sectional stress components of the cylindrical shell structure under the action of the hydrostatic pressure load p;

[0020] S42. Calculate the axial normal stress σ Z of the cylindrical shell structure under the action of the hydrostatic axial force, which occurs in all regions of the pressure hull;

[0021] S43. Complete the transformation of the stress components from polar coordinates to rectangular coordinates;

[0022] S44. Calculate the principal stress at any point of the cylindrical shell structure;

[0023] S45. Calculate the maximum principal stress of the panel.

[0024] For further optimization, in steps S41 to S45, the superstructure pressure hull is based on the homogenization hypothesis of the core layer lattice superstructure, and at the same time, the Euler-Bernoulli beam hypothesis is adopted for the axial section, ignoring the shear deformation of the cross-section; it is assumed that the inner and outer panels and the core layer structure are perfectly bonded without delamination; it is assumed that the cylindrical shell structure is axially long enough, and the plane stress hypothesis is adopted, only considering the in-plane stress;

[0025] In step S41, the calculated cross-sectional stress components under the hydrostatic pressure load p are:

[0026]

[0027] Wherein, σ r is the radial normal stress, σ θ is the circumferential normal stress, a is the inner radius of the cylindrical shell structure, b is the outer radius of the cylindrical shell structure, r is the radius of any point of the cylindrical shell structure, and p is the hydrostatic load.

[0028] For further optimization, in step S42, the axial normal stress of the cylindrical shell structure is:

[0029]

[0030] Wherein, σ Z is the axial normal stress of the cylindrical shell structure, A is the cross-sectional area of the cylindrical shell structure, F N is the hydrostatic axial force received by the cylindrical shell structure, and F N is calculated according to the following formula:

[0031] F N = pA (8)

[0032] Wherein, p is the hydrostatic load and A is the cross-sectional area of the cylindrical shell structure;

[0033] Therefore, there is:

[0034] σ Z = p (9)

[0035] For further optimization, in step S43, the transformation formula of stress components from polar coordinates to rectangular coordinates is:

[0036]

[0037] Wherein, σ x is the normal stress in the x direction, σ y is the normal stress in the y direction, τ xy is the shear stress on the xy plane, the x direction is the horizontal direction, the y direction is the vertical direction, σ r is the radial normal stress, σ θ is the circumferential normal stress, τ rθ is the shear stress, and θ is the rotation angle of any point of the cylindrical shell structure.

[0038] For further optimization, since the calculation of the normal stress of the cylindrical shell structure is independent of the angle θ, therefore, θ can be any value. Let θ = 0, and formula (10) is simplified to:

[0039]

[0040] For further optimization, in step S44, the cubic state characteristic equation for solving the principal stress is:

[0041] σ 3 -I1σ 2 +I2σ - I3 = 0 (12)

[0042] The three real roots σ1, σ2, σ3 of this equation are the three principal stresses sought, arranged as σ1 ≥ σ2 ≥ σ3. I1, I2, I3 are three stress tensors and are defined by the following equations

[0043]

[0044] where σ x is the normal stress in the x - direction, σ y is the normal stress in the y - direction, σ Z is the axial normal stress of the cylindrical shell structure, τ xy is the shear stress in the xy - plane, τ yz is the shear stress in the yz - plane, τ zx is the shear stress in the zx - plane.

[0045] For further optimization, in step S45, the most dangerous areas of the panel may be on the outer surface of the outer panel and the inner surface of the inner panel. Substitute the numerical values of r at the corresponding positions and calculate the maximum principal stress σ1 when r = a and r = b according to steps S41 - S44.

[0046] For further optimization, in step S5, assume that the lattice units in contact with the radial rod elements of the lattice structure are in a planar state when calculating the forces on the radial rod elements of the lattice structure; the axial force calculation of the radial rod elements of the lattice structure is as follows

[0047] F Ng = pA b (33)

[0048] where F Ng is the axial force of the radial rod element of the lattice structure, p is the hydrostatic load, and A b is the radial cross - sectional area of the simple cubic unit cell, calculated as A b = f 2 ;

[0049] The calculation of the maximum normal stress of the rods in the simple cubic unit cell is as follows

[0050] σ Ng = F Ng / A g (34)

[0051] where σ Ng is the maximum normal stress of the rods in the simple cubic unit cell, and A g is the cross - sectional area of the rods in the simple cubic unit cell, calculated as A g = e 2 ;

[0052] Substituting Equation (34) into Equation (33) gives:

[0053]

[0054] In the formula, p is the hydrostatic load, e is the side length of the rod in the simple cubic cell, and f is the horizontal span of the simple cubic cell.

[0055] For further optimization, in step S6, both ends of the radial rod element of the lattice structure are fixed constraints, and the calculation formula for its critical buckling load is:

[0056]

[0057] In the formula, F cr is the critical buckling load, E L is the elastic modulus of the simple cubic cell, μ c is the length coefficient, taking 0.5, c is the thickness of the core layer structure, and I g is the moment of inertia of the cross-section of the rod element, calculated as Substituting into Equation (35), the calculation formula for the critical buckling load of the radial rod element of the lattice structure is:

[0058]

[0059] In the formula, F cr is the critical buckling load, E L is the elastic modulus of the simple cubic cell, e is the side length of the rod in the simple cubic cell, and c is the thickness of the core layer structure.

[0060] The beneficial effects of the present invention are:

[0061] The theoretical calculation method for the load-bearing safety of the underwater superstructure pressure hull proposed by the present invention can quickly calculate the load-bearing safety of the superstructure pressure hull under known materials and geometric dimensions. On the one hand, compared with the load-bearing safety of the panel calculated by the traditional homogeneous finite element, the load-bearing safety of the lattice structure, and the stability of the lattice structure, the present invention can shorten the calculation time and reduce the calculation resources. On the other hand, on the basis of the original deep-water pressure hull, the present invention further considers the influence of the axial load of the hull in the deep-water environment, so that the original theory has been further improved. Description of the Drawings

[0062] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained according to these drawings.

[0063] Figure 1It is the flowchart of the theoretical calculation method for the load-bearing safety of the underwater superstructure pressure-resistant body of the present invention;

[0064] Figure 2 It is the structural schematic diagram of the underwater superstructure pressure-resistant body targeted by the present invention;

[0065] Figure 3 is Figure 2 The schematic diagram of the geometric design parameters of the simple cubic cell of the underwater superstructure pressure-resistant body shown;

[0066] Figure 4 It is the force diagram of the underwater superstructure pressure-resistant body targeted by the present invention under the action of hydrostatic pressure;

[0067] Figure 5 It is the simplified model diagram of the simple cubic cell under the plane stress state. Detailed implementation manners

[0068] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0069] It should be noted that the diagrams provided in the embodiments of the present invention only illustrate the basic concept of the present invention in a schematic manner. Therefore, only the components related to the present invention are shown in the diagrams, rather than being drawn according to the number, shape and size of the components in actual implementation. The types, numbers and proportions of the components in actual implementation can be arbitrarily changed, and the component layout type may also be more complex.

[0070] In the present invention, it should also be noted that when terms such as "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. appear, the orientation or positional relationship indicated is based on the orientation or positional relationship shown in the accompanying drawings. It is only for the convenience of describing the present application 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 therefore cannot be understood as a limitation to the present application. In addition, when terms such as "first" and "second" appear, they are only used for descriptive and distinguishing purposes and cannot be understood as indicating or implying relative importance.

[0071] As Figure 1 shown, the present invention proposes a theoretical calculation method for the load-bearing safety of an underwater superstructure pressure-resistant body, including the following steps:

[0072] S1. Determine the geometric parameters of the superstructure pressure-resistant body.

[0073] The superstructure pressure-resistant body targeted by the present invention is as Figure 2As shown, it includes an inner panel and an outer panel that form a cylindrical shell structure, and a core layer structure located between the inner panel and the outer panel. The core layer structure is a simple cubic cell lattice structure with a periodic arrangement as shown in Figure 3 . The inside of the simple cubic cell is filled with a polymer material that does not play a load-bearing role, such as a rubber material. The geometric parameters include: the inner radius a, the outer radius b, the thickness c of the core layer structure, the thickness d of the inner and outer panels, and the side length e and the horizontal span f of the rods of a single simple cubic cell;

[0074] S2. Determine the allowable stresses [σ f , [σ c of the panel and the core layer structure.

[0075] Furthermore, it is also necessary to determine the elastic modulus E L of the simple cubic cell.

[0076] S3. Determine the hydrostatic pressure load p on the superstructure pressure-resistant body.

[0077] S4. Calculate the maximum principal stress on the panel of the cylindrical shell structure under the hydrostatic pressure load p, specifically including:

[0078] S41. Calculate the cross-sectional stress components of the cylindrical shell structure under the hydrostatic pressure load p.

[0079] The superstructure pressure-resistant body targeted is based on the homogenization hypothesis of the core layer lattice superstructure. At the same time, the Euler-Bernoulli beam hypothesis is adopted for the axial section, and the shear deformation of the cross-section is ignored; it is assumed that the inner and outer panels and the core layer structure are perfectly bonded without delamination; it is assumed that the cylindrical shell structure is axially long enough, and the plane stress hypothesis is adopted, only considering the in-plane stress.

[0080] As shown in Figure 4 , the polar coordinate system is used for calculation, and the cross-sectional stress components are:

[0081]

[0082] In the formula, σ r is the radial normal stress, σ θ is the circumferential normal stress, τ rθ , τ θr are the shear stresses in the θ direction on the r plane and the shear stresses in the r direction on the θ plane respectively; A, B, and C are arbitrary constants, and r is the radius of any point on the cylindrical shell structure.

[0083] The boundary conditions under the hydrostatic pressure load p are:

[0084] (τ rθ ) r＝a = 0, (τ rθ ) r＝b = 0

[0085] (σ r ) r＝a =0,(σ r ) r＝b = -p (2)

[0086] where (τ rθ ) r＝a represents the shear stress of the cylindrical shell structure at r = a, and (τ rθ ) r＝b represents the shear stress of the cylindrical shell structure at r = b, (σ r ) r＝a represents the radial normal stress of the cylindrical shell structure at r = a, and (σ r ) r＝b represents that the radial normal stress of the cylindrical shell structure at r = b is -p; a is the inner radius of the cylindrical shell structure, b is the outer radius of the cylindrical shell structure, and p is the hydrostatic load.

[0087] It can be seen from (1) that the first two boundary conditions are satisfied, while the last two boundary conditions require:

[0088]

[0089] The displacement components in the axisymmetric stress state are:

[0090]

[0091] where u r is the radial displacement, u θ is the circumferential displacement, A, B, C, H, I, K are all arbitrary constants, E is the elastic modulus of the material used, μ is the Poisson's ratio of the material used, r is the radius of any point of the cylindrical shell structure, and θ is the rotation angle of any point of the cylindrical shell structure.

[0092] According to the displacement single-valued condition, it can be seen from the second term of Equation (4) that in the expression of the circumferential displacement u θ , one term is multi-valued. In the cylindrical shell structure, this is impossible because (r1, θ1) and (r1, θ1 + 2π) are the same point and cannot have different displacements. Thus, it can be seen that B = 0 must hold.

[0093] Substituting B = 0 into Equation (3) gives:

[0094]

[0095] Substituting Equation (5) into Equation (1) and solving gives:

[0096]

[0097] where σ ris the radial normal stress, σ θ is the circumferential normal stress, a is the inner radius of the cylindrical shell structure, b is the outer radius of the cylindrical shell structure, r is the radius of any point on the cylindrical shell structure, and p is the hydrostatic pressure load.

[0098] S42. Calculate the axial normal stress σ Z of the cylindrical shell structure under the action of the hydrostatic axial force, which occurs in all regions of the pressure-resistant body.

[0099]

[0100] In the formula, σ Z is the axial normal stress of the cylindrical shell structure, A b is the cross-sectional area of the cylindrical shell structure, F N is the hydrostatic axial force received by the cylindrical shell structure, F N is calculated according to the following formula:

[0101] F N = pA b (8)

[0102] In the formula, p is the hydrostatic pressure load, and A b is the cross-sectional area of the cylindrical shell structure;

[0103] Therefore, there is:

[0104] σ Z = p (9)

[0105] S43. Complete the transformation of the stress components from polar coordinates to rectangular coordinates.

[0106] The transformation formula of the stress components from polar coordinates to rectangular coordinates is:

[0107]

[0108] In the formula, σ x is the normal stress in the x direction, σ y is the normal stress in the y direction, τ xy is the shear stress in the xy plane. The x direction is the horizontal direction, the y direction is the vertical direction, σ r is the radial normal stress, σ θ is the circumferential normal stress, τ rθ is the shear stress, and θ is the rotation angle of any point on the cylindrical shell structure.

[0109] Since the calculation of the normal stress of the cylindrical shell structure is independent of the angle θ, therefore, θ can be any value. Let θ = 0, and formula (10) is simplified to:

[0110]

[0111] S44. Calculate the principal stress of any point on the cylindrical shell structure.

[0112] The cubic state characteristic equation for solving the principal stress is as follows:

[0113] σ 3 - I1σ 2 + I2σ - I3 = 0 (12)

[0114] The three real roots σ1, σ2, σ3 of this equation are the three principal stresses sought, and I1, I2, I3 are three stress tensors, and are defined by the following formula

[0115]

[0116] In the formula, σ x is the normal stress in the x direction, σ y is the normal stress in the y direction, σ Z is the axial normal stress of the cylindrical shell structure, τ xy is the shear stress in the xy plane, τ yz is the shear stress in the yz plane, τ zx is the shear stress in the zx plane.

[0117] Let σ = y + I1 / 3, where y represents any point on the y-axis. Substituting it into equation (12) gives:

[0118] y 3 + my + n = 0 (14)

[0119] In the formula,

[0120] Let z represents any point on the z-axis. Substituting it into equation (14) gives:

[0121]

[0122] Equation (15) is a quadratic equation of z 3 , and its solutions are:

[0123]

[0124] In the formula, Let

[0125]

[0126] Substituting into the first formula of equation (16), we can get:

[0127] z 3 - D 3 = (z - D)(z 2 + zD + D 2 ) = 0 (18)

[0128] The three roots of z are as follows:

[0129]

[0130] where z1, z2, and z3 represent the three roots of equation (18), and i represents the imaginary unit.

[0131] Substitute z1, z2, and z3 into and use equation (17) to obtain the three roots of the corresponding y:

[0132]

[0133] Equation (20) is the Cardano formula for solving a cubic equation. Based on this, adding I1 / 3 gives the expressions for σ1, σ2, and σ3.

[0134] For the cubic equation y 3 + my + n = 0, the discriminant is When R > 0, one root of y is real and two are imaginary. When R ≤ 0, y has three real roots. Therefore, only the case of R ≤ 0 is considered for solving equation (12). When R = 0, from equation (17), we get Substituting into equation (20) gives the three roots of y as:

[0135]

[0136] Let D = (j + ki) 1 / 3 = r + si, F = (j - ki) 1 / 3 = r1 - si. Here, r1, s, j, and k are constants. Substituting into equation (20) gives:

[0137]

[0138] Introducing the trigonometric expression of complex numbers, we get:

[0139]

[0140] where ρ and are determined by the following expressions:

[0141]

[0142] Then introduce the complex number square root operation formula:

[0143]

[0144] where A1, B1 represent Cardano constants, and r1, s, j, k are constants. is the central angle, and t = 0, 1, 2 are positive integers.

[0145] Substituting Equation (25) into any one of Equation (22) can obtain three roots of y. Taking the substitution into the first equation as an example, we can get:

[0146]

[0147] That is:

[0148]

[0149] Substituting Equation (21) and Equation (27) into σ = y + I1 / 3 respectively, the calculation formulas for the three principal stresses σ1, σ2, and σ3 (arranged in the order of σ1≥σ2≥σ3) are finally obtained as:

[0150] When At this time

[0151] If m = 0, then

[0152] σ1 = σ2 = σ3 = I1 / 3 (28)

[0153] If m < 0, then

[0154]

[0155] If m > 0, then

[0156]

[0157] When At this time

[0158]

[0159] In the above formula, I1 is the stress tensor in the 1 direction. m and n are defined as follows

[0160]

[0161] S45. Calculate the maximum principal stress of the panel.

[0162] The most dangerous area of the panel may be on the outer surface of the outer panel and the inner surface of the inner panel. Substitute the numerical values of r at the corresponding positions and calculate the maximum principal stress σ1 when r = a and r = b according to steps S41 - S44.

[0163] S5. Calculate the axial force F Ng and the maximum normal stress σ Ng .

[0164] As Figure 5 shown, when calculating the force on the radial rod element of the lattice structure, it is assumed that the lattice element it contacts is in a plane state.

[0165] The axial force calculation of the radial rod element of the lattice structure is as follows:

[0166] F Ng = pA b (33)

[0167] In the formula, F Ng is the axial force of the radial rod element of the lattice structure, p is the hydrostatic pressure load, and A b is the radial cross-sectional area of the simple cubic cell, calculated as A b = f 2 .

[0168] The calculation of the maximum normal stress of the rod in the simple cubic cell is as follows:

[0169] σ Ng = F Ng / A g (34)

[0170] In the formula, σ Ng is the maximum normal stress of the rod in the simple cubic cell, and A g is the cross-sectional area of the rod in the simple cubic cell, calculated as A g = e 2 .

[0171] Substituting Equation (34) into Equation (33) gives:

[0172]

[0173] In the formula, p is the hydrostatic pressure load, e is the side length of the rod in the simple cubic cell, and f is the horizontal span of the simple cubic cell.

[0174] S6. Calculate the critical buckling load F cr .

[0175] Both ends of the radial rod element of the lattice structure are fixed constraints, and its critical buckling load calculation formula is:

[0176]

[0177] In the formula, F cr is the critical buckling load, E L is the elastic modulus of the simple cubic cell, μ c is the length coefficient, taking 0.5, c is the core layer structure thickness, and I g is the cross-sectional moment of inertia of the rod element, calculated as Substituting into Equation (35) gives the critical buckling load calculation formula of the radial rod element of the lattice structure as:

[0178]

[0179] In the formula, Fcr is the critical buckling load, E L is the elastic modulus of the simple cubic unit cell, e is the side length of the rod in the simple cubic unit cell, and c is the thickness of the core structure.

[0180] S7. Compare and verify the load-bearing safety of the superstructure pressure hull, including:

[0181] Compare the maximum principal stress σ1 when the radius r of the cylindrical shell structure takes r = a and r = b, and extract the larger value to compare with the allowable stress [σ f to verify the load-bearing safety of the panel;

[0182] Compare the maximum principal stress σ Ng of the radial rod element of the lattice structure with the allowable stress [σ c of the core structure to verify the load-bearing safety of the lattice structure;

[0183] Compare the axial force F Ng of the radial rod element of the lattice structure with the critical buckling load F cr to verify the stability of the lattice structure.

[0184] It should be noted that according to the needs of implementation, each step / component described in this application can be split into more steps / components, or two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of the present invention.

[0185] The magnitude of the sequence numbers of the steps in the above embodiments does not mean the order of execution. The order of execution of each process should be determined by its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of this application.

[0186] It should be understood that those of ordinary skill in the art can make improvements or transformations according to the above description, and all such improvements and transformations should fall within the protection scope of the appended claims of the present invention.

Claims

1. A theoretical calculation method for the bearing safety of an underwater superstructure pressure-resistant body, characterized in that, It includes the following steps: S1. Determine the geometric parameters of the superstructure pressure-resistant body The superstructure pressure-resistant body includes an inner panel and an outer panel that form a cylindrical shell structure, and a core layer structure located between the inner panel and the outer panel. The core layer structure is a periodically arranged simple cubic cell lattice structure, and the inside of the simple cubic cell is filled with a polymer material; the geometric parameters include the inner radius a, the outer radius b of the cylindrical shell structure, the thickness c of the core layer structure, the thickness d of the inner and outer panels, the side length e of a single simple cubic cell rod, and the horizontal span f of the rod S2. Determine the allowable stresses [σ f , [σ c of the panel and core layer structure; S3. Determine the hydrostatic pressure load p borne by the superstructure pressure-resistant body S4. Calculate the maximum principal stress on the panel of the cylindrical shell structure under the action of the hydrostatic pressure load p S5. Calculate the axial force F of the radial rod element of the lattice structure Ng and the maximum normal stress σ Ng ; S6. Calculate the critical buckling load F of the radial rod elements of the lattice structure cr ; S7. Compare and verify the load-bearing safety of the superstructure pressure-resistant body, including: Compare the maximum principal stresses when the radius r of the cylindrical shell structure takes r = a and r = b respectively, extract the larger value and compare it with the allowable stress [σ f to verify the bearing safety of the panel; Compare the maximum principal stress σ of the lattice structure radial rod element Ng with the allowable stress [σ c of the core layer structure to verify the load-bearing safety of the lattice structure; Compare the axial force F of the radial rod element of the lattice structure Ng with the critical buckling load F cr to verify the stability of the lattice structure.

2. The theoretical calculation method for the load-bearing safety of the underwater superstructure pressure-resistant body according to claim 1, characterized in that, In step S4, calculating the maximum principal stress on the panel includes the following steps: S41. Calculate the cross-sectional stress components of the cylindrical shell structure under the action of the hydrostatic pressure load p S42. Calculate the axial normal stress σ of the cylindrical shell structure under the action of hydrostatic axial force Z , which occurs in all areas of the pressure hull; S43. Complete the transformation of the stress components from polar coordinates to rectangular coordinates S44. Calculate the principal stress at any point of the cylindrical shell structure S45. Calculate the maximum principal stress of the panel 3. The theoretical calculation method for the load-bearing safety of the underwater superstructure pressure-resistant body according to claim 2, characterized in that, In steps S41 to S45, the superstructure pressure-resistant body is based on the homogenization hypothesis of the core layer lattice superstructure, and at the same time, the Euler-Bernoulli beam hypothesis is adopted for the axial section, ignoring the shear deformation of the cross-section; it is assumed that the inner and outer panels and the core layer structure are perfectly bonded without delamination It is assumed that the cylindrical shell structure is axially long enough, and the plane stress hypothesis is adopted, only considering the in-plane stress In step S41, the calculated cross-sectional stress components under the hydrostatic pressure load p are: where σ r is the radial normal stress, σ θ is the circumferential normal stress, a is the inner radius of the cylindrical shell structure, b is the outer radius of the cylindrical shell structure, r is the radius of any point on the cylindrical shell structure, and p is the hydrostatic pressure load.

4. The theoretical calculation method for the bearing safety of the underwater superstructure pressure-resistant body according to claim 3, wherein In step S42, the axial normal stress of the cylindrical shell structure is: Where, σ Z is the axial normal stress of the cylindrical shell structure, A is the cross-sectional area of the cylindrical shell structure, and F N is the hydrostatic axial force on the cylindrical shell structure. F N is calculated according to the following formula: F N = pA (8) In the formula, p is the hydrostatic pressure load, and A is the cross-sectional area of the cylindrical shell structure Therefore, there is: σ Z = p (9).

5. The theoretical calculation method for the load-bearing safety of the underwater superstructure pressure-resistant body according to claim 4, characterized in that, In step S43, the transformation formula of the stress components from polar coordinates to rectangular coordinates is: In the formula, σ x is the normal stress in the x direction, σ y is the normal stress in the y direction, τ xy is the shear stress on the xy plane. The x direction is the horizontal direction, and the y direction is the vertical direction. σ r is the radial normal stress, σ θ is the circumferential normal stress, τ rθ is the shear stress, and θ is the rotation angle of any point on the cylindrical shell structure.

6. The theoretical calculation method for the load-bearing safety of the underwater superstructure pressure-resistant body according to claim 5, characterized in that, Since the calculation of the normal stress of the cylindrical shell structure is independent of the angle θ, θ can be any value. Let θ = 0, and formula (10) is simplified to:

7. The theoretical calculation method for the load-bearing safety of the underwater superstructure pressure-resistant body according to claim 5 or 6, characterized in that In step S44, the cubic state characteristic equation for solving the principal stress is: σ 3 -I1σ 2 +I2σ - I3 = 0 (12) The three real roots σ1, σ2, and σ3 of this equation are the three principal stresses sought, arranged in the order of σ1 ≥ σ2 ≥ σ3. I1, I2, and I3 are three stress tensors and are defined by the following formula In the formula, σ x is the normal stress in the positive x direction, σ y is the normal stress in the positive y direction, σ Z is the axial normal stress of the cylindrical shell structure, τ xy is the shear stress in the xy plane, τ yz is the shear stress in the yz plane, τ zx is the shear stress in the zx plane.

8. The theoretical calculation method for the load-bearing safety of the underwater superstructure pressure-resistant body according to claim 7, characterized in that In step S45, the most dangerous areas of the panel may be on the outer surface of the outer panel and the inner surface of the inner panel. Substitute the numerical values of r at the corresponding positions and calculate the maximum principal stress σ1 when r = a and r = b according to steps S41 to S44 9. The theoretical calculation method for the load-bearing safety of the underwater superstructure pressure-resistant body according to claim 1, characterized in that, In step S5, when calculating the force on the radial rod element of the lattice structure, it is assumed that the lattice unit it contacts is in a plane state; the axial force calculation of the radial rod element of the lattice structure is: F Ng = pA b (33) where F Ng is the axial force of the radial rod element of the lattice structure, p is the hydrostatic load, and A b is the radial cross-sectional area of the simple cubic cell, calculated as A b = f 2 ; The calculation of the maximum normal stress of the rod in the simple cubic cell is: σ Ng = F Ng / A g (34) where σ Ng is the maximum normal stress of the rod in the simple cubic unit cell, A g is the cross-sectional area of the rod in the simple cubic unit cell, calculated as A g = e 2 ; Substituting formula (34) into formula (33) gives: In the formula, p is the hydrostatic pressure load, e is the side length of the rod of the simple cubic cell, and f is the horizontal span of the simple cubic cell 10. The theoretical calculation method for the load-bearing safety of the underwater superstructure pressure-resistant body according to claim 1, characterized in that, In step S6, both ends of the radial rod element of the lattice structure are fixed constraints, and its critical buckling load calculation formula is: where F cr is the critical buckling load, E L is the elastic modulus of the simple cubic unit cell, μ c is the length coefficient, taking 0.5, c is the thickness of the core structure, I g is the moment of inertia of the rod element cross-section, calculated as Substituting into Equation (35), the formula for calculating the critical buckling load of the radial rod element of the lattice structure is: where F cr is the critical buckling load, E L is the elastic modulus of the simple cubic unit cell, e is the side length of the rod in the simple cubic unit cell, and c is the thickness of the core layer structure.

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