Composite material-metal hybrid structure impact dynamic response analysis method

Abstract

The invention relates to a composite material-metal hybrid structure impact dynamic response analysis method. The method comprises the following steps: S1, simplifying an impact load according to the impulse size of the actual impact load within saturation response time; s2, when the actual deformation of the fiber metal laminated plate is increased until the fibers are damaged, analyzing and calculating the influence degree of the rigidity reduction coefficient of the introduced fiber composite material layer on the damage; and S3, according to different deformation modes of the actual fiber metal laminated plate under the impact load, performing dynamic response calculation in stages. According to the method disclosed by the invention, the influence of the reduction coefficient of the large deformation damage stage of the fiber metal laminated plate and the boundary slippage of the test piece can be considered from a fiber metal laminated plate response theoretical analysis model under the impact load; and calculating the theoretical model by stages through software programmed by Matlab. The method for effectively evaluating the dynamic response of the fiber metal laminated plate under the impact load is a method for effectively evaluating the dynamic response of the fiber metal laminated plate under the impact load.

Description

Technical Field

[0001] The invention relates to the field of ships, and more specifically to an impact dynamic response analysis method for a composite material-metal hybrid structure. Background Art

[0002] With the development of new composite materials and their successful application in engineering structures such as aircraft, new composite structures have gradually been applied to ship structures due to their excellent specific strength, specific stiffness, damage tolerance and acoustic stealth characteristics. The fiber-reinforced metal laminates (FMLs) composed of fiber-reinforced composite materials and metal overlap have higher overall damage tolerance, not only have good specific strength, specific stiffness and fatigue resistance, but also have greatly improved impact resistance. They have been successfully applied in automobile anti-collision structures and aircraft explosion-proof luggage compartments. With its many advantages, fiber metal laminates have broad application prospects in ship structures, especially in the protective structures of key cabins of ships. Therefore, it is necessary to study the dynamic response of fiber metal laminates under impact loads. Since fiber metal laminates are anisotropic super-hybrid structures, their deformation and failure mechanisms under impact loads are complex. Using experimental and numerical simulation methods to study the dynamic response of fiber metal laminates under impact loads has high research costs and time cycles. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a method for analyzing the impact dynamic response of a composite material-metal hybrid structure. The method derives a simplified theoretical calculation model of the deformation of a laminate under an impact load based on the laminate deformation theory, which can effectively shorten the calculation cost and provide effective theoretical support for the protection design of ship composite material structures.

[0004] The technical solution adopted by the present invention to solve the technical problem is: constructing a composite material-metal hybrid structure impact dynamic response analysis method, comprising the following steps:

[0005] S1. Simplify the impact load according to the impulse size of the actual impact load within the saturation response time;

[0006] S2. When the deformation of the actual fiber metal laminate increases to the point where the fiber is damaged, the degree of damage is analyzed and calculated by introducing the stiffness reduction coefficient of the fiber composite material layer;

[0007] S3. According to the different deformation modes of the actual fiber metal laminate under impact load, the dynamic response calculation is carried out in stages.

[0008] According to the above scheme, step S1 includes:

[0009] The impulse magnitude of the simplified load and the actual load within the saturation response time is the same, that is:

[0010] I0=I sat

[0011] Where: I0 = p0t0, I0 represents the impulse of the equivalent rectangular load, P0 represents the pressure of the equivalent rectangular load, and t0 represents the equivalent time; I sat It represents the impulse of the actual impact load within the saturation response time of the structure, t sat represents the saturation response time, and p(t) represents the pressure of the actual impact load;

[0012] The centroid of the simplified rectangular load is the same as the centroid of the actual load.

[0013]

[0014] Based on the above simplified conditions, different impact equivalent loads are calculated.

[0015] According to the above scheme, in step S2, the xoy coordinate system is established with the center of the plate as the origin, and the curve expression of the reduction factor D of the fiber reinforced composite material changing with the displacement C of the center point of the fiber metal laminate is obtained as follows:

[0016] D = 8 × 10 -5 ×(C-10) 3 -0.0051(C-10) 2 +0.1171(C-10).

[0017] According to the above scheme, in step S3, combined with the stress-strain curve of the fiber reinforced composite material, the deformation stages of the fiber metal laminate response process can be divided into deformation stage 1, deformation stage 2, deformation stage 3 and deformation stage 4 through different strain sizes. The deformation stage 1 is before the slip stage, and the deformation stage 4 is after the oscillation stage.

[0018] In the slip stage, both the metal layer and the fiber layer are elastic. The fiber metal laminate only generates bending deformation energy but no membrane deformation energy during the deformation process. After obtaining the total potential energy and kinetic energy, the Lagrangian motion differential equation is established and solved.

[0019] According to the above scheme, in the first deformation stage, after the slip stage ends, the plate generates membrane deformation energy, but the mid-surface tensile deformation is in the elastic deformation, the metal layer and the fiber layer are both in the elastic stage, and the bending deformation energy and membrane deformation energy of the fiber metal laminate are calculated using the stress-strain relationship in the elastic stage, and the Lagrangian motion differential equation is established and solved.

[0020] According to the above scheme, in the second deformation stage, the metal layer enters the quadratic linear state, and the fiber layer is still elastic. At this time, it is assumed that the fiber layer and the metal layer are still deformed in a coordinated manner and no stratification occurs. The bending deformation energy and membrane deformation energy are solved for each layer. After calculating the total potential energy and kinetic energy, the Lagrangian motion differential equation is established and solved.

[0021] According to the above scheme, in the third deformation stage, the metal is still in the quadratic linear stage, but the fiber layer suffers fiber fracture damage due to excessive impact load. At this time, it is assumed that the laminate has local failure inside after fiber fracture, and the damage reduction factor is introduced. The bending deformation energy and membrane deformation energy are solved for each layer. After calculating the total potential energy and kinetic energy, the Lagrangian motion differential equation is established and solved.

[0022] According to the above scheme, in the fourth deformation stage, the metal layer enters the ideal plastic stage, but does not fail, and the fiber layer is damaged. The damage reduction factor is also used to solve the bending deformation energy and membrane deformation energy of each layer. After calculating the total potential energy and kinetic energy, the Lagrangian motion differential equation is established and solved.

[0023] According to the above scheme, in the oscillation stage, after the plastic deformation stage ends, the fiber metal laminate will produce elastic oscillation at a certain deformation position; at this time, the fiber layer and the metal layer in the fiber metal laminate are deformed in the elastic stage, generating bending deformation energy and membrane deformation energy, and the Lagrangian motion differential equation is established and the oscillation deformation is calculated.

[0024] According to the above scheme, in step S3, the method of performing dynamic response calculation in stages includes:

[0025] S301, running the sliding stage, the initial deformation of the specimen plate in the sliding stage is 0, the initial time is 0, if the displacement of the center point of the specimen plate exceeds the displacement threshold value C0 of the sliding stage during the calculation process, then through C0 linear interpolation, the calculation time and speed of the center point of the specimen plate at the displacement C0 are obtained, and saved as the initial value of the deformation stage 1 for input calculation; if the displacement of the center point of the specimen plate does not exceed the displacement threshold value C0 of the sliding stage during the calculation process, then the maximum value max of the center point during the calculation process, and the corresponding time and speed are saved, and used as the initial value of the oscillation stage and the oscillation stage is run until the calculation is completed;

[0026] S302, entering deformation stage 1, if the displacement of the center point of the specimen plate exceeds the displacement threshold C1 of deformation stage 1 during the calculation process, the calculation time and speed of the center point of the specimen plate at the displacement C1 are obtained through C1 linear interpolation, and saved as the initial value of deformation stage 2 for input calculation; if the displacement of the center point of the specimen plate does not exceed the displacement threshold C1 of deformation stage 1 during the calculation process, the maximum value max of the center point during the calculation process, and the corresponding time and speed are saved, and used as the initial value of the oscillation stage and the oscillation stage is run until the calculation is completed;

[0027] S303, entering deformation stage 2, if the displacement of the center point of the specimen plate exceeds the displacement threshold C2 of deformation stage 2 during the calculation process, the calculation time and speed of the center point of the specimen plate at the displacement C2 are obtained through C2 linear interpolation, and saved as the initial value of deformation stage 3 for input calculation; if the displacement of the center point of the specimen plate does not exceed the displacement threshold C2 of deformation stage 2 during the calculation process, the maximum value max of the center point during the calculation process, and the corresponding time and speed are saved, and used as the initial value of the oscillation stage and the oscillation stage is run until the calculation is completed;

[0028] S304, entering deformation stage three, if the displacement of the center point of the specimen plate exceeds the displacement threshold C3 of deformation stage three during the calculation process, the calculation time and speed of the center point of the specimen plate at the displacement C3 are obtained through C3 linear interpolation, and saved as the initial value of deformation stage four for input calculation; if the displacement of the center point of the specimen plate does not exceed the displacement threshold C3 of deformation stage three during the calculation process, the maximum value max of the center point during the calculation process, and the corresponding time and speed are saved, and used as the initial value of the oscillation stage and the oscillation stage is run until the calculation is completed;

[0029] S305, entering deformation stage 4, saving the maximum value of the center point during the calculation process, and the corresponding time and speed, using it as the initial value of the oscillation stage and running the oscillation stage until the calculation is completed;

[0030] S306. For the sliding stage, deformation stage one, deformation stage two, deformation stage three, deformation stage four and oscillation stage, the displacement history of the center point of the specimen plate is solved. The calculation method is to calculate the kinetic energy and potential energy of the specimen plate in the system at this stage, establish the Lagrangian motion differential equation of the system through energy, and finally solve it through numerical calculation of the Runge-Kutta method.

[0031] The composite material-metal hybrid structure impact dynamic response analysis method of the present invention has the following characteristics:

[0032] Beneficial effects:

[0033] 1. The curve pattern of the center point response history curve of the fiber metal laminate under impact load obtained by theoretical calculation in the present invention is well consistent with the curve pattern of the center point response history curve of the specimen plate measured in the test, both of which are composed of a deformation rising stage and an oscillation stage. Among them, the curve of the initial rising stage obtained by theoretical calculation is basically consistent with the experimental measurement curve, which verifies the rationality of the theoretical calculation method of the deformation rising stage;

[0034] 2. The saturation response time of the center point of the specimen plate obtained by theoretical calculation in the present invention is in good agreement with the saturation response time measured by the test method, which verifies the rationality of performing theoretical calculation in stages from the beginning of deformation to the maximum deformation, and also explains that the assumptions in the theoretical analysis and the simplified load input are more reasonable in the calculation process;

[0035] 3. There is a certain error between the maximum displacement of the center point of the specimen plate obtained by theoretical calculation and the test result in the same ply form under the condition of large TNT dosage. The main reason is that the theoretical calculation does not take into account the delamination damage of the fiber metal laminate under a large impact load, and does not take into account the tensile deformation of the clamping boundary of the specimen plate under a large impact load;

[0036] 4. The theoretical calculation model of the present invention takes about 20 minutes to calculate one working condition, with good accuracy and high calculation efficiency. In particular, for the final deformation of the fiber metal laminate explosion-proof structure, which is of great concern in engineering practice, the calculation results obtained by theoretical calculation are relatively reasonable, which has certain engineering value in guiding the preliminary explosion-proof evaluation of ship composite material structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0038] Figure 1 It is a schematic diagram of a four-side constrained rectangular plate model of the present invention;

[0039] Figure 2 It is the curve of the reduction coefficient D of the present invention changing with the center point displacement C;

[0040] Figure 3 is the stress-strain curve of the fiber metal laminate in the deformation stage of the present invention;

[0041] Figure 4 is a flow chart of the overall calculation of the impact response of the fiber metal laminate of the present invention;

[0042] Figure 5 It is a flow chart of the response process of solving the center point of the test piece plate at each stage of the present invention;

[0043] Figure 6 It is a software framework diagram corresponding to the composite material-metal hybrid structure impact dynamic response analysis method of the present invention. DETAILED DESCRIPTION

[0044] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0045] like Figure 1-6As shown, the composite material-metal hybrid structure impact dynamic response analysis method of the present invention comprises the following steps:

[0046] S1. Simplify the impact load according to the impulse size of the actual impact load within the saturation response time;

[0047] The impulse magnitude of the simplified load and the actual load within the saturation response time is the same, that is,

[0048] I0=I sat (1)

[0049] Where: I0 = p0t0, I0 represents the impulse of the equivalent rectangular load, P0 represents the pressure of the equivalent rectangular load, and t0 represents the equivalent time; I sat It represents the impulse of the actual impact load within the saturation response time of the structure, t sat represents the saturation response time, and p(t) represents the pressure of the actual impact load.

[0050] The centroid of the simplified rectangular load is the same as the centroid of the actual load.

[0051]

[0052] Based on the above simplified conditions, the impact equivalent load under different TNT masses is calculated.

[0053] S2. When the deformation of the actual fiber metal laminate increases to the point where the fiber is damaged, the degree of damage is analyzed and calculated by introducing the stiffness reduction coefficient of the fiber composite material layer;

[0054] First, the xoy coordinate system is established with the center of the plate as the origin. The fiber metal laminate will reach the maximum deformation in a very short time under the explosion load. At the same time, a large bending moment will be generated on the surrounding boundaries, making it easy for the fiber metal laminate to rotate at the clamping boundary. Therefore, the deformation deflection equation of FMLs is similar to that of the simply supported boundary. The deformation deflection function of FMLs is as follows:

[0055]

[0056] In the formula, u and v are displacements in the x and y directions respectively; u0 and v0 are the maximum displacements in the x and y directions respectively; w is the deflection of the plate in the z direction, C is the deflection at the center of the plate, that is, the maximum deflection of the plate; a and b represent half of the length and width of the plate respectively. The deformation deflection function expressed in the above formula satisfies the boundary conditions of four-sided simple support, that is, on the boundary w(x,y)=w″(x,y)=0, such as Figure 1 shown.

[0057] When the deformation of the fiber metal laminate is small, the influence of the mid-surface force on the bending is not considered. The aluminum layer and the fiber layer in the laminate are regarded as thin plates. The basic assumptions of the thin plate small deformation bending theory are as follows:

[0058] (1)σ z , τ xz , and τ yz is zero, that is, plane stress state, only considering σ x , σ y and τ xy ;

[0059] (2) Using the straight normal assumption, the thickness of the plate remains unchanged, γ xz =γ yz =ε z =0;

[0060] (3) The displacement u and v are smaller than w, there is no deformation along the in-plane direction, and the moment of inertia is negligible.

[0061] 1. Strain component

[0062] According to the small deformation assumption,

[0063]

[0064] in, γ0 is the mid-surface strain. According to assumption 3, the mid-surface strain is 0. Then the strain component is:

[0065]

[0066] in, are the curvature and twist rate of the deflected surface respectively.

[0067] 2. Stress components

[0068] For the aluminum plate in the small deformation stage, according to the elastic body dynamics physics equation, we have:

[0069]

[0070] Wherein, v=0.3, which is the Poisson's ratio of the initial linear elastic stage of the aluminum alloy; E represents the elastic modulus of the aluminum alloy; G=E / (2(1+v))=28.115 GPa, which represents the shear modulus of the initial linear elastic stage of the aluminum alloy.

[0071] For the fiber reinforced composite plate in the small deformation stage, since it is an orthotropic material, the x-axis and y-axis are coincident with the main direction of the fiber reinforced composite plate during analysis. Then the stress-strain relationship in the main direction of the orthotropic fiber reinforced composite material is:

[0072]

[0073] Among them, Q is the two-dimensional stiffness matrix, Q ij It is expressed as follows using engineering elastic constants:

[0074]

[0075] Where, E1 and E2 are the elastic moduli of the fiber reinforced composite material plate in the 1st and 2nd directions respectively; v 12 , v 21 is the Poisson's ratio in the 1 and 2 directions, where v 21 / E1=v 12 / E2.

[0076] At this time, the thickness direction is the 3 direction, and the main directions in the plane are the 1 and 2 directions.

[0077] When the deformation of the fiber metal laminate is large, the mid-surface membrane force is the main bearing form, so the influence of the mid-surface force cannot be ignored. The large deflection deformation problem of the flat plate still uses the assumptions 1 and 2 in the small deformation, that is, the straight normal assumption and plane stress state.

[0078] 1. Strain component

[0079] The displacement relationship taking into account the mid-surface displacements u0 and v0 is:

[0080]

[0081] Ignore the nonlinear terms of the first-order derivatives of u and v, retain the nonlinear terms of the first-order derivatives of w, and ignore the third-order and above traces, then the nonlinear displacement-strain relationship is:

[0082]

[0083] When the fiber metal laminate produces large deflection deformation, the displacement u and v are small compared with the deflection w, and the plane displacement u and v can be ignored. Then the strain component of the plate under large deflection deformation is:

[0084]

[0085] 2. Stress components

[0086] In the initial linear stage, the stress-strain relationship in the aluminum plate is as follows:

[0087]

[0088] Wherein, v=0.3, which is the Poisson's ratio of the initial linear elastic stage of the aluminum alloy; E represents the elastic modulus of the aluminum alloy; G=E / (2(1+v))=28.115 GPa, which represents the shear modulus of the initial linear elastic stage of the aluminum alloy.

[0089] In the quadratic linear stage, the stress-strain relationship in the aluminum plate is:

[0090]

[0091] Expressing stress in terms of strain is

[0092]

[0093] In the formula, v p is the Poisson’s ratio of aluminum alloy in the quadratic linear stage; is the shear modulus of aluminum alloy in the secondary linear stage; τ0 is the maximum shear stress of aluminum alloy in the initial elastic stage. According to the Mises stress yield criterion, γ0=τ0 / G represents the maximum shear strain in the initial elastic stage of aluminum alloy.

[0094] In the ideal plastic stage, σ x =σ y =σ p , where τ p is the shear strain of aluminum alloy in the ideal plastic stage.

[0095] For fiber reinforced composite plates in the large deformation stage, when the deformation of the plate exceeds the fracture strain of the fiber reinforced composite material, the fiber reinforced composite material will be damaged and the bearing capacity of the fiber metal laminate will decrease. Therefore, the fiber reinforced composite stiffness damage reduction factor D is introduced to characterize the stress-strain relationship of the fiber composite layer after damage.

[0096] The stiffness matrix after damage is:

[0097]

[0098] In the formula, the stiffness reduction factor D changes nonlinearly with the deformation size.

[0099] The fracture strain of the fiber reinforced composite material is 0.0153. When the strain on the specimen plate exceeds 0.0153, it is considered that the fiber reinforced composite material has fracture damage.

[0100] Substituting equation (3) into equation (11), the expression of strain in the x-direction is obtained as follows:

[0101]

[0102] The reduction factor of fiber reinforced composite materials is

[0103]

[0104] In the formula, S d For x or ε yWhen >0.0153, the area corresponding to the deformation function of the fiber metal laminate is the projection area on the xoy plane; S is the area of ​​the fiber metal laminate before deformation.

[0105] The above theoretical formula was written into a program through MATLAB software to obtain the curve of the reduction factor D of fiber reinforced composite material changing with the center point displacement C of fiber metal laminate, as shown in Figure 2 shown.

[0106] The curve is fitted with a polynomial, and the fitted curve expression is as follows:

[0107] D = 8 × 10 -5 ×(C-10) 3 -0.0051(C-10) 2 +0.1171(C-10) (18)

[0108] The fitting variance of the reduction coefficient curve by formula (18) is 0.9994, so the above formula can be used to calculate the damage reduction coefficient of the fiber composite material layer in the fiber metal laminate during the deformation process.

[0109] S3. According to the different deformation modes of the actual fiber metal laminate under impact load, the dynamic response calculation is carried out in stages.

[0110] When the actual fiber metal laminate is deformed slightly, the fiber composite material layer and the aluminum alloy layer deform in coordination, and the influence of the mid-surface force is not taken into account, so it can be described by the assumption of small deformation of thin plate; when the actual fiber metal laminate is deformed greatly but no internal damage occurs, the fiber layer and the aluminum alloy layer still deform in coordination, and the thin plate large deflection deformation theory is used to describe it. When the deformation of the actual fiber metal laminate continues to increase and the fiber is damaged, the stiffness reduction coefficient of the fiber composite layer is used to calculate the influence of the damage.

[0111] Since the stress-strain curve of aluminum alloy is transformed into a piecewise linear stress-strain curve, combined with the stress-strain curve of fiber reinforced composite materials, the deformation stage of the fiber metal laminate response process can be divided into four deformation stages according to different strain sizes. Figure 3 shown.

[0112] Slip stage: The aluminum alloy layer and the fiber layer are both elastic. The fiber metal laminate only generates bending deformation energy during the deformation process, and no membrane deformation energy. The strain components of the aluminum plate and the fiber plate adopt the small deformation theory strain component of formula (5), the aluminum plate adopts the stress component of formula (6), and the fiber composite material layer adopts the stress component of formula (7). Then the deformation energy per unit volume of the aluminum plate and the fiber plate is:

[0113]

[0114] Under different ply forms, the bending strain energy of the aluminum layer is:

[0115]

[0116] The bending deformation energy of the fiber layer is:

[0117]

[0118] In the formula, M represents the metal layer in the fiber metal laminate; the number after M represents the number of metal plate layers in the fiber metal laminate; F represents the composite material layer in the fiber metal laminate; the number after F represents the number of composite material plate layers in the fiber metal laminate; h1 represents the thickness of the aluminum alloy layer, h2 represents the thickness of the fiber reinforced composite material layer; a represents half of the plate length, and b represents half of the plate width.

[0119] Deformation stage 1: After the slip stage, the plate generates membrane deformation energy, but the mid-surface tensile deformation is in the elastic deformation. The aluminum alloy layer and the fiber layer are both in the elastic stage. At this time, the plate deformation energy includes the bending deformation energy and tensile deformation energy in the elastic stage. The bending deformation energy is the same as that in the slip stage and is calculated by equations (19), (20), (21), and (22). In the calculation of tensile strain energy, the strain adopts the large deformation theory equation (11). Since no mid-surface stretching occurs in the boundary slip stage, the membrane strain at this time should start from zero. The deformation type function of the specimen plate at the end of the slip stage is defined as:

[0120]

[0121] The tensile strain energy per unit volume of the aluminum plate is:

[0122]

[0123] The tensile strain energy per unit volume of fiberboard is:

[0124]

[0125] Under different lamination forms, the tensile strain energy of the aluminum layer is:

[0126]

[0127] The tensile strain energy of the fiber layer is:

[0128]

[0129] Deformation stage 2: FMLs have undergone significant deformation, and the aluminum alloy has entered the secondary linear stage. At this time, the fiberboard is still in the linear elastic stage. The bending strain energy and tensile strain energy of the fiber composite layer are the same as those in deformation stage 1. The bending strain energy of the fiber composite layer is calculated by equations (20) and (22), and the tensile strain energy is calculated by equations (23) and (25).

[0130] The bending strain energy of the aluminum alloy layer is smaller than its tensile strain energy. Therefore, the bending strain energy of the aluminum alloy layer is the same as that in the first deformation stage and is calculated by equations (19) and (21).

[0131] Since FMLs have undergone large deformation, mid-surface tensile membrane force is generated, and the aluminum alloy enters the quadratic linear state, when calculating the tensile strain energy of the aluminum alloy layer, the strain component adopts the large deformation theory formula (11), where the deformation type function is w-w0, and the stress component of the aluminum plate adopts formula (14). At the same time, the tensile strain energy per unit volume of the aluminum layer in the second stage FMLs is:

[0132]

[0133] Substituting equations (11) and (14) into the equation, we can obtain:

[0134]

[0135] Under different layup forms, the tensile strain energy of the aluminum layer and the fiber layer is:

[0136]

[0137] Deformation stage three: The aluminum alloy layer in the fiber metal laminate is still in the quadratic linear stage. The bending deformation energy and tensile deformation energy of the aluminum alloy layer are the same as those in deformation stage two. The bending deformation energy is calculated by equations (19) and (21), and the tensile deformation energy is calculated by equations (25) and (26). At the same time, the bending deformation energy of the fiber composite material layer is smaller than the tensile deformation energy, so the bending deformation energy of the fiber composite material layer is still calculated using (22) and (24).

[0138] However, in the third deformation stage, the fiber composite material layer is fractured and damaged. Therefore, the strain component formula (11) in the large deformation theory is used to calculate the tensile strain energy of the fiber composite material layer. In the formula, the deformation function is w-w0, and the stress component uses the formula (7), but its stiffness matrix uses the stiffness matrix after damage (15). The tensile strain energy per unit volume of the fiber composite material is obtained as:

[0139]

[0140] Substituting formula (11) into the equation:

[0141]

[0142] The tensile strain energy of fiber composite material layers with different layup forms is:

[0143]

[0144] Deformation stage four: The fiber composite material layer is still in the fracture damage stage. The bending deformation energy and tensile deformation energy of the fiber composite material layer are the same as those in deformation stage three. Therefore, the bending deformation energy of the fiber composite material layer is still calculated using (20) and (22); the tensile strain energy of the fiber composite material layer is calculated using equations (28) and (29).

[0145] For the aluminum alloy layer, the ideal plastic stage is reached in the fourth deformation stage, that is, as the strain increases, the stress remains unchanged. At this time, the bending deformation energy of the aluminum alloy layer is smaller than the membrane deformation, so the calculation is still based on equations (19) and (21). For the membrane deformation energy of the aluminum alloy layer, the strain component equation (11) in the large deformation theory is used, where the deformation type function is w-w0, and the membrane deformation energy per unit volume is:

[0146]

[0147] The membrane strain energy corresponding to each ply form is the same as equation (26).

[0148] Oscillation stage: After the FMLs reach the maximum deformation, the fiber layer and the aluminum alloy layer oscillate within the elastic range to generate mid-surface tensile membrane force and bending. At this time, the deformation energy of the specimen includes the bending deformation energy and membrane deformation energy in the elastic stage. The bending deformation energy is the same as that in the slip stage and is calculated by equations (19), (20), (21), and (22). The membrane strain energy is the same as that in the first deformation stage and is calculated by equations (24), (25), (26), and (27).

[0149] So far, the potential energy of each part of the fiber metal laminate in different layup forms at different deformation stages under the in-cabin explosion impact load has been solved.

[0150] The total potential energy of the entire fiber metal laminate system in the dynamic response process under the cabin explosion load is

[0151] V=∑U Alb +∑U fb +∑U Alm +∑U fm +P E +U l (31)

[0152] The kinetic energy of the entire fiber metal laminate system during the dynamic response process is

[0153]

[0154] Where H is the total thickness of the fiber metal laminate, T FMLs is the average density of the fiber metal laminate.

[0155]

[0156] In the formula, ρ Al is the density of aluminum alloy in FMLs; h Al is the total thickness of the aluminum alloy layer in FMLs; ρ Fiber is the density of fiber reinforced composite materials in FMLs; h Fiber Fiber reinforced composites in FMLs.

[0157] like Figure 4 As shown in the figure, the calculation process of the impact response of the fiber metal laminate includes three parts: the calculation of the boundary slip stage; the calculation of the deformation stage; and the calculation of the oscillation stage. For the calculation process of the deformation stage, the displacement of the center point of the specimen reaches a certain stage, which needs to be calculated. The method of sequentially connecting each stage is adopted to finally obtain the response history of the center point of the fiber metal laminate under the impact load. The specific process is explained as follows:

[0158] First, the sliding stage is run. The initial deformation of the specimen plate in the sliding stage is 0, and the initial time is 0. If the displacement of the center point of the specimen plate exceeds the displacement threshold C0 of the sliding stage during the calculation process, the calculation time and speed of the center point of the specimen plate at the displacement C0 are obtained through C0 linear interpolation, and saved as the initial value of the deformation stage 1 for input calculation; if the displacement of the center point of the specimen plate does not exceed the displacement threshold C0 of the sliding stage during the calculation process, the maximum value max of the center point during the calculation process, as well as the corresponding time and speed, are saved and used as the initial value of the oscillation stage and the oscillation stage is run until the calculation is completed.

[0159] Entering deformation stage 1, if the displacement of the center point of the specimen plate exceeds the displacement threshold C1 of deformation stage 1 during the calculation process, the calculation time and speed of the center point of the specimen plate at displacement C1 are obtained through C1 linear interpolation, and saved as the initial value of deformation stage 2 for input calculation; if the displacement of the center point of the specimen plate does not exceed the displacement threshold C1 of deformation stage 1 during the calculation process, the maximum value max of the center point during the calculation process, as well as the corresponding time and speed, are saved and used as the initial value of the oscillation stage and the oscillation stage is run until the calculation is completed.

[0160] Entering the deformation stage 2, if the displacement of the center point of the specimen plate exceeds the displacement threshold C2 of the deformation stage 2 during the calculation process, the calculation time and speed of the center point of the specimen plate at the displacement C2 are obtained through C2 linear interpolation, and saved as the initial value of the deformation stage 3 for input calculation; if the displacement of the center point of the specimen plate does not exceed the displacement threshold C2 of the deformation stage 2 during the calculation process, the maximum value max of the center point during the calculation process, as well as the corresponding time and speed, are saved and used as the initial value of the oscillation stage and the oscillation stage is run until the calculation is completed.

[0161] Entering deformation stage three, if the displacement of the center point of the specimen plate exceeds the displacement threshold C3 of deformation stage three during the calculation process, the calculation time and speed of the center point of the specimen plate at displacement C3 are obtained through C3 linear interpolation, and saved as the initial value of deformation stage four for input calculation; if the displacement of the center point of the specimen plate does not exceed the displacement threshold C3 of deformation stage three during the calculation process, the maximum value max of the center point during the calculation process, as well as the corresponding time and speed, are saved and used as the initial value of the oscillation stage and the oscillation stage is run until the calculation is completed.

[0162] Entering the fourth deformation stage, save the maximum value of the center point during the calculation process, as well as the corresponding time and speed, use it as the initial value of the oscillation stage and run the oscillation stage until the calculation is completed.

[0163] For the displacement history of the center point of the specimen plate in the sliding stage, deformation stage 1, deformation stage 2, deformation stage 3, deformation stage 4 and oscillation stage, the calculation method is to calculate the kinetic energy and potential energy of the specimen plate system in this stage, establish the Lagrangian motion differential equation of the system through energy, and finally solve it through numerical calculation of the Runge-Kutta method. The flow chart of the response history of the center point of the actual plate in each stage is as follows: Figure 5 As shown in the figure. After analyzing the solution process of the center point response of the specimen plate at each stage and the center point response process of the specimen at the corresponding stage, the solution process is programmed. The theoretical calculation program of the center point response of the fiber metal laminate under the internal impact load is obtained.

[0164] like Figure 6As shown, this software is written in C language and Matlab is used under Windows 10 system. The software is divided into two parts according to the functional modules, the main program and the function file. The software includes 1 script file and 10 function files. Among them, the main program, namely the script file, is the focus of the whole program, and mainly completes the coordination and cooperation with other function modules. The maximum time value in the equation solving parameter can be input and assigned to a new matrix for storage. The matrix is ​​used for interpolation operations, clearing the variables of each stage, retaining the useful variables, and the initial value of the equation solution adopts the final value of the matrix of each previous stage. This software is written based on the Matlab platform. Starting from the theoretical analysis model of the response of fiber metal laminates under impact loads, considering the reduction coefficient of the large deformation damage stage of fiber metal laminates and the influence of the boundary slip of the specimen, the entire deformation process is considered in stages, and the theoretical calculation method is written as a program solution, and a method for rapid analysis of the dynamic response of fiber metal laminates under impact loads is formed.

[0165] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A composite material-metal hybrid structure impact dynamic response analysis method, characterized in that: The following steps are involved: S1. Simplify the impact load according to the impulse size of the actual impact load within the saturation response time; S2. When the deformation of the actual fiber metal laminate increases to the point where the fiber is damaged, the degree of damage is analyzed and calculated by introducing the stiffness reduction coefficient of the fiber composite material layer; S3. According to the different deformation modes of the actual fiber metal laminate under impact load, the dynamic response calculation is carried out in stages.

2. The composite material-metal hybrid structure impact dynamic response analysis method according to claim 1, characterized in that: The step S1 comprises: The impulse magnitude of the simplified load and the actual load within the saturation response time is the same, that is: I0=I sat Where: I0 = p0t0, I0 represents the impulse of the equivalent rectangular load, P0 represents the pressure of the equivalent rectangular load, and t0 represents the equivalent time; I sat It represents the impulse of the actual impact load within the saturation response time of the structure, t sat represents the saturation response time, and p(t) represents the pressure of the actual impact load; The centroid of the simplified rectangular load is the same as the centroid of the actual load. Based on the above simplified conditions, different impact equivalent loads are calculated.

3. The composite material-metal hybrid structure impact dynamic response analysis method according to claim 1, characterized in that: In step S2, the xoy coordinate system is established with the center of the plate as the origin, and the curve expression of the reduction factor D of the fiber reinforced composite material changing with the displacement C of the center point of the fiber metal laminate is obtained as follows: D=8×10 -5 ×(C-10) 3 -0.0051(C-10) 2 +0.1171(C-10)。 4. The impact dynamic response analysis method of composite material-metal hybrid structure according to claim 3 is characterized in that: In step S3, combined with the stress-strain curve of the fiber reinforced composite material, the deformation stages of the fiber metal laminate response process can be divided into deformation stage 1, deformation stage 2, deformation stage 3 and deformation stage 4 according to different strain sizes. The deformation stage 1 is preceded by a slip stage, and the deformation stage 4 is followed by an oscillation stage. In the slip stage, both the metal layer and the fiber layer are elastic. The fiber metal laminate only generates bending deformation energy but no membrane deformation energy during the deformation process. After obtaining the total potential energy and kinetic energy, the Lagrangian motion differential equation is established and solved.

5. The impact dynamic response analysis method of composite material-metal hybrid structure according to claim 4 is characterized in that: In the first deformation stage, after the slip stage, the plate generates membrane deformation energy, but the mid-surface tensile deformation is in the elastic deformation. Both the metal layer and the fiber layer are in the elastic stage. The bending deformation energy and membrane deformation energy of the fiber metal laminate are calculated using the stress-strain relationship in the elastic stage, and the Lagrangian motion differential equation is established and solved.

6. The composite material-metal hybrid structure impact dynamic response analysis method according to claim 5, characterized in that: In the second deformation stage, the metal layer enters the quadratic linear state, and the fiber layer is still elastic. At this time, it is assumed that the fiber layer and the metal layer are still deformed in a coordinated manner and no stratification occurs. The bending deformation energy and membrane deformation energy are solved for each layer. After calculating the total potential energy and kinetic energy, the Lagrangian motion differential equation is established and solved.

7. The composite material-metal hybrid structure impact dynamic response analysis method according to claim 6, characterized in that: In the third deformation stage, the metal is still in the quadratic linear stage, but the fiber layer suffers fiber fracture damage due to excessive impact load. At this time, it is assumed that the laminate has local failure inside after fiber fracture, and a damage reduction factor is introduced. The bending deformation energy and membrane deformation energy are solved for each layer. After calculating the total potential energy and kinetic energy, the Lagrangian motion differential equation is established and solved.

8. The composite material-metal hybrid structure impact dynamic response analysis method according to claim 7, characterized in that: In deformation stage four, the metal layer enters the ideal plastic stage but does not fail. The fiber layer is damaged. The damage reduction factor is also used to solve the bending deformation energy and membrane deformation energy for each layer. After calculating the total potential energy and kinetic energy, the Lagrangian motion differential equation is established and solved.

9. The composite material-metal hybrid structure impact dynamic response analysis method according to claim 8, characterized in that: In the oscillation stage, after the plastic deformation stage, the fiber metal laminate will produce elastic oscillation at a certain deformation position; at this time, both the fiber layer and the metal layer in the fiber metal laminate are deformed in the elastic stage, generating bending deformation energy and membrane deformation energy, and the Lagrangian motion differential equation is established and the oscillation deformation is calculated.

10. The composite material-metal hybrid structure impact dynamic response analysis method according to claim 9, characterized in that: In step S3, the method of performing dynamic response calculation in stages includes: S301, running the sliding stage, the initial deformation of the specimen plate in the sliding stage is 0, the initial time is 0, if the displacement of the center point of the specimen plate exceeds the displacement threshold value C0 of the sliding stage during the calculation process, then through C0 linear interpolation, the calculation time and speed of the center point of the specimen plate at the displacement C0 are obtained, and saved as the initial value of the deformation stage 1 for input calculation; if the displacement of the center point of the specimen plate does not exceed the displacement threshold value C0 of the sliding stage during the calculation process, then the maximum value max of the center point during the calculation process, and the corresponding time and speed are saved, and used as the initial value of the oscillation stage and the oscillation stage is run until the calculation is completed; S302, entering deformation stage 1, if the displacement of the center point of the specimen plate exceeds the displacement threshold C1 of deformation stage 1 during the calculation process, the calculation time and speed of the center point of the specimen plate at the displacement C1 are obtained through C1 linear interpolation, and saved as the initial value of deformation stage 2 for input calculation; if the displacement of the center point of the specimen plate does not exceed the displacement threshold C1 of deformation stage 1 during the calculation process, the maximum value max of the center point during the calculation process, and the corresponding time and speed are saved, and used as the initial value of the oscillation stage and the oscillation stage is run until the calculation is completed; S303, entering deformation stage 2, if the displacement of the center point of the specimen plate exceeds the displacement threshold C2 of deformation stage 2 during the calculation process, the calculation time and speed of the center point of the specimen plate at the displacement C2 are obtained through C2 linear interpolation, and saved as the initial value of deformation stage 3 for input calculation; if the displacement of the center point of the specimen plate does not exceed the displacement threshold C2 of deformation stage 2 during the calculation process, the maximum value max of the center point during the calculation process, and the corresponding time and speed are saved, and used as the initial value of the oscillation stage and the oscillation stage is run until the calculation is completed; S304, entering deformation stage three, if the displacement of the center point of the specimen plate exceeds the displacement threshold C3 of deformation stage three during the calculation process, the calculation time and speed of the center point of the specimen plate at the displacement C3 are obtained through C3 linear interpolation, and saved as the initial value of deformation stage four for input calculation; if the displacement of the center point of the specimen plate does not exceed the displacement threshold C3 of deformation stage three during the calculation process, the maximum value max of the center point during the calculation process, and the corresponding time and speed are saved, and used as the initial value of the oscillation stage and the oscillation stage is run until the calculation is completed; S305, entering deformation stage 4, saving the maximum value of the center point during the calculation process, and the corresponding time and speed, using it as the initial value of the oscillation stage and running the oscillation stage until the calculation is completed; S306. For the sliding stage, deformation stage one, deformation stage two, deformation stage three, deformation stage four and oscillation stage, the displacement history of the center point of the specimen plate is solved. The calculation method is to calculate the kinetic energy and potential energy of the specimen plate in the system at this stage, establish the Lagrangian motion differential equation of the system through energy, and finally solve it through numerical calculation of the Runge-Kutta method.

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