Method for analyzing impact dynamic response of composite-metal hybrid structure

Abstract

The present application relates to a kind of composite-metal hybrid structure impact dynamic response analysis method, comprising the following steps: S1, according to the impulse size of actual impact load in saturation response time, impact load is simplified;S2, when actual fiber metal laminated plate deformation increases to the damage of fiber, then the influence degree of damage is analyzed and calculated by introducing the stiffness reduction coefficient of fiber composite layer;S3, according to the different deformation mode of actual fiber metal laminated plate under impact load, dynamic response calculation is carried out in stages.The present application can start from the response theoretical analysis model of fiber metal laminated plate under impact load, consider the influence of large deformation damage stage reduction coefficient and specimen boundary slip of fiber metal laminated plate, according to the effective evaluation method of fiber metal laminated plate dynamic response under impact load that theoretical model is calculated in stages by the software of Matlab programming under large deformation stage.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of ships, more particularly, to a composite-metal hybrid structure impact dynamic response analysis method. BACKGROUND

[0002] With the development of new composite technology and its successful application in engineering structures such as aircraft, new composite structures have gradually been applied in ship structures due to their excellent specific strength, specific stiffness, damage tolerance and acoustic stealth characteristics. Fiber metal laminates (FMLs) composed of fiber reinforced composite materials and metal overlap have higher overall damage tolerance, not only have better specific strength, specific stiffness and fatigue resistance, but also have greatly improved impact resistance, and have been successfully applied in automobile crash structures and aircraft explosion-proof luggage compartments. Fiber metal laminates have wide application prospects in ship structures, especially in the protection structures of key cabins of ships. Therefore, it is necessary to study the dynamic response of fiber metal laminates under impact load. Since fiber metal laminates are anisotropic super-hybrid structures, their deformation and failure mechanism under impact load are complex, and using experimental and numerical simulation methods to study the dynamic response of fiber metal laminates under impact load has high research cost and time period. SUMMARY

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

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

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

[0006] S2, when the actual fiber metal laminate deformation increases to the damage of the fiber, the influence degree of the damage is analyzed and calculated by introducing the stiffness reduction coefficient of the fiber composite layer;

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

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

[0009] The simplified load and the actual load have the same impulse size in the saturated response time, that is:

[0010] I0=I sat

[0011] In the formula, 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 represents the impulse of the actual impact load in the structure saturated response time, t sat represents the saturated response time, and p(t) represents the pressure of the actual impact load;

[0012] The center of the simplified rectangular load is the same as the center of the actual load,

[0013]

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

[0015] According to the above scheme, in the step S2, the xoy coordinate system is established with the plate center as the origin, and the curve expression of the fiber reinforced composite material reduction coefficient D changing with the fiber metal laminated plate center point displacement C is 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 the step S3, in combination with the stress-strain curve of the fiber reinforced composite material, the deformation stage of the fiber metal laminated plate response process can be divided into deformation stage one, deformation stage two, deformation stage three and deformation stage four through different strain sizes, the deformation stage one is before the slip stage, and the deformation stage four is after the vibration stage.

[0018] In the slip stage, the metal layer and the fiber layer are both elastic, the fiber metal laminated plate only produces bending deformation energy in the deformation process, and no membrane deformation energy, after the total potential energy and kinetic energy are obtained, the Lagrange motion differential equation is established and solved.

[0019] According to the above scheme, in the deformation stage one, after the slip stage ends, the plate produces membrane deformation energy, but the middle surface tensile deformation is in the elastic deformation, the metal layer and the fiber layer are both in the elastic stage, the bending deformation energy and the membrane deformation energy of the fiber metal laminated plate are calculated by using the stress-strain relationship in the elastic stage, and the Lagrange motion differential equation is established and solved.

[0020] According to the above scheme, in the second deformation stage, the metal layer enters the second linear stage, 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 coordination and do not appear delamination. The bending deformation energy and the membrane deformation energy of each layer are solved, the total potential energy and the kinetic energy are calculated, and then the Lagrange motion differential equation is established and solved.

[0021] According to the above scheme, in the third deformation stage, the metal is still in the second linear stage, but the fiber layer appears fiber fracture damage due to excessive impact load. At this time, the damage reduction coefficient is introduced by assuming that the internal partial failure of the laminated plate occurs after the fiber fracture, the bending deformation energy and the membrane deformation energy of each layer are solved, the total potential energy and the kinetic energy are calculated, and then the Lagrange 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 is not failed, and the fiber layer appears damage. Similarly, the damage reduction coefficient is used, the bending deformation energy and the membrane deformation energy of each layer are solved, the total potential energy and the kinetic energy are calculated, and then the Lagrange motion differential equation is established and solved.

[0023] According to the above scheme, in the oscillation stage, after the plastic deformation stage of the fiber metal laminated plate ends, elastic oscillation will occur at a certain deformation position. At this time, the fiber layer and the metal layer in the fiber metal laminated plate are deformed in the elastic stage, and the bending deformation energy and the membrane deformation energy are generated. The Lagrange motion differential equation is established and the oscillation deformation is calculated.

[0024] According to the above scheme, in the step S3, the method for calculating dynamic response in stages comprises:

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

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

[0027] S303, entering the second deformation stage, if the displacement of the center point of the test piece plate in the calculation process exceeds the displacement threshold C2 of the second deformation stage, the calculation time and speed of the center point of the test piece plate at the displacement C2 are obtained through the linear interpolation of C2, and are saved as the initial value of the third deformation stage for input calculation, if the displacement of the center point of the test piece plate in the calculation process does not exceed the displacement threshold C2 of the second deformation stage, the maximum value max of the center point in the calculation process and the corresponding time and speed are saved as the initial value of the shock stage and run the shock stage until the calculation is completed;

[0028] S304, entering the third deformation stage, if the displacement of the center point of the test piece plate in the calculation process exceeds the displacement threshold C3 of the third deformation stage, the calculation time and speed of the center point of the test piece plate at the displacement C3 are obtained through the linear interpolation of C3, and are saved as the initial value of the fourth deformation stage for input calculation, if the displacement of the center point of the test piece plate in the calculation process does not exceed the displacement threshold C3 of the third deformation stage, the maximum value max of the center point in the calculation process and the corresponding time and speed are saved as the initial value of the shock stage and run the shock stage until the calculation is completed;

[0029] S305, entering the fourth deformation stage, the maximum value max of the center point in the calculation process and the corresponding time and speed are saved as the initial value of the shock stage and run the shock stage until the calculation is completed;

[0030] S306, for the slip stage, the first deformation stage, the second deformation stage, the third deformation stage, the fourth deformation stage and the shock stage, the displacement history of the center point of the test piece plate is solved, the calculation method is that the kinetic energy and potential energy of the test piece plate in the system of the stage are calculated, the Lagrange motion differential equation of the system is established through energy, and finally the numerical calculation is solved through the Runge-Kutta method.

[0031] The composite-metal hybrid structure impact dynamic response analysis method of the application has the following advantages

[0032] Beneficial effects:

[0033] 1, the center point response history curve of the fiber metal laminated plate under impact load obtained by theoretical calculation is consistent with the curve mode of the center point response history curve measured in the test, and is composed of a deformation rising stage and a shock stage, wherein the initial rising stage curve obtained by theoretical calculation is basically coincided with the test measured curve, and the rationality of the deformation rising stage theoretical calculation method is verified;

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

[0035] 3、The maximum displacement of the center point of the test piece plate obtained by theoretical calculation and the test results exist certain error in the same layer form under the larger TNT amount condition, the main reason is that the delamination damage of the fiber metal laminated plate under the larger impact load is not considered in the theoretical calculation, and the tensile deformation of the clamping boundary of the test piece plate under the larger impact load is not considered;

[0036] 4、The theoretical calculation model of the present application needs about 20 minutes for calculation under one condition, has good precision and high calculation efficiency; Especially for the final deformation of the fiber metal laminated plate explosion-resistant structure which is more concerned in engineering practice, the calculation result obtained by theoretical calculation is more reasonable, and has certain engineering value for guiding the preliminary explosion-resistant evaluation of the ship composite material structure. BRIEF DESCRIPTION OF DRAWINGS

[0037] The present application will be further described below in combination with the drawings and examples, wherein:

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

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

[0040] Figure 3 It is a stress-strain curve of the fiber metal laminated plate deformation stage of the present application;

[0041] Figure 4 It is a whole calculation flow chart of the impact response of the fiber metal laminated plate of the present application;

[0042] Figure 5 It is a response history flow chart of the center point of the test piece plate in each stage of the present application;

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

[0044] In order to have a clearer understanding of the technical features, objects and effects of the present application, the specific implementation mode of the present application will be described in detail with reference to the drawings.

[0045] As Figures 1-6As shown, the impact dynamic response analysis method of the composite-metal hybrid structure of the application comprises the following steps:

[0046] S1, according to the impulse size of the actual impact load in the saturated response time, the impact load is simplified;

[0047] The impulse size of the simplified load and the actual load in the saturated response time is the same, that is

[0048] I0 = I sat (1)

[0049] In the formula: 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 represents the impulse of the actual impact load in the structure saturated response time, t sat represents the saturated 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 simplification conditions, the impact equivalent load under different TNT mass is calculated.

[0053] S2, when the actual fiber metal laminated plate deformation increases to the damage of the fiber, the influence degree of the 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 laminated plate will reach the maximum deformation under the explosion load in a very short time, and the surrounding boundary will produce a large bending moment, so the fiber metal laminated plate is also easy to produce rotation at the clamping boundary. Therefore, the deformation deflection equation of FMLs is similar to the simply supported boundary, and the deformation deflection function of FMLs is as follows:

[0055]

[0056] In the formula, u and v are the displacements in x and y directions respectively; u0 and v0 are the maximum displacements in x and y directions respectively; w is the deflection of the plate in z direction, C is the deflection at the center point 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 represented by the above formula satisfies the boundary condition of four simply supported edges, that is, w(x,y) = w″(x,y) = 0 on the boundary, 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 displacements 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 torsion 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 aluminum alloy in the initial linear elastic stage; E represents the elastic modulus of the aluminum alloy; G=E / (2(1+v))=28.115GPa, which represents the shear modulus of the aluminum alloy in the initial linear elastic stage.

[0071] For fiber reinforced composite plates in the small deformation stage, since they are orthotropic materials, the x-axis and y-axis are aligned with the main directions of the fiber reinforced composite plates during analysis. The stress-strain relationship in the main directions of the orthotropic fiber reinforced composite materials is:

[0072]

[0073] where Q is a two-dimensional stiffness matrix, Q ij In terms of engineering elastic constants, we have

[0074]

[0075] where E1, E2 are the elastic moduli of the fiber reinforced composite plates 1, 2 in the 1, 2 directions, respectively; v 12 , v 21 are the Poisson's ratios in the 1, 2 directions, respectively, where v 21 / E1 = v 12 / E2.

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

[0077] When the fiber metal laminates are deformed greatly, the middle surface membrane force is the main load bearing form, and thus the influence of the middle surface force cannot be ignored. The small deformation 1, 2 assumptions, i.e., the straight normal assumption and the plane stress state, are still used for the large deflection deformation problem of the plate.

[0078] 1. Strain components

[0079] The displacement relationship formula taking into account the middle surface displacement u0, v0 is:

[0080]

[0081] Ignoring the first-order derivative nonlinear terms of u, v and retaining the first-order derivative nonlinear terms of w, and ignoring the third-order and higher-order infinitesimals, the nonlinear displacement-strain relationship is:

[0082]

[0083] When the fiber metal laminates are deformed greatly, the displacements u, v are small compared with the deflection w, and the in-plane displacements u, v can be ignored, and thus the strain components of the plate under large deflection deformation are:

[0084]

[0085] 2. Stress components

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

[0087]

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

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

[0090]

[0091] The stress is expressed by the strain as

[0092]

[0093] where v p is the Poisson's ratio of the aluminum alloy in the quadratic-linear stage; is the shear modulus of the aluminum alloy in the quadratic-linear stage; and τ0 is the maximum shear stress of the aluminum alloy in the initial elastic stage, according to the Mises stress yield criterion, γ0 = τ0 / G represents the maximum shear strain of the aluminum alloy in the initial elastic stage.

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

[0095] For the fiber-reinforced composite plate in the large deformation stage, when the deformation of the plate exceeds the fracture strain of the fiber-reinforced composite, the fiber-reinforced composite will be damaged, and the load-carrying capacity of the fiber metal laminated plate will decrease. Therefore, a fiber-reinforced composite stiffness damage reduction coefficient D is introduced to represent the stress-strain relationship of the fiber composite layer after damage.

[0096] The stiffness matrix after damage is

[0097]

[0098] where the stiffness reduction coefficient D nonlinearly changes with the deformation.

[0099] The fracture strain of the fiber-reinforced composite is 0.0153, and when the strain on the test plate exceeds 0.0153, it is considered that the fiber-reinforced composite is damaged by fracture.

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

[0101]

[0102] The fiber-reinforced composite reduction coefficient is

[0103]

[0104] where S d is the strain at which the fiber-reinforced composite is damaged in the x direction, and S x or S y>0.0153, the projection area of the fiber metal laminates deformation function in the xoy plane; S is the area of the fiber metal laminates before deformation.

[0105] Through MATLAB software, the above theoretical formula is programmed to obtain the curve of the reduction coefficient D of the fiber reinforced composite material changing with the center point displacement C of the fiber metal laminates, as shown in the following formula (18). Figure 2

[0106] The curve is polynomial fitted to obtain the fitting curve expression 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 through 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 laminates during the deformation process.

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

[0110] When the actual fiber metal laminates are small deformation, the deformation of the fiber composite material layer and the aluminum alloy layer is coordinated, and the influence of the middle surface force is not considered, so the thin plate small deformation assumption can be used for description; when the actual fiber metal laminates are large deformation but no internal damage, the deformation of the fiber layer and the aluminum alloy layer is still coordinated, at this time, the thin plate large deflection deformation theory is used for description. When the actual fiber metal laminates continue to increase, the fiber appears damage, the influence of the stiffness reduction coefficient of the fiber composite material layer on the damage is calculated.

[0111] Since the aluminum alloy stress-strain curve is transformed into a piecewise linear stress-strain curve, combined with the stress-strain curve of the fiber reinforced composite material, the deformation stage of the fiber metal laminates response process can be divided into four deformation stages through different strain sizes. The stress-strain curve of the fiber metal laminates deformation stage is shown in the following formula (18). Figure 3

[0112] Slip stage: the aluminum alloy layer and the fiber layer are elastic, the fiber metal laminates only produce bending deformation energy in the deformation process, 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 in unit volume of the aluminum plate and the fiber plate is respectively:

[0113] ​​

[0114] The bending strain energy of the aluminum layer under different lay-up forms 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 laminated plate; the number after M represents the number of metal plates in the fiber metal laminated plate; F represents the composite material layer in the fiber metal laminated plate; the number after F represents the number of composite material plates in the fiber metal laminated plate; 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 length of the plate, and b represents half of the width of the plate.

[0119] The first deformation stage: after the end of the sliding stage, the film deformation energy of the plate is generated, but the middle surface tensile deformation is within the elastic deformation, and the aluminum alloy layer and the fiber layer are in the elastic stage, at this time the deformation energy of the plate includes the bending deformation energy and the tensile deformation energy in the elastic stage. The bending deformation energy is the same as that in the sliding stage, which is calculated by formulas (19), (20), (21), and (22). In the calculation of the tensile strain energy, the strain adopts the large deformation theory formula (11), and since the middle surface tensile deformation does not occur in the boundary sliding stage, the film strain at this time should start from zero, and the deformation mode function of the test plate at the end of the sliding 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 the fiber plate is:

[0124]

[0125] The tensile strain energy of the aluminum layer under different lay-up forms is:

[0126]

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

[0128]

[0129] Stage two: FMLs have produced large deformation, the aluminum alloy enters the second linear stage, and the fiber plate 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 stage one. 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, so the bending strain energy of the aluminum alloy layer is the same as that in stage one, and is calculated by equations (19) and (21).

[0131] Since FMLs have produced large deformation, a middle surface tensile membrane force is generated, and the aluminum alloy enters the second linear stage. Therefore, when calculating the tensile strain energy of the aluminum alloy layer, the strain component uses the large deformation theory equation (11), and the stress component of the aluminum plate uses equation (14). Thus, the tensile strain energy of the aluminum layer per unit volume in the second stage FMLs is:

[0132]

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

[0134]

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

[0136]

[0137] Stage three: the aluminum alloy layer in the fiber metal laminates is still in the second linear stage, and the bending deformation energy and the tensile deformation energy of the aluminum alloy layer are the same as those in 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). Meanwhile, the bending deformation energy of the fiber composite layer is smaller than the tensile deformation energy, so the bending deformation energy of the fiber composite layer is still calculated by equations (22) and (24).

[0138] However, in stage three, the fiber composite layer appears to be damaged, so when calculating the tensile strain energy of the fiber composite layer, the strain component uses the large deformation theory equation (11), and the stress component uses equation (7), but the stiffness matrix uses the damaged stiffness matrix (15). Thus, the tensile strain energy of the fiber composite layer per unit volume is:

[0139]

[0140] Substituting equation (11) into the above equation, we get:

[0141]

[0142] The tensile strain energy of the fiber composite layer in different lay-up forms is:

[0143]

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

[0145] For the aluminum alloy layer, in deformation stage four, the ideal plastic stage is reached, that is, as the strain increases, the stress remains unchanged, at this time, the bending deformation energy of the aluminum alloy layer is smaller compared with the film deformation, so equations (19) and (21) are still used for calculation. For the film deformation energy of the aluminum alloy layer, the strain component equation (11) in the large deformation theory is used, in which the deformation function is w-w0, and the film deformation energy per unit volume is:

[0146]

[0147] The film strain energy corresponding to each lay-up 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 are oscillated in the elastic range, the fiber metal laminates produce the middle surface tensile film force and bending, at this time, the deformation energy of the test specimen plate includes the bending deformation energy and the film 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), (22). The film strain energy is the same as that in deformation stage one, and is calculated by equations (24), (25), (26), (27).

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

[0150] The total potential energy of the whole fiber metal laminates 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 whole fiber metal laminates system in the dynamic response process is

[0153]

[0154] where H is the total thickness of the FML, T FMLs is the average density of the FML.

[0155]

[0156] where p Al is the density of the aluminum alloy in the FML; h Al is the total thickness of the aluminum alloy layer in the FML; p Fiber is the density of the fiber reinforced composite in the FML; h Fiber is the fiber reinforced composite in the FML.

[0157] As Figure 4 shown, the FML impact response calculation process includes three parts: a calculation boundary slip stage; a calculation deformation stage; and a calculation oscillation stage. For the calculation process of the deformation stage, depending on the impact load of each working condition, the specimen layer form determines which stage the specimen center point displacement reaches, and which stage needs to be calculated. Using the method of sequentially connecting each stage, the response history of the center point of the FML under impact load is finally obtained. The specific process is explained as follows:

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

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

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

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

[0162] Into the deformation stage four, the maximum value max of the center point in the calculation process and the corresponding time and speed are saved as the initial value of the oscillation stage and run the oscillation stage until the calculation is completed.

[0163] For the slip stage, the deformation stage one, the deformation stage two, the deformation stage three, the deformation stage four and the oscillation stage, the displacement history of the specimen plate center point is solved, and the calculation method is to calculate the kinetic energy and potential energy of the specimen plate in the system of the stage, to establish the Lagrange motion differential equation of the system through energy, and finally to solve through numerical calculation by Runge-Kutta method. The response history process diagram of the actual plate center point in each stage is shown in Figure 5 After analyzing the response solving process of the specimen plate center point in each stage and the overall corresponding stage specimen center point response process, the solving process is programmed. The theoretical calculation program of the specimen center point response under impact load in the fiber metal laminated plate is obtained.

[0164] As shown in Figure 6As shown, the software is written in C language and is written in Matlab under Windows 10 system. The software is divided into two parts according to the function module, the main program and the function file, and the software includes one script file and ten function files. The main program, i.e. the script file, is the key of the whole program, mainly completes the coordination and cooperation with other function modules. The maximum time value in the equation solving parameter can be input, and is assigned to a new matrix storage. The matrix is used for interpolation operation, clears the variables of each stage, and keeps useful variables. The initial value of equation solving is the end value of the matrix of each previous stage. The program written based on the Matlab platform starts from the theoretical analysis model of the fiber metal laminated plate under the impact load, considers the influence of the damage stage reduction coefficient of the fiber metal laminated plate and the specimen boundary slip, considers the whole deformation process in stages, writes the theoretical calculation method into the program for solving, and forms a method for quickly analyzing the dynamic response of the fiber metal laminated plate under the impact load.

[0165] The embodiments of the present application are described above in combination with the drawings, but the present application is not limited to the above specific embodiments, and the above specific embodiments are only illustrative but not restrictive. Those skilled in the art can make many forms under the inspiration of the present application without departing from the purpose of the present application and the scope protected by the claims, and these all belong to the protection of the present application.

Claims

1. A method for analyzing the impact dynamic response of a composite-metal hybrid structure, 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 fiber damage occurs, the degree of damage is analyzed and calculated by introducing the stiffness reduction coefficient of the fiber composite material layer; In step S2, an xoy coordinate system is established with the center of the plate as the origin, and a curve expression of the stiffness reduction coefficient 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: ； S3. Based on the different deformation modes of actual fiber metal laminates under impact loads, dynamic response calculations are performed in stages; The displacement history of the center point of the specimen plate in the slip stage, deformation stage one, deformation stage two, deformation stage three, deformation stage four, and oscillation stage is solved by calculating the kinetic energy and potential energy of the specimen plate in each stage, establishing the Lagrangian motion differential equation of the system through the energy, and finally solving it numerically through the Runge-Kutta method.

2. The impact dynamic response analysis method of composite-metal hybrid structure 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: Where: , I 0 represents the impulse of the equivalent rectangular load, p 0 represents the pressure of the equivalent rectangular load, t 0 indicates equivalent time; , I sat Indicates the impulse of the actual impact load within the saturation response time of the structure, t sat represents the saturation response time, 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 impact dynamic response analysis method of composite-metal hybrid structure according to claim 1, characterized in that: In step S3, based on 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 magnitudes. The deformation stage 1 is preceded by a slip stage, and the deformation stage 4 is followed by an oscillation stage. During the slip stage, both the metal layer and the fiber layer are in the elastic stage. The fiber metal laminate only generates bending deformation energy during the deformation process, and no membrane deformation energy. After obtaining the total potential energy and kinetic energy, the Lagrangian motion differential equation is established and solved.

4. The impact dynamic response analysis method of composite-metal hybrid structure according to claim 3, characterized in that: In the first deformation stage, after the slip stage ends, the plate generates membrane deformation energy, but the mid-surface tensile deformation is within the elastic deformation. The metal layer and the fiber layer are both 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.

5. The impact dynamic response analysis method of composite-metal hybrid structure according to claim 4, characterized in that: In the second deformation stage, the metal layer enters the quadratic linear stage, and the fiber layer is still elastic. At this time, it is assumed that the fiber layer and the metal layer still deform 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.

6. The impact dynamic response analysis method of composite-metal hybrid structure according to claim 5, 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, by assuming that the fiber breaks, local failure inside the laminate is considered, a stiffness reduction coefficient is introduced, and 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 method for analyzing the impact dynamic response of a composite material-metal hybrid structure according to claim 6, characterized in that: In deformation stage four, the metal layer enters the ideal plastic stage but does not fail, while the fiber layer is damaged. The stiffness reduction coefficient 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.

8. The method for analyzing the impact dynamic response of a composite-metal hybrid structure according to claim 7, 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.

9. The impact dynamic response analysis method of composite-metal hybrid structure according to claim 8, characterized in that: In step S3, the method of performing dynamic response calculation in stages includes: S301, running the slip phase, in which the initial deformation of the specimen plate in the slip phase is 0, and the initial time is 0. If the displacement of the center point of the specimen plate exceeds the displacement threshold value C0 of the slip phase during the calculation process, the calculation time and speed of the center point of the specimen plate at the displacement C0 are obtained through linear interpolation of C0, and saved as the initial values ​​for input calculation of the deformation phase 1; if the displacement of the center point of the specimen plate does not exceed the displacement threshold value C0 of the slip phase 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 values ​​of the oscillation phase, and the oscillation phase 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 displacement C1 are obtained through linear interpolation of C1, and saved as the initial values ​​for input calculation in deformation stage 2; 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 values ​​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 displacement C2 are obtained through linear interpolation of C2, and saved as the initial values ​​for input calculation in deformation stage 3; 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, as well as the corresponding time and speed, are saved and used as the initial values ​​of the oscillation stage, and the oscillation stage is run until the calculation is completed; S304: Entering deformation stage 3. If the displacement of the center point of the specimen plate exceeds the displacement threshold C3 of deformation stage 3 during the calculation process, the calculation time and speed of the center point of the specimen plate at displacement C3 are obtained through linear interpolation of C3, and saved as the initial values ​​for input calculation in deformation stage 4. If the displacement of the center point of the specimen plate does not exceed the displacement threshold C3 of deformation stage 3 during the calculation process, the maximum value of the center point (max) during the calculation process, as well as the corresponding time and speed, are saved and used as the initial values ​​of the oscillation stage. The oscillation stage is then 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 them 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 1, deformation stage 2, deformation stage 3, deformation stage 4, 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 each stage, establish the Lagrangian motion differential equation of the system through the energy, and finally solve it numerically through the Runge-Kutta method.

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