A method for calculating the ultimate load of a metal-lined composite cylindrical shell

Abstract

The present invention discloses a method for calculating the ultimate load of a metal-lined composite cylindrical shell. The cylindrical shell includes an outer fiber composite layer and an inner metal layer. First, a geometric equation is established to divide the fiber composite layer into a number of composite unit layers; the metal layer is cut into a number of metal unit layers with the same thickness; the relationship between stress and strain in each composite unit layer and metal unit layer is established respectively; the in-plane stiffness matrix, coupling stiffness matrix and bending stiffness matrix of the cylindrical shell are calculated based on the equilibrium relationship; a linear buckling load model is established; the linear buckling load model is corrected considering the damage of the material after being subjected to force; and the ultimate load is calculated using the corrected model. By considering the material damage model, the ultimate load of the metal-lined composite cylindrical shell is obtained through quantitative analysis, the crushing load of this type of multi-layer cylindrical shell is reliably predicted, and the compressive failure assessment of the multi-layer composite cylindrical shell under external pressure is improved, thereby making the structural design safer and more reliable.

Description

Technical Field

[0001] The invention relates to deep-sea diving equipment materials, and in particular to a method for calculating the ultimate load of a metal-lined composite material cylindrical shell. Background Art

[0002] The pressure-resistant structures of deep-sea major scientific and technological equipment such as deep-sea manned or unmanned submersibles, deep-sea workstations, deep-sea unmanned transport submersibles, and underwater manifold systems are mostly column-shaped. Metal-lined composite cylindrical shells have attracted much attention because they combine the advantages of both metal materials and composite materials. The outer composite layer of the metal-lined composite cylindrical shell can improve the safety and corrosion resistance of the metal structure while reducing the overall weight; the good ductility of the inner metal layer is beneficial to the equipment layout. For example, the patent application with publication number CN107891634 A discloses a composite material lattice sandwich double-skin cylindrical shell structure containing a metal lining that withstands internal pressure and its preparation process. The outer skin is formed on the outer wall of the thin-walled metal lining by fiber winding, which meets the strength requirements and achieves the purpose of lightweight when subjected to internal pressure.

[0003] However, the material properties of metals and composites differ significantly. The constitutive relations of metals are isotropic, while those of composites are anisotropic. Research on the mechanics of multilayer shells composed of metal and composite materials has been limited to the numerical analysis of GLARE layers (sandwich stacking). Prior art applications, such as patent application CN 108804790 A, disclose a numerical simulation method for the curing deformation of fiber metal laminates. This method takes into account the interaction between the metal sheets and the composite layers within the FMLs during the heating process, making the prediction of the curing deformation of the FMLs more accurate. However, there are few reports on theoretical mechanics research on metal-lined composite cylindrical shells in the prior art. Theoretical mechanics analysis of metal-lined composite cylindrical shells has important guiding significance for optimizing process parameters for major deep-sea scientific and technological equipment. Summary of the Invention

[0004] Purpose of the invention: In view of the above shortcomings, the present invention provides a method for calculating the ultimate load of a metal-lined composite cylindrical shell.

[0005] Technical solution: To solve the above problems, the present invention adopts a method for calculating the ultimate load of a metal-lined composite cylindrical shell. The cylindrical shell includes an outer fiber composite layer and an inner metal layer. The calculation method includes the following steps:

[0006] (1) Establishing the geometric equation of the fiber composite material layer, dividing the fiber composite material layer into several composite material unit layers, and obtaining the strain-displacement relationship of the fiber composite material unit layer;

[0007] (2) establishing an equivalent model of the metal layer; dividing the metal layer into a plurality of metal unit layers, wherein the thickness of the metal unit layer is the same as the thickness of the composite material unit layer;

[0008] (3) Establish the relationship between stress and strain in each composite unit layer and metal unit layer respectively;

[0009] (4) According to the equilibrium relationship: the resultant force of the stress in each layer multiplied by the area of ​​the corresponding layer is equal to the component of the external force on the corresponding coordinate axis under the reference system coordinate axis; the in-plane stiffness matrix, coupling stiffness matrix and bending stiffness matrix of the metal-lined composite cylindrical shell are calculated;

[0010] (5) According to the constraints of cylindrical shells and thin shell theory, the theoretical model of linear buckling load of metal-lined composite cylindrical shells is obtained;

[0011] (6) Considering the linear buckling of the metal-lined composite cylindrical shell and the degree of damage to the material after being subjected to stress, the linear buckling theoretical model is modified based on the Merchant–Rankine formula; the ultimate load of the metal-lined composite cylindrical shell is calculated using the modified model according to the in-plane stiffness matrix, coupling stiffness matrix and bending stiffness matrix of the metal-lined composite cylindrical shell obtained in step (4).

[0012] Furthermore, in step (1), the composite material layer is divided into a number of micro-elements with planar surfaces, and based on the assumption of classical laminate theory, the strain-displacement relationship of the micro-element of the composite material unit layer is obtained:

[0013] {ε}={ε0}+z{q}

[0014] in, z is the radial distance between point C and point O on the mid-plane; ε x , ε y , ε z is the normal strain of the element along the x, y, and z directions, u o is the displacement of point O in the x direction after deformation, v o is the displacement of point O in the y direction after deformation, and w is the displacement of point C in the z direction.

[0015] Furthermore, in step (3), the relationship between stress and strain in each composite material unit layer is calculated according to the following formula:

[0016]

[0017] Among them, σ x is the stress in the fiber direction of the composite material layer, σ y is the transverse stress in the composite material layer, τ xy is the stress in the shear direction, γ xyis the shear strain;

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024] Q 11 , Q 22 , Q 12 , Q 66 is the relationship constant between stress and strain, θ k lay angles for fibers in composite materials;

[0025] The relationship between stress and strain in each metal unit layer is calculated according to the following formula:

[0026]

[0027] Furthermore, the calculation formulas of the stiffness matrix [A], the coupling stiffness matrix [B] and the bending stiffness matrix [D] are:

[0028]

[0029] Among them, N x is the internal force in the x direction, N y is the internal force in the y direction, N xy is the internal force in the xy plane, M x is the torque in the x direction, M y is the torque in the y direction, M xy is the torque in the xy plane, ε xo is the strain in the x direction, ε yo is the strain in the y direction, γ xyo is the in-plane shear strain, κ x is the torsion rate in the x direction, κ y is the torsion rate in the y direction, κ xy is the inward torsion in the xy plane.

[0030] Furthermore, in step (5), the constraint condition of the cylindrical shell is that both ends are simply supported. At this time, the shell displacement when the cylindrical shell buckles satisfies the following formula:

[0031]

[0032] Where u is the displacement of the cylindrical shell in the x-direction, v is the displacement of the cylindrical shell in the y-direction, ω is the displacement of the cylindrical shell in the z-direction, α = mπ / L, β = n / R; m and n are the axial and circumferential wave numbers of the cylindrical shell, respectively; L is the length of the cylindrical shell, and R is the radius of the cylindrical shell; U, V, and W are the maximum displacements of the cylindrical shell in the x-, y-, and z-directions, respectively, and are all non-zero constants.

[0033] Furthermore, according to the thin shell theory of cylindrical shells, the relationship between strain and displacement on the cylindrical shell surface satisfies the following relationship:

[0034]

[0035] Among them, q x is the curvature of the cylindrical shell along the x direction, q y is the curvature of the cylindrical shell along the y direction, q xy is the cylindrical shell torsion.

[0036] Furthermore, the theoretical model of linear buckling load of the metal-lined composite cylindrical shell is:

[0037]

[0038] P e =min{P em};

[0039] Among them, P e is the buckling load,

[0040]

[0041] K 11 =A 11 α 2 +A 66 β 2 ;K 12 =K 21 =(A 12 +A 66 )αβ,

[0042] K 22 =A 22 β 2 +A 66 α 2 ,

[0043]

[0044]

[0045] L 11 =L 12 =L 13 =L 21 =L22 =L 23 =L 31 =L 32 =0,

[0046] Furthermore, the modified formula of the linear buckling theoretical model of the metal-lined composite cylindrical shell is:

[0047]

[0048]

[0049] Among them, P c is the corrected buckling load, b is the damage factor, P0 is the external load of the metal-lined composite cylindrical shell, P f is the material damage load, and H is the material damage judgment index.

[0050] Beneficial effect: Compared with the existing technology, the significant advantage of the present invention is that by considering the material damage model, quantitative analysis is performed to obtain the ultimate load of the metal-lined composite column shell, reliably predict the crushing load of such multi-layer column shell, and improve the compressive failure assessment of the multi-layer composite column shell under external pressure, thereby making the structural design safer and more reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a schematic diagram of the steps of the method for calculating the ultimate load of the present invention.

[0052] Figure 2 It is a schematic diagram of the composite material layer microelement in the present invention.

[0053] Figure 3 It is a schematic diagram of the deformation of the composite material layer microelement in the present invention.

[0054] Figure 4 It is a schematic diagram of the metal lined composite cylindrical shell model in the present invention.

[0055] Figure 5 This is an equivalent model diagram of the metal lined composite cylindrical shell section in the present invention.

[0056] Figure 6 It is a schematic diagram of the two-dimensional internal stress of the composite material layer in the present invention.

[0057] Figure 7 It is a schematic diagram of the fiber stacking angle of the composite material layer in the present invention.

[0058] Figure 8 It is a schematic diagram of the internal force of the composite material layer in the present invention. DETAILED DESCRIPTION

[0059] like Figure 1As shown, a method for calculating the ultimate load of a metal-lined composite cylindrical shell in this embodiment mainly includes the following steps:

[0060] Step 1: Establish the geometric equation. Divide the fiber composite material layer into several composite unit layers, and set the infinitesimal element of the composite layer in the metal lined composite cylindrical shell as follows: Figure 2 As shown, the surface of the microelement is a plane, and the microelement consists of several layers. When a single layer of microelement is subjected to an external force, it deforms, as shown in Figure 3 shown.

[0061] Based on the classical laminate theory assumptions: first, the thickness of a single composite layer is much smaller than the length of the cylindrical shell; second, the mid-surface of a single composite layer is aligned with the normal to the mid-surface ( Figure 3 The center line ab) is vertical, that is, the shear deformation in the thickness direction is not considered. The former assumption is the basis of the latter assumption.

[0062] Let point C be any point on the two-dimensional xz infinitesimal surface, and its radial distance from point O on the mid-surface be z. After deformation, the displacement of point O in the X direction is u o According to the above assumption 2, the deformation of point O on the middle surface is 0, which satisfies the following formula:

[0063]

[0064] It can be obtained that the displacement w of any point in the Z direction on the two-dimensional xz infinitesimal surface satisfies the following formula:

[0065] w=w(x,y)=w0 (2)

[0066] According to the displacement of point C before and after deformation, as Figure 3 As shown, it can be seen that its displacement u in the X direction c It can be obtained by the following formula:

[0067] u c =u0-c′c″=u0-zsinβ (3)

[0068] Where: β is the rotation angle between the mid-plane after deformation and the mid-plane before deformation.

[0069] From the assumption, it can be seen that the deformation in the thickness direction is extremely small, and the following equation can be obtained:

[0070] sinβ=β=tanβ (4)

[0071] In addition, on the two-dimensional xz infinitesimal surface, the tangent of the angle is the partial derivative of the radial displacement of the point in the X direction:

[0072]

[0073] Substituting equations (4) and (5) into equation (3), we can obtain the displacement u of point C in the X direction after deformation: c The conversion formula is:

[0074]

[0075] Similarly, the displacement v of point C in the Y direction on the two-dimensional yz infinitesimal surface can be obtained, satisfying the following formula:

[0076]

[0077] Therefore, the displacement of any point on the infinitesimal element after deformation can be expressed as follows:

[0078]

[0079]

[0080] w(x,y,z)=w0(x,y) (10)

[0081] In addition, according to the infinitesimal deformation and strain equations:

[0082]

[0083]

[0084] Substituting Equations (8) to (10) into the deformation and strain equations of Equations (11) and (12), we can obtain the relationship between strain and displacement, that is, the geometric equation:

[0085]

[0086]

[0087] γ yz =γ zy =γ xz =γ zx =0 (15)

[0088]

[0089] Where: q x ,q y is the mid-surface curvature; q xy is the mid-surface torsion. The above formula can be simplified into matrix form:

[0090] {ε}={ε0}+z{q}, (17)

[0091] Where: According to the assumption of the mid-normal line of the laminate before and after deformation, ε z =0,γ zx =γzy =0.

[0092] Step 2: Establish an equivalent model of the inner metal layer. The outer radius of the inner metal layer of the metal lined composite cylindrical shell is R s ,like Figure 4 In order to facilitate the stress analysis of the metal-lined composite cylindrical shell and obtain its physical equations in a more convenient way, the model is simplified by reasonably dividing the lining metal layer.

[0093] Assume that the thickness of the metal layer in the composite cylindrical shell is t s , the thickness of the composite material layer is t c , then the total wall thickness of the composite cylindrical shell is h = t s +t c ,like Figure 5 As shown. The thickness of each layer of fiber composite material unit layer is t ply , a total of Nn layers, satisfying the following formula:

[0094] t c =(Nn)t ply (18)

[0095] There are n metal unit layers in total, and the thickness of each metal layer after cutting is kept equal to that of the fiber layer, that is, the thickness Δt of each small layer after the metal layer is cut meets the following requirements:

[0096] Δt=t ply , t s =nt ply (19)

[0097] Considering that the strain of the thin shell structure is small relative to the length of the cylindrical shell when critical instability occurs, after the equivalent simplification of the lining metal layer, the two assumptions of the first step are still valid. According to the equivalent method of formula (18) and formula (19), the stacking order of the metal-lined composite cylindrical shell is as follows: Figure 5 As shown in the figure, the cylindrical surface at the radial direction r+h / 2 of the cylindrical shell is used as the mid-surface in the thickness direction, which can facilitate the establishment of the equilibrium equation in the fourth step.

[0098] Step 3: Establish physical equations to obtain the relationship between stress and strain in each composite unit layer and metal unit layer. For the composite layer in the composite cylindrical shell, its fiber material is anisotropic. According to Hooke's law, the relationship between in-plane stress and strain in the fiber direction, in-plane transverse direction and shear direction can be obtained by equations (20) and (21), as follows: Figure 6 shown.

[0099]

[0100]

[0101] Equations (20) and (21) can be converted into matrix form and expressed as follows:

[0102]

[0103] Where: E1 is Young's modulus in the fiber direction, ν 21 is the in-plane Poisson's ratio, G 12 is the in-plane shear modulus; for isotropic materials, that is, in the metal layer of the composite cylindrical shell,

[0104] In order to facilitate subsequent substitution into the equilibrium equation, the inverse transformation of Equation (22) can be performed to obtain the relationship between stress and strain:

[0105]

[0106] Where: Q = S -1 .

[0107] In addition, formula (23) is only for the stress-strain relationship when the fiber laying direction happens to be the reference coordinate direction. In the actual fiber laying process, in order to obtain excellent load performance, the fiber laying angle is generally at a certain angle to the reference coordinate direction and is laid orthogonally. For the reference coordinate of the metal-lined composite cylindrical shell, as shown in Figure 4 The angle between the fiber laying direction and the reference coordinate x-axis is the fiber winding angle, which is the angle θ with the cylindrical shell axis. Its microelement is shown as follows: Figure 7 As shown. i That is the fiber laying angle of this layer.

[0108] According to the internal stress in the direction of the coordinate axis balance ( Figure 8 ), the equilibrium equation of the stress components can be obtained.

[0109] σ x =σ1cosθcosθ+σ2sinθsinθ-2τ 12 sinθcosθ (24)

[0110] Substituting equations (17) and (23) into equation (24), the components of the in-plane stress of any layer (set as the kth layer) in the composite material layer of the composite cylindrical shell can be expressed in the following matrix form, and equation (25) can be obtained:

[0111]

[0112] Where:

[0113]

[0114]

[0115]

[0116]

[0117]

[0118] In addition, for the metal layer of the metal-lined composite cylindrical shell, according to the metal layer equivalent model in the second step and the single-layer physical equation, considering that the metal material is isotropic, the laying angle is not involved here, that is, the laying angle is set to 0. Then, the stress component in the reference coordinate direction in any split layer facing the metal layer can be expressed by the following formula:

[0119]

[0120] Substituting equations (17) and (23) into equation (26), we can obtain the component of stress in any layer of the metal layer of the composite cylindrical shell in the direction of the reference coordinate axis:

[0121]

[0122] Step 4: Based on the equilibrium relationship, the in-plane stiffness matrix, coupling stiffness matrix, and bending stiffness matrix of the metal-lined composite cylindrical shell are calculated. According to the physical equation, the resultant force of the stress in each layer multiplied by the area of ​​the corresponding layer should be equal to the component of the external force (force and moment) on the corresponding coordinate axis in the reference system coordinate axis, that is, the following formula is obtained:

[0123]

[0124]

[0125] Substituting equations (25) and (27) into equations (28) and (29), we can obtain the equilibrium relationship of forces in the directions of each coordinate axis:

[0126]

[0127]

[0128]

[0129] After combining similar terms in equations (30) to (32), we can obtain the following relationship:

[0130]

[0131]

[0132]

[0133] From the above, we can see that A 11 , A 12 , A 22 , A 16 , A 26 , B 11 , B 12 , B 22 , B 16 , B 26 Satisfy the following formulas respectively:

[0134]

[0135]

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143] After expanding formula (39) and combining similar terms, we can also obtain the corresponding D 11 , D 12 , D 22 , D 16 , D 26 The expression can be obtained by A in formula (33)-(35) 66 , B 66 The same expression as in (36)-(44) is obtained. The sub-terms of the [D] series are also obtained from the moment equation. The solution is similar and will not be repeated here. Combining (28) and (29) into a matrix form, we can obtain (45):

[0144]

[0145] Where: matrices [A], [B], and [D] are the in-plane stiffness matrix, coupling stiffness matrix, and bending stiffness matrix of the metal-lined composite cylindrical shell, which can all be solved using equations (29) to (35). The above matrices [A], [B], and [D] are the basis for studying the mechanical properties of this type of composite cylindrical shell.

[0146]

[0147] Step 5: Combine the linear buckling control equations of cylindrical shells. Extensive theoretical research has been conducted on the buckling behavior of cylindrical pressure shells under external uniformly distributed pressure. In 1993, Vasiliev proposed three typical partial differential equations that cylindrical shells satisfy when buckling occurs, as shown in Equations (47) to (49):

[0148]

[0149]

[0150]

[0151] Where: are the axial and circumferential forces of the cylindrical shell under uniform pressure.

[0152] In addition, according to the constraint conditions of the cylindrical shell, that is, the ends are closed with rigid supports, that is, the ends are simply supported, the shell displacement when the cylindrical shell is buckled satisfies formula (50):

[0153]

[0154] Where: α = mπ / L, β = n / R; m and n are the wave numbers in the axial and circumferential directions of the cylindrical shell; U, V, and W are the maximum displacements in the X, Y, and Z directions, all of which are non-zero constants.

[0155] According to the thin shell theory of cylindrical shells, the relationship between the strain and displacement on the surface satisfies the following relationship:

[0156]

[0157] Substituting Equation (50) into Equation (51), and substituting the combined equation into Equations (28) and (29), we can obtain the components of each axial force in the reference coordinate system. Finally, substituting the equation into Equations (47) to (49), we can obtain the theoretical model of linear buckling load of metal-lined composite cylindrical shell after simplification, as shown in Equation (52).

[0158]

[0159] Where: P e is the buckling load,

[0160]

[0161] K 11 =A 11 α 2 +A 66 β 2 , K 12 =K 21 =(A 12 +A 66)αβ,

[0162] K 22 =A 22 β 2 +A 66 α 2 ,

[0163]

[0164]

[0165] L 11 =L 12 =L 13 =L 21 =L 22 =L 23 =L 31 =L 32 =0,

[0166] The above matrices [A], [B], and [D] can be obtained from equation (46). Since U, V, and W are non-zero constants, equation (52) can be further transformed into a polynomial for solution, as shown in equation (53):

[0167] P e =min{P em},|[K]+P em [L]|=0 (53)

[0168] Because P em Dependent on m and n, where m = 1 and n = [1-30]. Buckling load P e Take a positive integer for n and P em Minimum value.

[0169] Step 6: Establish the buckling control equation under the material damage model. In order to simultaneously consider the linear buckling of the metal-lined composite cylindrical shell and the degree of damage to the material after being subjected to stress, the linear buckling theoretical model was modified based on the Merchant–Rankine formula, taking into account the internal stress change index of the material under external force:

[0170]

[0171] Where: b is the damage factor, b = [0, 1].

[0172] P f It can be calculated by formula (55):

[0173]

[0174] Where: P0 is the external load of the combined cylindrical shell; XT , X C , Y T , Y C , S C are the tensile strength, compressive strength, transverse tensile and compressive strength of the composite material layer in the fiber direction of the metal lined composite cylinder shell; T S , C S , S S are the tensile strength, compressive strength and shear strength of the metal layer respectively.

[0175] The internal stress of the composite material layer and the metal layer in equation (55) can be obtained by equations (25) and (27), where the relationship between strain and internal force can be calculated by the following equation:

[0176] {ε}=[A ij ] -1 {N} (56)

[0177] Where: N x =-P0R / 2, N y =-P0R.

[0178] Substitute equations (56) and (55) into equation (54) to obtain P f , and after simplified transformation, the buckling limit load theoretical model considering the material damage model can be obtained, as shown in Equation (57).

[0179]

[0180] Through the modified buckling limit load model considering material damage, the limit load of the metal-lined composite cylindrical shell is calculated according to the in-plane stiffness matrix, coupling stiffness matrix and bending stiffness matrix of the metal-lined composite cylindrical shell. The crushing load of this type of multi-layer cylindrical shell is predicted by the limit load, and then the compressive failure assessment of the multi-layer composite cylindrical shell under external pressure is improved, thereby making the structural design safer and more reliable.

Claims

1. A method for calculating the ultimate load of a metal-lined composite cylindrical shell, characterized in that: The cylindrical shell includes an outer fiber composite layer and an inner metal layer. The calculation method includes the following steps: (1) Establishing the geometric equation of the fiber composite material layer, dividing the fiber composite material layer into several composite material unit layers, and obtaining the strain-displacement relationship of the fiber composite material unit layer; (2) establishing an equivalent model of the metal layer; dividing the metal layer into a plurality of metal unit layers, wherein the thickness of the metal unit layer is the same as the thickness of the composite material unit layer; (3) Establish the relationship between stress and strain in each composite unit layer and metal unit layer respectively; (4) According to the equilibrium relationship: the resultant force of the stress in each layer multiplied by the area of ​​the corresponding layer is equal to the component of the external force on the corresponding coordinate axis under the reference system coordinate axis; the in-plane stiffness matrix, coupling stiffness matrix and bending stiffness matrix of the metal-lined composite cylindrical shell are calculated; (5) According to the constraints of cylindrical shells and thin shell theory, the theoretical model of linear buckling load of metal-lined composite cylindrical shells is obtained; (6) Considering the linear buckling of the metal-lined composite cylindrical shell and the degree of damage to the material after being subjected to stress, the linear buckling theoretical model is modified based on the Merchant–Rankine formula; the ultimate load of the metal-lined composite cylindrical shell is calculated using the modified model according to the in-plane stiffness matrix, coupling stiffness matrix and bending stiffness matrix of the metal-lined composite cylindrical shell obtained in step (4).

2. The method for calculating the ultimate load according to claim 1, wherein: In step (1), the composite material layer is divided into a number of micro-elements with planar surfaces. Based on the assumption of classical laminate theory, the strain-displacement relationship of the composite material unit layer micro-element is obtained: {ε}={ε0}+z{q} in, z is the radial distance between point C and point O on the mid-plane; ε x , ε y , ε z is the normal strain of the element along the x, y, and z directions, u o is the displacement of point O in the x direction after deformation, v o is the displacement of point O in the y direction after deformation, and w is the displacement of point C in the z direction.

3. The method for calculating the ultimate load according to claim 2, wherein: In step (3), the relationship between stress and strain in each composite material unit layer is: Among them, σ x is the stress in the fiber direction of the composite material layer, σ y is the transverse stress in the composite material layer, τ xy is the stress in the shear direction, γ xy is the shear strain; Q 11 , Q 22 , Q 12 , Q 66 is the relationship constant between stress and strain, θ k lay angles for fibers in composite materials; The relationship between stress and strain in each metal unit layer is:

4. The method for calculating the ultimate load according to claim 3, wherein: The calculation formulas of the stiffness matrix [A], coupling stiffness matrix [B] and bending stiffness matrix [D] are: Among them, N x is the internal force in the x direction, N y is the internal force in the y direction, N xy is the internal force in the xy plane, M x is the torque in the x direction, M y is the torque in the y direction, M xy is the torque in the xy plane, ε xo is the strain in the x direction, ε yo is the strain in the y direction, γ xyo is the in-plane shear strain, κ x is the torsion rate in the x direction, κ y is the torsion rate in the y direction, κ xy is the inward torsion in the xy plane.

5. The method for calculating the ultimate load according to claim 4, wherein: The constraint condition of the cylindrical shell in step (5) is that both ends are simply supported. At this time, the shell displacement when the cylindrical shell buckles satisfies the following formula: Where u is the displacement of the cylindrical shell in the x-direction, v is the displacement of the cylindrical shell in the y-direction, ω is the displacement of the cylindrical shell in the z-direction, α = mπ / L, β = n / R; m and n are the axial and circumferential wave numbers of the cylindrical shell, respectively; L is the length of the cylindrical shell, and R is the radius of the cylindrical shell; U, V, and W are the maximum displacements of the cylindrical shell in the x-, y-, and z-directions, respectively, and are all non-zero constants.

6. The method for calculating the ultimate load according to claim 5, characterized in that: According to the thin shell theory of cylindrical shells, the relationship between strain and displacement on the cylindrical shell surface satisfies the following relationship: Among them, q x is the curvature of the cylindrical shell along the x direction, q y is the curvature of the cylindrical shell along the y direction, q xy is the cylindrical shell torsion.

7. The method for calculating the ultimate load according to claim 6, wherein: The theoretical model of linear buckling load of metal lined composite cylindrical shell is: P e =min{P em }; Among them, P e is the buckling load, K 11 =A 11 a 2 +A 66 b 2 ;K 12 =K 21 =(A 12 +A 66 )ab, K 22 =A 22 b 2 +A 66 a 2 , L 11 =L 12 =L 13 =L 21 =L 22 =L 23 =L 31 =L 32 =0, 8. The method for calculating the ultimate load according to claim 7, wherein: The modified formula of the linear buckling theoretical model of the metal-lined composite cylindrical shell is: Among them, P c is the corrected buckling load, b is the damage factor, P f is the material damage load.

9. The method for calculating the ultimate load according to claim 8, wherein: The P f The calculation formula is: Among them, P0 is the external load of the metal-lined composite cylindrical shell, and H is the material damage judgment index.

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