Analysis Method for Dynamic Response of Sandwich Composite Structure under Blast Impact

Abstract

The invention discloses a method for analyzing the dynamic response of a sandwich composite structure under blast shock. First, a blast shock model of a sandwich composite structure with multiple types of pores and various elastic substrate reinforcements is constructed. Then, based on the classical plate and shell theory, the sandwich composite structure models with different forms of elastic substrates are described. Subsequently, linear discretization is performed in the spatial and temporal domains respectively, and the iterative method is used to solve the problem. The invention discloses a method for analyzing the dynamic response of a sandwich composite structure under blast shock, which can accurately characterize the influence of material property parameters, structural geometric parameters, forms and action positions of multi-point blast shock loads, pore distribution types, types of elastic substrates and compensation capabilities on the dynamic response of a porous and elastic substrate FGM sandwich hyperbolic plate under multi-point blast shock in a thermal environment.

Description

Technical Field

[0001] The present invention relates to the technical field of composite material structure dynamics, and specifically relates to a method for analyzing the dynamic response of a sandwich composite structure under blast shock. Background Art

[0002] Functionally graded materials were initially created to solve the problem of thermal stress relaxation in rocket propulsion systems. They are a new type of material developed to meet the special requirements of high-tech fields such as aerospace. Currently, they have broad application prospects in engineering. The basic components of functionally graded materials are a ceramic matrix with high thermal resistance and a metal matrix with high strength performance. The two matrices are on the surfaces of the functionally graded material and gradually mix and transition in a gradient manner to each other. Furthermore, the gentle transition characteristic of the material components realizes a gradient change in the physical properties of the structure. In particular, the smooth matching of the thermal expansion parameters effectively improves and enhances the problem of thermal stress concentration caused by sudden cooling and severe temperature rise of the structure. It is this material design concept that promotes the emergence and rapid technological development and application of various new functionally graded composite materials with specific components.

[0003] A hyperbolic plate is a common engineering structure. By adjusting the curvature, it can be transformed into various engineering structures such as flat plates, cylindrical shells, and variable curvature shells. Due to the two-way curvature elements of its structure, this structure exhibits geometric nonlinearity in mechanical principles. Especially in nonlinear dynamics problems, considering the influence of factors such as local structure enhancement of the structure, nonlinear elastic substrate compensation, material parameter nonlinearity, and load action nonlinearity, it is easy to form complex nonlinear dynamics problems. Due to the needs of engineering practical applications, the influence of the elastic substrate on the plate and shell structure has also attracted people's attention.

[0004] The sandwich structure consists of a faceplate - core layer - faceplate and is a common impact protection structure. Based on composite material mechanics, elastic mechanics, heat and mass transfer, nonlinear dynamics, and nonlinear plate and shell theory, etc., a multi-field response mechanical model of FGM sandwich hyperbolic plate structures with various geometric structures and composite material reinforcements is established. Facing blast nonlinear dynamics problems, considering the influence of factors such as material pore distribution, clarifying the influence laws of environmental factors, component content and distribution form, pore type effect, elastic substrate parameters, structural geometric elements, and dynamic action influence, etc. on the multi-field dynamic behavior, and giving full play to the excellent performance of functionally graded materials will promote the development of related research on the nonlinear mechanics of composite material structures with performance compensation effects, and will also provide a theoretical basis and support for the design of functionally graded laminated hyperbolic structures, which has important scientific research significance and engineering application value. Summary of the Invention

[0005] The technical problem to be solved by the present invention is: the present invention provides a method for analyzing the dynamic response of a sandwich composite structure under explosion shock, gives the main parameters affecting the composite structure under explosion shock, so that when the composite structure is subjected to an explosion load, the minimum deformation occurs and the optimal protection effect is achieved.

[0006] To solve the above technical problem, the technical solution proposed by the present invention is:

[0007] A method for analyzing the dynamic response of a sandwich composite structure under explosion shock, the sandwich composite structure includes a sandwich layer containing porous composite material and isotropic material surfaces on both sides of the sandwich layer, the sandwich layer is provided with pores, and the pores are non-uniformly distributed; the dynamic response analysis method includes the following steps:

[0008] Step S1, construct a mechanical model of the sandwich composite structure with non-uniform pore distribution effect

[0009] The improved expression of the general material properties of the pore effect is as follows:

[0010] P(z) = (P FM-1 -P FM-2 )(0.5 - z / h p ) n +P FM-2 -(P FM-1 +P FM-2 )ξ b (z) / 2

[0011] Where, when ξ b (z)≠0; P(z) is the general material property of the sandwich layer; P FM-1 and P FM-2 are the material properties of material 1 and material 2 of the sandwich layer respectively; h p is the thickness of the sandwich layer; z is the coordinate parameter in the thickness direction of the composite structure; ξ b (z) is the pore distribution function;

[0012] Step S2, construct a mathematical expression of the elastic foundation

[0013] The displacement generated by the sandwich layer in each direction due to explosion shock is compensated by using the deflection and rebound elastic foundation to enhance the performance of the composite structure to resist shock.

[0014] Step S3, construct a dynamic nonlinear equilibrium equation set for the multi-point explosion shock dynamics problem

[0015] According to the Hamilton variational principle, establish a dynamic equilibrium equation for the composite material sandwich layer under the action of movement, and the expression is:

[0016] δ∫0 t (U - W - K)dt = 0

[0017] Wherein, U, W, and K respectively refer to the strain energy, the work done by the external force, and the kinetic energy of the composite structure;

[0018] The expression of the strain energy U of the sandwich composite structure is:

[0019]

[0020] Wherein, h is the plate thickness of the sandwich composite structure; σ x , σ y , σ xy respectively represent the normal stress and shear stress components of the k-th material layer (k = 1, 2, 3); respectively represent the normal strain and shear strain components of the k-th material layer (k = 1, 2, 3); ζ represents the integral micro-element variable of the transverse strain;

[0021] The expression of the work W generated due to the explosion load is:

[0022]

[0023] Wherein, P i and (x i , y i ) respectively refer to the i-th explosion load and the specific position of the explosion action; n i represents the total number of explosion loads, δ p represents the specific position of the explosion action; w represents the transverse deflection of the sandwich composite structure;

[0024] The kinetic energy of the sandwich composite structure with pore effect can be expressed by the following formula

[0025]

[0026] Wherein, ρ is the mass density; is the derivative of the x-direction displacement u with respect to time t; is the derivative of the y-direction displacement v with respect to time t; is the derivative of the z-direction displacement w with respect to time t;

[0027] Step S4, discretize the dynamic equilibrium equations obtained in step S3 in the spatial domain and the time domain, and use the quadratic extrapolation method for iterative solution.

[0028] As a further improvement of the technical solution:

[0029] Preferably, in step S1, for each layer of the sandwich composite structure, according to the plane stress constitutive relationship, the constitutive relationship of each layer is expressed as:

[0030]

[0031] Among them, the stiffness coefficient is expressed as follows:

[0032]

[0033] Among them, represents the stiffness coefficient of the k-th layer of material (k = 1, 2, 3); represents the normal strain and shear strain of the k-th layer of material (k = 1, 2, 3); E (k) , v (k) , represents the elastic modulus, Poisson's ratio and shear modulus of the k-th layer of material (k = 1, 2, 3).

[0034] Preferably, in the step S2, the elastic foundation expression is constructed according to the Winkler form as:

[0035] f e = K w w

[0036] Among them, f e represents the elastic foundation, w is the transverse deflection of the sandwich composite hyperbolic plate, and K w is the linear stiffness coefficient.

[0037] Preferably, the second implementation manner is: in the step S2, the elastic foundation expression is constructed according to the Pastemak form as:

[0038]

[0039] Among them, f e represents the elastic foundation, w is the transverse deflection of the sandwich composite hyperbolic plate, K w is the linear stiffness coefficient, and G p is the shear stiffness coefficient.

[0040] Preferably, the third implementation manner is: in the step S2, the elastic foundation expression is constructed according to the Kerr form as:

[0041]

[0042] Among them, f e represents the elastic foundation, w is the transverse deflection of the sandwich composite hyperbolic plate, K l is the linear stiffness coefficient, K u is the stiffness coefficient of the top elastic layer, and K s is the shear stiffness coefficient.

[0043] Preferably, in the step S3, the Friedlander explosion load expression is adopted:

[0044]

[0045] Among them, P0 represents the peak value of the explosion load, t p represents the action time history of the explosion load, γ represents the attenuation coefficient of the explosion action, and t is the process time of the explosion shock.

[0046] Preferably, in the step S4, the Chebyshev collocation method is used for discretization in the spatial domain, and the total time t is divided into multiple time intervals Δt by using the Newmark-β method in the time domain, and the iterative method is used to solve; in each iterative step J, the nonlinear terms and boundary conditions of the equation are linearized.

[0047] The method for analyzing the dynamic response of the sandwich composite structure under explosion shock provided by the present invention has the following advantages compared with the prior art:

[0048] (1) The method for analyzing the dynamic response of the sandwich composite structure under explosion shock of the present invention aims at the problem of the dynamic response relationship of the sandwich composite structure under multi-point explosion shock loads, comprehensively considering the performance loss caused by material pore defects and the enhancement effect of multi-type elastic bases. The present invention provides a method for analyzing the dynamic response of the sandwich composite structure under explosion shock, which is used to study the action mechanism of each influencing parameter on the dynamic response performance of the structure.

[0049] (2) The method for analyzing the dynamic response of the sandwich composite structure under explosion shock of the present invention can accurately characterize the influence of the material property parameters, structural geometric parameters, multi-point explosion shock load forms and action positions, pore distribution types, elastic base types and compensation capabilities of the porous and elastic base FGM sandwich hyperbolic plates under multi-point explosion shock in the thermal environment on the dynamic response.

[0050] (3) The method for analyzing the dynamic response of the sandwich composite structure under explosion shock of the present invention provides an effective analysis method that can analyze the deformation performance of the hyperbolic plate, guide the integrated design of the material structure of the hyperbolic plate, and the analysis results are detailed, clear, the impact response curves of each physical quantity can be extracted flexibly, and the calculation is efficient and accurate. Description of the Drawings

[0051] Figure 1 is a schematic diagram of the sandwich composite structure of the present invention under explosion shock.

[0052] Figure 2(a) is a schematic diagram of the intermediate agglomeration distribution of the pore distribution in the sandwich layer.

[0053] Figure 2(b) is a schematic diagram of the double-surface agglomeration distribution of the pore distribution in the sandwich layer.

[0054] Figure 2(c) is a schematic diagram of the single-surface layer aggregation distribution of the pore distribution in the sandwich layer.

[0055] Figure 3(a) shows the influence of the intermediate aggregation distribution type in the embodiment of the present invention on the dimensionless nonlinear amplitude of the sandwich hyperbolic plate.

[0056] Figure 3(b) shows the influence of the double-surface layer aggregation distribution type in the embodiment of the present invention on the dimensionless nonlinear amplitude of the sandwich hyperbolic plate.

[0057] Figure 3(c) shows the influence of the single-surface layer aggregation distribution type in the embodiment of the present invention on the dimensionless nonlinear amplitude of the sandwich hyperbolic plate. Specific Embodiments

[0058] The following provides a detailed description of the specific embodiments of the present invention. It should be understood that the specific embodiments described herein are only for the purpose of illustrating and explaining the present invention, and are not intended to limit the present invention.

[0059] As Figure 1 shown in and Figure 2, the dynamic response analysis method of the sandwich composite structure under explosion shock according to the present invention, the sandwich composite structure is a sandwich hyperbolic plate, the sandwich hyperbolic plate has three layers, including a sandwich layer of porous composite material and isotropic material surface layers on both sides of the sandwich layer, and the pores in the sandwich layer are non-uniformly distributed.

[0060] In this embodiment, the commonly used functionally graded material (FGM) components stainless steel and alumina are taken as examples for specific illustration. The sandwich layer is a functionally graded material of stainless steel and alumina. In addition, the stainless steel surface layer is rich on the outer side of the sandwich layer of the sandwich hyperbolic plate and is connected to the stainless steel surface layer of the sandwich hyperbolic plate structure. Alumina is rich on the inner side of the sandwich layer of the sandwich hyperbolic plate and realizes material transition with the alumina bottom layer of the sandwich hyperbolic plate structure.

[0061] As Figure 1 shown, the sandwich layer of porous composite material and the isotropic material surface layers bear multi-point explosion loads P1 and P2 and other multi-point impacts. The plate thickness, principal curvature radius, and side length of the sandwich hyperbolic plate are respectively represented as h, R1 - R2, and a - b, and are placed in the Cartesian coordinate system (x, y, z). The xy - working surface is placed below the xy - plane in the positive direction of the z - axis of the hyperbolic plate structure. The thickness of the sandwich layer is h p , and z is the coordinate parameter representing the thickness direction of the sandwich hyperbolic plate structure. The stainless steel layer is at z = -h p / 2, and alumina is rich on the inner side of the hyperbolic plate sandwich layer. The alumina layer is at z = h p / 2.

[0062] The dynamic response analysis method of this embodiment includes the following steps:

[0063] Step S1, construct a mechanical model of a sandwich composite structure with non-uniform pore distribution effect

[0064] The general material property of the FGM of the hyperbolic plate sandwich layer is P, the mass density is ρ, the elastic modulus is E, the material property P varies gradually along the thickness direction of the hyperbolic plate following an exponential distribution, while the Poisson's ratio v is a constant value, and the material property P can be expressed by the following formula:

[0065] P = P FM-1 V FM-1 + P FM-2 V FM-2 (1)

[0066] Among them, P FM-1 and P FM-2 respectively refer to the material properties of material 1 and material 2 of the FGM sandwich layer, V FM-1 and V FM-2 respectively represent the volume fraction of material 1 and material 2.

[0067] The volume relationship between material - 1 and material - 2 of the FGM sandwich layer is:

[0068] V FM-1 + V FM-2 = 1 (2)

[0069] The volume fraction coefficient V FM-1 or V FM-2 varies along the thickness direction of the hyperbolic plate and is expressed in the form of an exponential equation as:

[0070]

[0071] Among them, h p is the thickness of the hyperbolic plate, and the volume ratio exponent n ranges from (0, ∞).

[0072] That is, the general material property P of the FGM can be expressed as

[0073] P(z) = (P FM-1 - P FM-2 )(0.5 - z / h p ) n + P FM-2 (4)

[0074] According to the exponential equation distribution principle, the FGM material property P varies gradually from P FM-1 (z = -h p / 2) to P FM-2 (z = h p / 2) along the thickness direction of the hyperbolic plate.

[0075] As shown in Figure 2, to explain the comparative analysis research process of the present invention, three pore distribution forms of sandwich composite hyperbolic plates are used in this embodiment for illustration.

[0076] The pore distribution function ξ b (z) is associated with the volume ratio index of the material, and the improved expression of the general material properties of the pore effect is as follows:

[0077] P(z) = (P FM-1 -P FM-2 )(0.5 - z / h p ) n +P FM-2 -(P FM-1 +P FM-2 )ξ b (z) / 2 (5)

[0078] Where, when ξ b (z) ≠ 0.

[0079] For each layer of the sandwich hyperbolic plate according to the plane stress constitutive relationship, the constitutive relationship of each layer is expressed as

[0080]

[0081] Among them, the stiffness coefficient is expressed as follows

[0082]

[0083] As shown in Figure 2, to accurately describe the non-uniform distribution pore effect, three types of non-uniform distributions are listed for illustration. Figure 2(a) is the intermediate agglomerated distribution (Type1), Figure 2(b) is the double-surface layer agglomerated distribution (Type2), and Figure 2(c) is the single-surface layer agglomerated distribution (Type3). The material performance degradation due to the pore effect on the dynamic response. The expression for the gradual change of the volume fraction of pores in the FGM sandwich layer is:

[0084]

[0085] According to the classical plate and shell theory, the strains (ε x , ε y , ε xy ) varying along the thickness of the hyperbolic plate are expressed in terms of the mid-plane strain components and the bending strain components as follows:

[0086]

[0087] Among them, the mid-plane strain components The relational expressions for the displacements (u0, v0, w0) relative to the middle surface can be expressed as follows

[0088]

[0089] The bending strain can be defined by the following formula:

[0090]

[0091] In this embodiment, Formulas (1)-(4) define the relational expressions for the physical properties of the FGM sandwich core exponential material;

[0092] Formula (5) describes the relational expressions for the physical properties of the FGM sandwich core exponential material considering the pore factor; Formula (6)

[0093] illustrates the overall stress-strain relationship of the sandwich hyperbolic plate; Formula (7) describes the mathematical relationship of the pore distribution; Formulas (8)-(10) give the overall geometric relationship (displacement-strain relationship) of the sandwich hyperbolic plate. The above overall constructs the constitutive relationship and geometric relationship of the porous sandwich hyperbolic plate, and provides the corresponding mechanical model relational expressions.

[0094] Step S2, constructing the mathematical expression of the elastic foundation

[0095] The sandwich porous functionally graded material FGM sandwich core hyperbolic plate and the isotropic material surface layer are subjected to multi-point explosion shock. The plate thickness, principal curvature radii, and side lengths of the hyperbolic plate of the sandwich hyperbolic plate are respectively denoted as h, R1 - R2, and a - b, and it is placed in the Cartesian coordinate system (x, y, z), with the xy - working surface placed on the sandwich core of the hyperbolic plate and the positive direction of the z - axis pointing downward below the xy - plane shown. The displacements generated by the explosion shock in each direction on the sandwich core are respectively represented by and To represent. Due to the reduction of the stiffness of the composite hyperbolic plate caused by pore defects, a deflection springback elastic foundation is used to enhance and compensate the impact resistance performance of the composite hyperbolic plate. Common elastic foundations have specific Winkler / Pastemak / Kerr forms, and the corresponding expressions are respectively:

[0096] f e (Winkler) = K w w

[0097]

[0098]

[0099] Among them, f e represents the elastic foundation. The elastic foundation constructed in the Kerr form includes a top elastic layer, a bottom elastic layer, and an intermediate shear layer, a total of three layers. w is the transverse deflection of the sandwich composite hyperbolic plate K w represents the linear stiffness coefficient characterized by the Winkler foundation, G p represents the shear stiffness coefficient described by the Pasternak elastic foundation, K l is the stiffness coefficient of the underlying elastic layer, K u is the stiffness coefficient of the top elastic layer, K s is the stiffness coefficient of the intermediate shear layer.

[0100] Step S3, construct the dynamic nonlinear equilibrium equations for the multi-point explosion shock dynamics problem

[0101] Introduce Hamilton's variational principle to obtain the dynamic equilibrium equation of the composite sandwich layer with wrinkling effect under moving action, expressed as follows:

[0102]

[0103] Among them, U, W, and K represent the strain energy, the work done by external forces, and the kinetic energy of the sandwich hyperbolic plate structure, respectively.

[0104] The strain energy of the sandwich hyperbolic plate can be obtained by the following formula:

[0105]

[0106] The work generated due to the explosion load action can be obtained by the following formula:

[0107]

[0108] In the above formula, P i and (x i , y i ) represent the i-th explosion load and the specific position of the explosion action, respectively; n i represents the total number of explosion loads, and δ p represents the two-dimensional Dirac's delta function used to determine the specific position of the explosion action.

[0109] The kinetic energy of the sandwich hyperbolic plate with pore effect can be expressed by the following formula:

[0110]

[0111] The internal forces and moments of the hyperbolic plate are N i , M i (i = x, y, xy) and are specifically expressed as follows:

[0112]

[0113]

[0114] The strain expressions of internal forces and moments are as follows:

[0115]

[0116]

[0117] Among them, A ij and D ij represent the extensional and flexural stiffness coefficients respectively (i, j = 1, 2, 6), and are defined specifically as follows:

[0118]

[0119] The dynamic equilibrium equations can be expressed as follows:

[0120]

[0121]

[0122]

[0123] In the formula, ρ and I P represent the mass density and moment of inertia of the sandwich hyperbolic plate respectively, and are specifically expressed as follows

[0124]

[0125] The overall governing differential equation is obtained:

[0126]

[0127]

[0128]

[0129]

[0130] Introduce dimensionless variables

[0131]

[0132]

[0133]

[0134] The dimensionless nonlinear motion control equations for the whole problem are obtained:

[0135]

[0136]

[0137]

[0138]

[0139] Consider studying in the form of simply supported four sides of a hyperbolic plate and performing dimensionless treatment. The specific expressions are as follows:

[0140]

[0141]

[0142] The present invention adopts the Friedlander explosion load expression

[0143]

[0144] In the above formula, P0 represents the peak value of the explosion load, t p represents the action time history of the explosion load, γ represents the attenuation coefficient of the explosion action, and t refers to the process time.

[0145] Step S4, discretize the dynamic equilibrium equations obtained in step S3 in the spatial domain and the time domain, and use the quadratic extrapolation method for iterative solution.

[0146] In order to obtain the numerical solution of the motion control equation that satisfies the boundary conditions, the displacements u, v, and w are discretized in the spatial domain and the time domain. The present invention uses the Chebyshev collocation method for discretization in the spatial domain and uses the Newmark-β method in the time domain to divide the total time t into multiple time intervals Δt, and uses the iterative method to solve. In each iterative step J, the nonlinear terms and boundary conditions of the equation are linearized, and the corresponding expressions are as follows:

[0147]

[0148] In the formula, is the average value of the starting two iterative steps. Using the quadratic extrapolation method to solve for the initial iterative step, we can obtain:

[0149]

[0150] For different iterative steps, the coefficients A, B, and C in the above formula will have different values:

[0151] J = 1: A = 1, B = 0, C = 0 (35a)

[0152] J = 2: A = 2, B = -1, C = 0 (35b)

[0153] J = 3: A = 3, B = -3, C = 1 (35c)

[0154] The time term Δt and the acceleration term w in the equation set are linearized using the Newmark-β method ，ττ , and the velocity term w ，τ is linearly processed

[0155]

[0156]

[0157]

[0158] Through the above processing, the governing equations and boundary conditions can be transformed into a series of discrete points by linearization, and these linear equation sets are relatively easy to obtain and solve. For each iteration step, it is set that the error between two adjacent iteration results must be less than 10 -5 . After obtaining the convergent solution, the iteration terminates and then enters the next iteration calculation j + 1

[0159] In this embodiment, through linearization, the nonlinear relationship between multiple physical quantities can be discretized into a linear relationship, which is convenient for subsequent iterative solution to obtain the displacement response and stress response relationship of the sandwich hyperbolic plate under blast shock; further, by substituting the mathematical relationship formula (7) of the pore type and the parameter values, the displacement response and stress response relationship of the sandwich hyperbolic plate under blast shock under different pore types and porosities can be calculated and obtained

[0160] Example: The radius of the sandwich hyperbolic plate R1 = R2 = 10m, the side length a = b = 1m, the plate thickness h = 0.08m (the core layer FGM is 0.04mm, and both surface layers are 0.02mm), and the relevant coefficients of the Winkler - Pastemak elastic matrix to which the hyperbolic plate adheres are K1 = 1GPa / m and K2 = 1GPa·m. The volume coefficient n of the relevant material components of the core layer FGM is 5. The inner radius of the hyperbolic plate is rich in material (Alumina), the outer radius is rich in material (SUS304), the inner surface layer material of the hyperbolic plate radius is (Si3N4), and the outer radius material is (Ti - 6Al - 4V). To further explore the influence of blast shock on the dynamic behavior of the sandwich hyperbolic plate with pore effect, ξ0 = (0, 0.2, 0.4), and the sandwich hyperbolic plate bears the blast load impact (P = -10 6 N / m 2 , t p= 0.25 ms, γ = 0.1). Dynamic response analysis was carried out on the three pore distribution forms in Figure 2, and the results are shown in Figure 3. It can be seen that the analysis of the dynamic response of the composite hyperbolic plate mainly focuses on the influence of the pore distribution form on the explosion shock response of the sandwich hyperbolic plate with pore effect. As shown in Figure 3, both the material porosity and the pore distribution pattern have a significant impact on the dynamic performance of the hyperbolic plate. Further analysis reveals that the non-uniform pore Type1 causes the most prominent deflection change in the structure, while the non-uniform pore Type2 exhibits the best mechanical properties. It can be seen that the pore effect affects the mass distribution of the structure, reducing the structural weight while changing the structural stiffness.

[0161] The above embodiments are only preferred embodiments of the present invention and do not impose any form of limitation on the present invention. Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Therefore, any simple modifications, equivalent changes, and decorations made to the above embodiments based on the technical essence of the present invention without departing from the technical solution of the present invention shall fall within the scope of protection of the technical solution of the present invention.

Claims

1. A method for analyzing the dynamic response of a sandwich composite structure under blast shock, characterized in that, The sandwich composite structure includes a sandwich layer of porous composite material and isotropic material surfaces on both sides of the sandwich layer. The sandwich layer is provided with pores, and the pores are non-uniformly distributed. The dynamic response analysis method includes the following steps: Step S1, construct a mechanical model of the sandwich composite structure with the effect of non-uniform pore distribution The improved expression of the general material properties of the pore effect is as follows: P(z) = (P FM-1 - P FM-2 )(0.5 - z / h p ) n + P FM-2 -(P FM-1 + P FM-2 )ξ b (z) / 2 Among them, when ξ b (z) ≠ 0; P(z) is the general material property of the sandwich layer; P FM-1 and P FM-2 are the material properties of sandwich layer material 1 and material 2 respectively; h p is the thickness of the sandwich layer; z is the coordinate parameter in the thickness direction of the composite structure; ξ b (z) is the pore distribution function; Step S2, construct a mathematical expression of the elastic foundation The displacement generated in each direction of the sandwich layer due to the explosion shock is compensated by using the deflection and rebound elastic foundation to enhance the performance of the composite structure against shock. Step S3, construct a dynamic nonlinear equilibrium equation set for the dynamic problem of multi-point explosion shock According to the Hamilton variational principle, establish the dynamic equilibrium equation of the composite material sandwich layer under the moving action, and the expression is: δ∫0 t (U - W - K)dt = 0 Among them, U, W, and K respectively refer to the strain energy, the work done by the external force, and the kinetic energy of the composite structure; The expression of the strain energy U of the sandwich composite structure is: where h is the plate thickness of the sandwich composite structure; σ x , σ y , σ xy respectively represent the normal stress and shear stress components of the k-th material layer (k = 1, 2, 3); respectively represent the normal strain and shear strain components of the k-th material layer (k = 1, 2, 3); ζ represents the transverse strain integral differential variable; The expression of the work W generated due to the explosion load action is: Among them, P i and (x i , y i ) respectively represent the specific position of the i-th explosion load and the explosion action; n i represents the total number of explosion loads, δ p represents the specific position of the explosion action; w represents the lateral deflection of the sandwich composite structure; The kinetic energy of the sandwich composite structure with pore effect can be expressed by the following formula where ρ is the mass density; is the derivative of the displacement u in the x - direction with respect to time t; is the derivative of the displacement v in the y - direction with respect to time t; is the derivative of the displacement w in the z - direction with respect to time t; Step S4, discretize the dynamic equilibrium equation set obtained in Step S3 in the spatial domain and the time domain, and use the quadratic extrapolation method for iterative solution.

2. The dynamic response analysis method of the sandwich composite structure under explosion shock according to claim 1, characterized in that, In the said Step S1, each layer of the sandwich composite structure is based on the plane stress constitutive relationship, and the constitutive relationship of each layer is expressed as: Among them, the stiffness coefficient is expressed as follows: Among them, represents the stiffness coefficient of the k-th material layer (k = 1, 2, 3); represents the normal strain and shear strain of the k-th material layer (k = 1, 2, 3); E (k) , v (k) , represent the elastic modulus, Poisson's ratio and shear modulus of the k-th material layer (k = 1, 2, 3).

3. The dynamic response analysis method of the sandwich composite structure under explosion shock according to claim 2, characterized in that, In the said Step S2, according to the Winkler form, the elastic foundation expression is: f e = K w w where f e represents the elastic substrate, w is the transverse deflection of the sandwich composite hyperbolic plate, and K w is the linear stiffness coefficient.

4. The dynamic response analysis method of the sandwich composite structure under explosion shock according to claim 2, characterized in that In the said Step S2, according to the Pasternak form, the elastic foundation expression is: Among them, f e represents the elastic substrate, w is the transverse deflection of the hyperbolic plate of the sandwich composite material, K w is the linear stiffness coefficient, G p is the shear stiffness coefficient.

5. The dynamic response analysis method of the sandwich composite structure under explosion shock according to claim 2, wherein In the said Step S2, according to the Kerr form, the elastic foundation expression is: Among them, f e represents the elastic substrate, w is the transverse deflection of the hyperbolic plate of the sandwich composite material, K l is the linear stiffness coefficient, K u is the stiffness coefficient of the top elastic layer, K s is the shear stiffness coefficient.

6. The dynamic response analysis method of the sandwich composite structure under explosion shock according to claim 1, wherein In the said Step S3, the Friedlander explosion load expression is adopted: Among them, P0 represents the peak value of the explosion load, t p represents the time history of the action of the explosion load, γ represents the attenuation coefficient of the explosion action, and t is the process time of the explosion shock.

7. The dynamic response analysis method of the sandwich composite structure under explosion shock according to claim 1, characterized in that In the said Step S4, the Chebyshev collocation method is used for discretization in the spatial domain, and the total time t is divided into multiple time intervals Δt by using the Newmark-β method in the time domain, and the iterative method is used for solution; in each iterative J step, the nonlinear terms and boundary conditions of the equation are linearized.

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