A method for calculating the high-speed impact characteristics of a composite cylindrical shell casing with a negative poisson's ratio honeycomb core

Abstract

This invention belongs to the field of mechanical dynamics technology, specifically relating to a method for calculating the high-speed impact characteristics of a composite cylindrical shell casing with a negative Poisson's ratio honeycomb core. The technical solution is as follows: Obtain the structural parameters, material parameters, and initial iteration parameters of the composite cylindrical shell casing and the projectile; establish an analytical dynamic model of the composite cylindrical shell casing; apply different failure criteria to the fiber / resin composite skin and the negative Poisson's ratio honeycomb core of the casing; based on the analytical dynamic model, solve for the impact velocity, impact time, and energy absorption characteristics after the failure of the first layer of the casing; iteratively calculate and solve the analytical dynamic model to obtain the remaining velocity and impact time of the projectile after the entire casing is penetrated. This invention establishes the displacement field of the composite cylindrical shell casing structure, corrects the material parameters to account for strain rate effects, and treats the core layer as an anisotropic single-layer material. Then, it solves for the high-speed impact parameters based on Hertz's contact law, progressive damage theory, and the law of conservation of energy.

Description

Technical Field

[0001] This invention belongs to the field of mechanical dynamics technology, specifically relating to a method for calculating the high-speed impact characteristics of a composite cylindrical shell casing with a negative Poisson's ratio honeycomb core. Background Technology

[0002] Compared to traditional metal casings, fiber / resin composite cylindrical casings offer superior specific strength, stiffness, damping and vibration reduction capabilities, impact energy absorption, and weight reduction. They have been widely used in aero-engines in recent years. However, during service, they may be subjected to high-speed or ultra-high-speed impacts from debris, bird strikes, hail, bullets, etc., leading to reduced casing strength, delamination damage, structural failure, and non-containment accidents.

[0003] Composite cylindrical shell casings with negative Poisson's ratio honeycomb cores represent a novel type of sandwich casing. The core layer is simple to manufacture and effectively reduces casing weight, while the fiber / resin composite skin significantly improves the casing's mechanical properties. In-depth research into the impact dynamics calculation methods for this structure is crucial for its dynamic design and fault diagnosis. However, current research in this area, both domestically and internationally, is limited. Therefore, it is necessary to conduct in-depth research on the dynamics calculations of composite cylindrical shell casing structures with negative Poisson's ratio honeycomb cores under high-speed impacts.

[0004] Most existing methods for calculating the impact characteristics of casings are designed for metal casings. Patent CN201810199427.7 establishes a finite element model that can plot the containment curve of a double-layer titanium alloy casing and solves the containment critical velocity. Similarly, patent CN201810088814.3 also conducts finite element simulation of the ballistic limit of a double-layer gapless metal casing. Similarly, Yang Shuyi et al. (PI Mech Eng GJ Aer, 2019, 233(10): 3635-3648) conducted simulation and experimental research on aluminum honeycomb sandwich structure casings and calculated the blade kinetic energy loss, casing deformation and casing internal energy change of single-structure casings, double-layer casings and sandwich structure casings. However, the above three models are only applicable to metal casings and cannot calculate the constitutive relations and failure modes of complex composite materials. Patent CN202011536091.2 established a finite element model of a blade obliquely impacting a casing, but only calculated the load and maximum deformation of the casing's containment area, without considering casing damage under penetration conditions. Patent CN202111392767.X provides a design method for a shear-thickened impregnated Kevlar-containing casing, which further solves the normalized shear rate by solving the projectile's residual velocity, but only considers the influence of the shear thickening fluid mass fraction, and cannot perform three-dimensional stress calculation on the composite material, resulting in poor accuracy in solving the projectile's residual velocity. Cui Huaitian et al. (Civil Aviation University of China, 2022) established a finite element model that can consider the constitutive relationship and failure criteria of braided composite material casings; however, like the aforementioned finite element simulation methods, it cannot overcome the problems of high computational cost, low computational efficiency, and black-box operation of finite element software. Patent CN202211256733.2 provides a design method for the containment of a graded laminated resin-based composite casing. It performs containment analysis on the established dynamic simulation model based on the maximum strain failure criterion, but can only obtain the casing failure mode and cannot solve for impact characteristic parameters. Patent CN202210321832.8 establishes empirical formulas for the containment of stiffened lightweight casings and double-layer casings based on energy absorption parameters, solving for the residual kinetic energy of the fly-off blades. However, it only considers the thickness effect of the resin-based composite material and cannot consider the influence of the actual failure mode on the energy absorption characteristics. Patent CN202210697077.3 simplifies the casing containment area to a target panel with several reinforcing ribs, solving for the residual velocity and ballistic limit of a flat strip blade after penetrating the casing. However, it is only applicable to metal target plates with reinforcing ribs, and this simplification ignores the influence of the structural characteristics of the cylindrical casing, resulting in poor solution accuracy.

[0005] In summary, while the aforementioned patents and literature have conducted numerical and analytical studies on the containment problem of casings to varying degrees, the vast majority rely on commercial finite element method (FEM) software. This approach suffers from drawbacks such as black-box operation, difficulty in revealing physical mechanisms, and long computation times. Furthermore, there are significant shortcomings in the analytical dynamic modeling and analysis of composite cylindrical shell casings. In particular, there are no reports on the energy absorption characteristics of sandwich composite cylindrical shell casings considering structural properties and high-speed impact strain rate effects, and corresponding analytical models and analysis / solution methods are lacking. Therefore, providing an analytical calculation method for the high-speed impact characteristics of sandwich composite cylindrical shell casings that does not rely on finite element method software has significant practical implications and broad application prospects. Summary of the Invention

[0006] This invention provides a method for calculating the high-speed impact characteristics of a composite cylindrical shell casing with a negative Poisson's ratio honeycomb core. After establishing the displacement field of the composite cylindrical shell casing structure, the material parameters are corrected to take into account the strain rate effect, and the core layer is equivalent to an anisotropic monolayer material. Then, the high-speed impact parameters are solved based on Hertz's contact law, progressive damage theory, and the law of conservation of energy. The calculation is simple and highly accurate.

[0007] The technical solution of the present invention is as follows:

[0008] A method for calculating the high-speed impact characteristics of a composite cylindrical casing with a negative Poisson's ratio honeycomb core includes the following steps:

[0009] Step 1: Obtain the structural parameters, material parameters, and initial iteration parameters of the composite cylindrical shell casing and projectile with negative Poisson's ratio honeycomb core;

[0010] Step 2: Based on the above structural and material parameters, establish an analytical dynamic model of the composite cylindrical shell casing;

[0011] Step 3: Apply different failure criteria to the fiber / resin composite skin and negative Poisson's ratio honeycomb core of the casing;

[0012] Step 4: Based on the analytical dynamic model, solve for the impact velocity, impact time, and energy absorption characteristics after the failure of the l-th layer of the casing;

[0013] Step 5: Iteratively calculate and solve the analytical dynamics model to obtain the remaining velocity and impact time of the projectile after the entire casing is penetrated;

[0014] Step 6: If the failure condition is not met, increase the initial displacement so that the initial displacement = initial displacement + initial step size, and repeat step 5.

[0015] Step 7: If the initial step size does not meet the accuracy requirements, reduce the initial step size so that the initial step size = initial step size / 2, reset the initial displacement so that the initial displacement = initial displacement - initial step size, and repeat step 5.

[0016] Step 8: If the strain rate does not meet the accurate calculation requirements of high-speed impact, then the material parameters of the composite cylindrical shell casing are corrected according to Step 2, and Step 5 is repeated.

[0017] Furthermore, in the method for calculating the high-speed impact characteristics of the composite cylindrical shell casing with a negative Poisson's ratio honeycomb core, step 1 includes the following process:

[0018] Step 1.1: Define a global coordinate system o-xθz on the composite cylindrical shell casing, located on the mid-surface of the structure; define local coordinate systems D1, D2, and D3 on the fiber / resin composite skin, representing the three principal material axes of the fiber / resin composite skin, θ... F The angle between direction D1 and the x-axis;

[0019] Step 1.2: Obtain the structural and material parameters, including the total length L, total thickness h, mid-surface radius R, and fiber / resin composite skin thickness h of the cylindrical shell. F negative Poisson ratio honeycomb core thickness h C Projectile radius R I Initial impact velocity V, hypotenuse length l of negative Poisson's ratio honeycomb core cell. a Horizontal side length l b The thickness of the horizontal edge l t Inclination angle Φ;

[0020] Step 1.3: Obtain the initial parameters for iteration, including the initial number of layers l, the initial displacement setting w0, the initial step size setting e, the initial accuracy c, and the initial strain rate ε. l Initial strain rate accuracy c e The initial velocity is V0.

[0021] Furthermore, in the method for calculating the high-speed impact characteristics of the composite cylindrical shell casing with a negative Poisson's ratio honeycomb core, step 2 includes the following process:

[0022] Step 2.1: Propose a modulus correction formula that considers the effect of strain rate:

[0023]

[0024]

[0025] in, The modulus of elasticity of fiber / resin composite skin in the corrected D2 direction (i.e., perpendicular to the fiber direction); The shear modulus of the corrected D1D2 planar fiber / resin composite skin; and E represents the modulus under the corresponding quasi-static conditions. C and G C E represents the elastic modulus and shear modulus of a negative Poisson's ratio honeycomb core. Q and G Q Core modulus under quasi-static conditions; For strain rate; A D2 A D1D2 A E B E C E D E A G B G C G and D G P represents the fitting coefficient; D2 and P D1D2 To fit a polynomial;

[0026] Step 2.2: Determine the constitutive relation of the composite cylindrical shell casing;

[0027] Based on Reddy's higher-order shear deformation theory, the displacement field at any point in the composite cylindrical shell casing structure is constructed. Then, according to the Love-Kirchhoff assumption and considering Novozhilov nonlinearity, the strain at any point in the composite cylindrical shell casing is defined as:

[0028]

[0029]

[0030] Where u0, v0, and w0 are the displacements of the mid-surface of the structure in the x, θ, and z directions;

[0031] According to the generalized Hooke's law, the stress (σ) of the composite cylindrical shell casing in the local coordinate system i′ , τ j′ )-Strain (ε i′ γ j′ The relation (i′=D1,D2,D3,j′=D2D3,D1D3,D1D2) is determined as follows:

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] Wherein, S and C represent fiber / resin composite skin and negative Poisson's ratio honeycomb core, respectively; and These represent Young's modulus, shear modulus, and Poisson's ratio in the corresponding direction or plane, respectively; based on the improved Gibson theory, the equivalent modulus and Poisson's ratio of the negative Poisson's ratio honeycomb core are determined:

[0038]

[0039]

[0040]

[0041]

[0042] Where a0 and b0 are structural coefficients:

[0043]

[0044] Step 2.3: Determine the residual stress distribution relationship of the composite cylindrical shell casing;

[0045] The transformation stiffness matrix of the composite cylindrical shell casing in the global coordinate system is expressed as:

[0046]

[0047]

[0048] The expression for the total off-axis stress of the composite cylindrical shell casing in the l-th layer of the global coordinate system is:

[0049]

[0050] in, The off-axis stress of the l-th layer is considered to account for the failure stress distribution; h (l) It is the thickness of the l-th layer; K represents the total off-axis stress component of the (l-1)th layer; mn The equivalent stiffness of the structure is expressed as:

[0051]

[0052]

[0053] in, and The equivalent modulus and Poisson's ratio of the structure are expressed as follows:

[0054]

[0055]

[0056]

[0057]

[0058] in, This is the tensile stiffness coefficient; coefficient

[0059] Furthermore, in the method for calculating the high-speed impact characteristics of the composite cylindrical shell casing with a negative Poisson's ratio honeycomb core, step 3 includes the following process:

[0060] The fiber / resin composite skin uses the Hashin three-dimensional composite material failure criterion as the criterion for damage initiation:

[0061] Fiber tensile failure σ D1 ≥0:

[0062]

[0063] Fiber compression failure σ D1 <0:

[0064]

[0065] Matrix tensile failure σ D2 +σ D3 ≥0:

[0066]

[0067] Matrix compressive failure σ D2 +σ D3 <0:

[0068]

[0069] in, and It refers to the tensile strength in the D1 and D2 directions. and The compressive strengths are in the D1 and D2 directions. Shear strength in three different planes;

[0070] For the negative Poisson's ratio honeycomb core, the compression-shear coupling failure criterion is selected:

[0071]

[0072] in, and These represent the corresponding compressive strength and shear strength.

[0073] Furthermore, in the method for calculating the high-speed impact characteristics of the composite cylindrical shell casing with a negative Poisson's ratio honeycomb core, step 4 includes the following process:

[0074] Step 4.1: Solve for the displacement and rotation components;

[0075] The displacement and rotation components of the composite cylindrical shell casing in the global coordinate system are defined as follows:

[0076]

[0077] in, These are the displacement and rotational components, M' and N' are the maximum cutoff coefficients, m' represents the number of polynomial terms, and n' corresponds to the circumferential wavenumber. The unknown eigenvector to be solved, q m' (t) is a generalized coordinate. Let m' be the m-th orthogonal polynomial obtained on the interval [0,1] through the Gram-Schmidt process.

[0078] The displacement equation and governing equation of the composite cylindrical shell casing at the impact center can be defined as follows:

[0079] w0(x0,θ0)=w0(x0+R con ,θ0)=w0(x0,θ0+L con ) = w max ,

[0080] φ D1 (x0,θ0)=φ D1 (x0+R con ,θ0)=φ D1 (x0,θ0+L con ) = 0,

[0081] φ D2 (x0,θ0)=φ D2 (x0+R con ,θ0)=φ D2 (x0,θ0+L con ) = 0,

[0082] N x =0,

[0083] Among them, w max R is the maximum displacement of the structure at the impact center of the projectile. con L represents the relatively small radius of the contact area. con The arc length of the contact area;

[0084] Based on the principle of virtual work, the governing differential equations are derived by substituting the expressions for generalized internal forces and torques. Based on the kinetic energy theorem, the formula for external force work, and the formula for strain energy, the impact contact force corresponding to the high-speed impact of the projectile on the casing is expressed as:

[0085]

[0086] Among them, U A U D U E U F U H These are the strain energies caused by different deformation modes of the structure, and their expressions are:

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] Among them, D mn E mn ,F mn H mn The corresponding stiffness coefficient is expressed as follows:

[0093]

[0094] The unknown eigenvectors can be obtained by solving the above equations. and displacement and rotational components u0, v0, w0, φ D1 φ D2 ;

[0095] Step 4.2: Determine the impact velocity and corresponding impact time of the projectile after it breaks through the lth layer of the receiver;

[0096] Then, the impact velocity of the projectile after breaking through the l-th layer of the structure is expressed as:

[0097]

[0098] in, The strain energy consumed when the lth layer fails. Energy consumed for layer l damage, T f l The energy consumed for tensile fracture of the l-th layer is expressed as:

[0099]

[0100] in, G II For type II interlayer energy release rate, σ IL e represents the interlaminar shear strength. up This represents the energy density of the innermost layer of the casing structure.

[0101] Finally, the impact time corresponding to the projectile breaking through the l-th layer of structure is expressed as:

[0102]

[0103] Step 4.3: Solve for the energy absorption characteristics of the receiver after the projectile breaks through the first layer of the receiver;

[0104] The energy absorbed by the receiver after the projectile penetrates the first layer of the receiver is:

[0105]

[0106] The specific energy absorbed by the receiver after the projectile penetrates the first layer of the receiver is:

[0107]

[0108] Where, m s This refers to the total mass of the casing.

[0109] Furthermore, in the method for calculating the high-speed impact characteristics of the composite cylindrical shell casing with a negative Poisson's ratio honeycomb core, step 5 includes the following process:

[0110] Step 5.1: Calculate the total off-axis stress;

[0111] Substitute the initial displacement of the projectile into the displacement equation and control equation of the casing at the impact center in step 4.1 to solve for the displacement component w0; substitute the displacement component and material parameters into steps 2.2-2.3 to obtain the total off-axis stress.

[0112] Step 5.2: Apply failure criteria to determine whether the innermost layer material of the casing has failed;

[0113] Use the failure criteria in step 3 to determine whether the innermost material of the casing has failed under the total off-axis stress in step 5.1; if it has failed, proceed to step 5.3.

[0114] Step 5.3: Determine whether the initial step size meets the accuracy requirements;

[0115] Determine if the initial step size is less than the initial step size precision; if it is less, proceed to step 5.4.

[0116] Step 5.4: Determine whether the strain rate meets the requirements for accurate calculation in high-speed impact problems;

[0117] Determine if the ratio of strain rate to initial strain rate is less than the initial strain rate accuracy; if it is less, proceed to step 5.5.

[0118] Step 5.5: Output the projectile's impact velocity, impact time, and energy absorption characteristics of the innermost layer of the casing after the innermost layer of the output casing is damaged;

[0119] Substitute the initial high-speed impact velocity and displacement component w0 of the projectile given in step 1.3 into step 4.2 to obtain the impact velocity and corresponding impact time of the projectile after the innermost layer of the casing is damaged. Further solve for the energy absorption and specific energy absorption of the casing as described in step 4.3; at this point, the solution for the energy absorption characteristics of the innermost layer of the casing is completed.

[0120] Step 5.6: Solve for the energy absorption characteristics of the l-th layer of the casing;

[0121] Treat the existing casing as the structure after removing the innermost layer, the initial layer number = initial layer number + 1, repeat steps 5.1-5.5 to obtain the energy absorption characteristics of the innermost layer of the existing casing. The innermost layer of the existing casing is the lth layer of the original casing.

[0122] Step 5.7: Repeat step 5.6 until the projectile impact velocity, impact time and energy absorption characteristics of the casing structure of all layers of the original casing are obtained.

[0123] Furthermore, in the method for calculating the high-speed impact characteristics of the composite cylindrical shell casing with a negative Poisson's ratio honeycomb core, in step 7, if the initial step size does not meet the accuracy requirements, the initial step size is reduced so that the initial step size = initial step size / 2, the initial displacement is reset so that the initial displacement = initial displacement - initial step size, and steps 5.2-5.7 are repeated.

[0124] The beneficial effects of this invention are as follows: After establishing a displacement field suitable for a cylindrical shell casing structure of medium thickness, the material parameters are corrected to account for strain rate effects, and the core layer is equivalent to an anisotropic monolayer material. Then, based on Hertz's contact law, progressive damage theory, and the law of conservation of energy, the residual velocity, ballistic limit, and damage area of ​​the inner and outer skins in high-speed impact are solved. This method is simple to calculate and highly accurate, applicable to high-speed impact conditions, and has high engineering application value. Attached Figure Description

[0125] Figure 1 Flowchart for solving high-speed impact parameters of a composite cylindrical shell casing with a negative Poisson's ratio honeycomb core;

[0126] Figure 2 A schematic diagram of a composite cylindrical casing with a negative Poisson's ratio honeycomb core;

[0127] Figure 3 A schematic diagram of a cell in a negative Poisson's ratio honeycomb core;

[0128] Figure 4 A photograph of a composite cylindrical shell casing specimen with a negative Poisson's ratio honeycomb core;

[0129] Figure 5 Photographs of a bullet flying at initial impact velocities of 140.1, 147.3, and 162.0 m / s for a composite cylindrical shell casing specimen with a negative Poisson's ratio honeycomb core;

[0130] Figure 6 Damage photographs of a composite cylindrical shell casing specimen with a negative Poisson's ratio honeycomb core at initial impact velocities of 140.1, 147.3, and 162.0 m / s;

[0131] Figure 7 The figure shows a comparison between the solved high-speed impact parameters of the specimen and the experimental results. Detailed Implementation

[0132] A method for calculating the high-speed impact characteristics of a composite cylindrical casing with a negative Poisson's ratio honeycomb core includes the following steps:

[0133] Step 1: Obtain the structural parameters, material parameters, and initial iteration parameters of the composite cylindrical shell casing and projectile with negative Poisson's ratio honeycomb core;

[0134] Step 1.1: Define a global coordinate system o-xθz on the composite cylindrical shell casing, located on the mid-surface of the structure; define local coordinate systems D1, D2, and D3 on the fiber / resin composite skin, representing the three principal material axes of the fiber / resin composite skin, θ... F The angle between direction D1 and the x-axis;

[0135] Step 1.2: Obtain the structural and material parameters, including the total length L, total thickness h, mid-surface radius R, and fiber / resin composite skin thickness h of the cylindrical shell. F negative Poisson ratio honeycomb core thickness h C Projectile radius R I Initial impact velocity V, hypotenuse length l of negative Poisson's ratio honeycomb core cell. a Horizontal side length l b The thickness of the horizontal edge l t Inclination angle Φ;

[0136] Step 1.3: Obtain the initial parameters for iteration, including the initial number of layers l, the initial displacement setting w0, the initial step size setting e, the initial accuracy c, and the initial strain rate ε. l Initial strain rate accuracy c e Initial velocity V0;

[0137] Step 2: Based on the above structural and material parameters, establish an analytical dynamic model of the composite cylindrical shell casing;

[0138] Step 2.1: Propose a modulus correction formula that considers the effect of strain rate:

[0139]

[0140]

[0141] in, The modulus of elasticity of fiber / resin composite skin in the corrected D2 direction (i.e., perpendicular to the fiber direction); The shear modulus of the corrected D1D2 planar fiber / resin composite skin; and E represents the modulus under the corresponding quasi-static conditions. C and G C E represents the elastic modulus and shear modulus of a negative Poisson's ratio honeycomb core. Q and G Q Core modulus under quasi-static conditions; For strain rate; A D2 A D1D2 A E B E C E D E A G B G C G and D G P represents the fitting coefficient; D2 and P D1D2 To fit a polynomial;

[0142] Step 2.2: Determine the constitutive relation of the composite cylindrical shell casing;

[0143] Based on Reddy's higher-order shear deformation theory, the displacement field at any point in the composite cylindrical shell casing structure is constructed. Then, according to the Love-Kirchhoff assumption and considering Novozhilov nonlinearity, the strain at any point in the composite cylindrical shell casing is defined as:

[0144]

[0145]

[0146] Where u0, v0, and w0 are the displacements of the mid-surface of the structure in the x, θ, and z directions;

[0147] According to the generalized Hooke's law, the stress (σ) of the composite cylindrical shell casing in the local coordinate systemi′ , τ j′ )-Strain (ε i′ γ j′ The relation (i′=D1,D2,D3,j′=D2D3,D1D3,D1D2) is determined as follows:

[0148]

[0149]

[0150]

[0151]

[0152]

[0153] Wherein, S and C represent fiber / resin composite skin and negative Poisson's ratio honeycomb core, respectively; and These represent Young's modulus, shear modulus, and Poisson's ratio in the corresponding direction or plane, respectively; based on the improved Gibson theory, the equivalent modulus and Poisson's ratio of the negative Poisson's ratio honeycomb core are determined:

[0154]

[0155]

[0156]

[0157]

[0158] Where a0 and b0 are structural coefficients:

[0159]

[0160] Step 2.3: Determine the residual stress distribution relationship of the composite cylindrical shell casing;

[0161] The transformation stiffness matrix of the composite cylindrical shell casing in the global coordinate system is expressed as:

[0162]

[0163]

[0164] The expression for the total off-axis stress of the composite cylindrical shell casing in the l-th layer of the global coordinate system is:

[0165]

[0166] in, The off-axis stress of the l-th layer is considered to account for the failure stress distribution; h (l) It is the thickness of the l-th layer; K represents the total off-axis stress component of the (l-1)th layer; mn The equivalent stiffness of the structure is expressed as:

[0167]

[0168]

[0169] in, and The equivalent modulus and Poisson's ratio of the structure are expressed as follows:

[0170]

[0171]

[0172]

[0173]

[0174] in, This is the tensile stiffness coefficient; coefficient

[0175] Step 3: Apply different failure criteria to the fiber / resin composite skin and negative Poisson's ratio honeycomb core of the casing;

[0176] The fiber / resin composite skin uses the Hashin three-dimensional composite material failure criterion as the criterion for damage initiation:

[0177] Fiber tensile failure σ D1 ≥0:

[0178]

[0179] Fiber compression failure σ D1 <0:

[0180]

[0181] Matrix tensile failure σ D2 +σ D3 ≥0:

[0182]

[0183] Matrix compressive failure σ D2 +σ D3 <0:

[0184]

[0185] in, and It refers to the tensile strength in the D1 and D2 directions. and The compressive strengths are in the D1 and D2 directions. Shear strength in three different planes;

[0186] For the negative Poisson's ratio honeycomb core, the compression-shear coupling failure criterion is selected:

[0187]

[0188] in, and For the corresponding compressive strength and shear strength;

[0189] Step 4: Based on the analytical dynamic model, solve for the impact velocity, impact time, and energy absorption characteristics after the failure of the l-th layer of the casing;

[0190] Step 4.1: Solve for the displacement and rotation components;

[0191] The displacement and rotation components of the composite cylindrical shell casing in the global coordinate system are defined as follows:

[0192]

[0193] in, These are the displacement and rotational components, M' and N' are the maximum cutoff coefficients, m' represents the number of polynomial terms, and n' corresponds to the circumferential wavenumber. The unknown eigenvector to be solved, q m' (t) is a generalized coordinate. Let m' be the m-th orthogonal polynomial obtained on the interval [0,1] through the Gram-Schmidt process.

[0194] The displacement equation and governing equation of the composite cylindrical shell casing at the impact center can be defined as follows:

[0195] w0(x0,θ0)=w0(x0+R con ,θ0)=w0(x0,θ0+L con ) = w max ,

[0196] φ D1 (x0,θ0)=φ D1 (x0+R con ,θ0)=φ D1 (x0,θ0+L con ) = 0,

[0197] φ D2 (x0,θ0)=φD2 (x0+R con ,θ0)=φ D2 (x0,θ0+L con ) = 0,

[0198] N x =0,

[0199] Among them, w max R is the maximum displacement of the structure at the impact center of the projectile. con L represents the relatively small radius of the contact area. con The arc length of the contact area;

[0200] Based on the principle of virtual work, the governing differential equations are derived by substituting the expressions for generalized internal forces and torques. Based on the kinetic energy theorem, the formula for external force work, and the formula for strain energy, the impact contact force corresponding to the high-speed impact of the projectile on the casing is expressed as:

[0201]

[0202] Among them, U A U D U E U F U H These are the strain energies caused by different deformation modes of the structure, and their expressions are:

[0203]

[0204]

[0205]

[0206]

[0207]

[0208] Among them, D mn E mn ,F mn H mn The corresponding stiffness coefficient is expressed as follows:

[0209]

[0210] The unknown eigenvectors can be obtained by solving the above equations. and displacement and rotational components u0, v0, w0, φ D1 φ D2 ;

[0211] Step 4.2: Determine the impact velocity and corresponding impact time of the projectile after it breaks through the lth layer of the receiver;

[0212] Then, the impact velocity of the projectile after breaking through the l-th layer of the structure is expressed as:

[0213]

[0214] in, The strain energy consumed when the lth layer fails. Energy consumed for layer l damage, T f l The energy consumed for tensile fracture of the l-th layer is expressed as:

[0215]

[0216] in, G II For type II interlayer energy release rate, σ IL e represents the interlaminar shear strength. up This represents the energy density of the innermost layer of the casing structure.

[0217] Finally, the impact time corresponding to the projectile breaking through the l-th layer of structure is expressed as:

[0218]

[0219] Step 4.3: Solve for the energy absorption characteristics of the receiver after the projectile breaks through the first layer of the receiver;

[0220] The energy absorbed by the receiver after the projectile penetrates the first layer of the receiver is:

[0221]

[0222] The specific energy absorbed by the receiver after the projectile penetrates the first layer of the receiver is:

[0223]

[0224] Where, m s The total mass of the casing;

[0225] Step 5: Iteratively calculate and solve the analytical dynamics model to obtain the remaining velocity and impact time of the projectile after the entire casing is penetrated;

[0226] Step 5.1: Calculate the total off-axis stress;

[0227] Substitute the initial displacement of the projectile into the displacement equation and control equation of the casing at the impact center in step 4.1 to solve for the displacement component w0; substitute the displacement component and material parameters into steps 2.2-2.3 to obtain the total off-axis stress.

[0228] Step 5.2: Apply failure criteria to determine whether the innermost layer material of the casing has failed;

[0229] Use the failure criteria in step 3 to determine whether the innermost material of the casing has failed under the total off-axis stress in step 5.1; if it has failed, proceed to step 5.3.

[0230] Step 5.3: Determine whether the initial step size meets the accuracy requirements;

[0231] Determine if the initial step size is less than the initial step size precision; if it is less, proceed to step 5.4.

[0232] Step 5.4: Determine whether the strain rate meets the requirements for accurate calculation in high-speed impact problems;

[0233] Determine if the ratio of strain rate to initial strain rate is less than the initial strain rate accuracy; if it is less, proceed to step 5.5.

[0234] Step 5.5: Output the projectile's impact velocity, impact time, and energy absorption characteristics of the innermost layer of the casing after the innermost layer of the output casing is damaged;

[0235] Substitute the initial high-speed impact velocity and displacement component w0 of the projectile given in step 1.3 into step 4.2 to obtain the impact velocity and corresponding impact time of the projectile after the innermost layer of the casing is damaged. Further solve for the energy absorption and specific energy absorption of the casing as described in step 4.3; at this point, the solution for the energy absorption characteristics of the innermost layer of the casing is completed.

[0236] Step 5.6: Solve for the energy absorption characteristics of the l-th layer of the casing;

[0237] Treat the existing casing as the structure after removing the innermost layer, the initial layer number = initial layer number + 1, repeat steps 5.1-5.5 to obtain the energy absorption characteristics of the innermost layer of the existing casing. The innermost layer of the existing casing is the lth layer of the original casing.

[0238] Step 5.7: Repeat step 5.6 until the projectile impact velocity, impact time and energy absorption characteristics of the casing structure of all layers of the original casing are obtained;

[0239] Step 6: If the failure condition is not met, increase the initial displacement so that the initial displacement = initial displacement + initial step size, and repeat step 5.

[0240] Step 7: If the initial step size does not meet the accuracy requirements, reduce the initial step size so that the initial step size = initial step size / 2, reset the initial displacement so that the initial displacement = initial displacement - initial step size, and repeat steps 5.2-5.7.

[0241] Step 8: If the strain rate does not meet the accurate calculation requirements of high-speed impact, then the material parameters of the composite cylindrical shell casing are corrected according to Step 2, and Step 5 is repeated.

[0242] Example

[0243] like Figure 2 As shown, the composite cylindrical shell casing with a negative Poisson's ratio honeycomb core includes a fiber / resin composite skin 1 and a negative Poisson's ratio honeycomb core layer 2, and the projectile 3 is a spherical cylinder. A physical image of the composite cylindrical shell casing specimen with a negative Poisson's ratio honeycomb core is shown below. Figure 4 The diagram illustrates the implementation of high-speed impact tests and the calculation method for the high-speed impact characteristics of the casing. The specimens were subjected to high-speed impacts with initial velocities of 140.1, 147.3, and 162.0 m / s, respectively. The material parameters of the specimens are shown in Table 1, and the structural dimensions are: L = 130 mm, h = 16 mm, R = 70 mm, l a =5.5mm, l b =10.5mm, l t =1mm, φ=-30°, h C =12.5mm, θ F = [0 / +45 / 90 / -45 / 0]° and R I =19.6mm.

[0244] Table 1 Specimen Material Parameters

[0245]

[0246] High-speed impact test results Figure 5-6 Based on the experimental results shown, the analytical process for solving the overall penetration impact characteristics of the casing described in step 4 is carried out, and the comparison results between the solution and the experiment are as follows. Figure 7 As shown, the maximum error of the ballistic limit is -2.56%, and the minimum error of the residual velocity is 2.91%. The solution results agree well with the experimental results.

Claims

1. A method for calculating the high-speed impact characteristics of a composite cylindrical shell casing with a negative Poisson's ratio honeycomb core, characterized in that, Includes the following steps: Step 1: Obtain the structural parameters, material parameters, and initial iteration parameters of the composite cylindrical shell casing and projectile with negative Poisson's ratio honeycomb core; Step 2: Based on the above structural and material parameters, establish an analytical dynamic model of the composite cylindrical shell casing; Step 3: Apply different failure criteria to the fiber / resin composite skin and negative Poisson's ratio honeycomb core of the casing; Step 4: Based on the analytical dynamic model, solve for the impact velocity, impact time, and energy absorption characteristics after the failure of the lth layer of the casing; Step 5: Iteratively calculate and solve the analytical dynamics model to obtain the remaining velocity and impact time of the projectile after the entire casing is penetrated; Step 6: If the failure condition is not met, increase the initial displacement so that the initial displacement = initial displacement + initial step size, and repeat step 5. Step 7: If the initial step size does not meet the accuracy requirements, reduce the initial step size so that the initial step size = initial step size / 2, reset the initial displacement so that the initial displacement = initial displacement - initial step size, and repeat step 5. Step 8: If the strain rate does not meet the accurate calculation requirements of high-speed impact, then the material parameters of the composite cylindrical shell casing are corrected according to Step 2, and Step 5 is repeated.

2. The method for calculating the high-speed impact characteristics of a composite cylindrical casing with a negative Poisson's ratio honeycomb core according to claim 1, characterized in that, Step 1 includes the following process: Step 1.1: define a global coordinate system o-xθz on the composite cylindrical shell case, located on the mid-plane of the structure; define a local coordinate system D1, D2, D3 on the fiber / resin composite skin, which are the three material principal axis directions of the fiber / resin composite skin respectively, θ F is the included angle between D1 direction and x axis; Step 1.2: Obtain the structural parameters and material parameters, including the total length L of the cylindrical shell, the total thickness h, the middle surface radius R, the thickness h of the fiber / resin composite skin F , the thickness h of the negative Poisson's ratio honeycomb core C , the projectile radius R I , the initial impact velocity V, the length l of the hypotenuse of the negative Poisson's ratio honeycomb core cell a , the length l of the horizontal side b , the thickness l of the horizontal side t , the inclination angle Φ; Step 1.3: Obtain the initial parameters for iteration, including the initial number of layers l, the initial displacement setting w0, the initial step size setting e, the initial accuracy c, and the initial strain rate ε. l Initial strain rate accuracy c e The initial velocity is V0.

3. The method for calculating the high-speed impact characteristics of a composite cylindrical casing with a negative Poisson's ratio honeycomb core according to claim 2, characterized in that, Step 2 includes the following process: Step 2.1: Propose a modulus correction formula that considers the effect of strain rate: in, The modulus of elasticity of fiber / resin composite skin in the corrected D2 direction (i.e., perpendicular to the fiber direction); The shear modulus of the corrected D1D2 planar fiber / resin composite skin; and E represents the modulus under the corresponding quasi-static conditions. C and G C E represents the elastic modulus and shear modulus of a negative Poisson's ratio honeycomb core. Q and G Q Core modulus under quasi-static conditions; For strain rate; A D2 A D1D2 A E B E C E D E A G B G C G and D G P represents the fitting coefficient; D2 and P D1D2 To fit a polynomial; Step 2.2: Determine the constitutive relation of the composite cylindrical shell casing; Based on Reddy's higher-order shear deformation theory, the displacement field at any point in the composite cylindrical shell casing structure is constructed. Then, according to the Love-Kirchhoff assumption and considering Novozhilov nonlinearity, the strain at any point in the composite cylindrical shell casing is defined as: Where u0, v0, and w0 are the displacements of the mid-surface of the structure in the x, θ, and z directions; According to the generalized Hooke's law, the stress (σ) of the composite cylindrical shell casing in the local coordinate system i′ , τ j′ )-Strain (ε i′ γ j′ The relation (i′=D1,D2,D3,j′=D2D3,D1D3,D1D2) is determined as follows: Wherein, S and C represent fiber / resin composite skin and negative Poisson's ratio honeycomb core, respectively; and These represent Young's modulus, shear modulus, and Poisson's ratio in the corresponding direction or plane, respectively; based on the improved Gibson theory, the equivalent modulus and Poisson's ratio of the negative Poisson's ratio honeycomb core are determined: Where a0 and b0 are structural coefficients: Step 2.3: Determine the residual stress distribution relationship of the composite cylindrical shell casing; The transformation stiffness matrix of the composite cylindrical shell casing in the global coordinate system is expressed as: The expression for the total off-axis stress of the composite cylindrical shell casing in the l-th layer of the global coordinate system is: in, The off-axis stress of the l-th layer is considered to account for the failure stress distribution; h (l) It is the thickness of the l-th layer; K represents the total off-axis stress component of the (l-1)th layer; mn The equivalent stiffness of the structure is expressed as: in, and The equivalent modulus and Poisson's ratio of the structure are expressed as follows: in, This is the tensile stiffness coefficient; coefficient 4. The method for calculating the high-speed impact characteristics of a composite cylindrical shell casing with a negative Poisson's ratio honeycomb core according to claim 3, characterized in that, Step 3 The process includes the following: The fiber / resin composite skin uses the Hashin three-dimensional composite material failure criterion as the criterion for damage initiation: Fiber tensile failure σ D1 ≥0: Fiber compression failure σ D1 <0: Matrix tensile failure σ D2 +σ D3 ≥0: Matrix compressive failure σ D2 +σ D3 <0: in, and It refers to the tensile strength in the D1 and D2 directions. and The compressive strengths are in the D1 and D2 directions. Shear strength in three different planes; For the negative Poisson's ratio honeycomb core, the compression-shear coupling failure criterion is selected: in, and These represent the corresponding compressive strength and shear strength.

5. The method for calculating the high-speed impact characteristics of a composite cylindrical casing with a negative Poisson's ratio honeycomb core according to claim 4, characterized in that, Step 4 includes the following process: Step 4.1: Solve for the displacement and rotation components; The displacement and rotation components of the composite cylindrical shell casing in the global coordinate system are defined as follows: in, These are the displacement and rotational components, M' and N' are the maximum cutoff coefficients, m' represents the number of polynomial terms, and n' corresponds to the circumferential wavenumber. The unknown eigenvector to be solved, q m' (t) is a generalized coordinate. Let m' be the m-th orthogonal polynomial obtained on the interval [0,1] through the Gram-Schmidt process. The displacement equation and governing equation of the composite cylindrical shell casing at the impact center can be defined as follows: w0(x0,θ0)=w0(x0+R con ,θ0)=w0(x0,θ0+L con )=w max , f D1 (x0,θ0)=φ D1 (x0+R con ,θ0)=φ D1 (x0,θ0+L con )=0, f D2 (x0,θ0)=φ D2 (x0+R con ,θ0)=φ D2 (x0,θ0+L con )=0, N x ＝0, Among them, w max R is the maximum displacement of the structure at the impact center of the projectile. con L represents the relatively small radius of the contact area. con The arc length of the contact area; Based on the principle of virtual work, the governing differential equations are derived by substituting the expressions for generalized internal forces and torques. Based on the kinetic energy theorem, the formula for external force work, and the formula for strain energy, the impact contact force corresponding to the high-speed impact of the projectile on the casing is expressed as: Among them, U A U D U E U F U H These are the strain energies caused by different deformation modes of the structure, and their expressions are: Among them, D mn E mn ,F mn H mn The corresponding stiffness coefficient is expressed as follows: The unknown eigenvectors can be obtained by solving the above equations. and displacement and rotational components u0, v0, w0, φ D1 φ D2 ; Step 4.2: Determine the impact velocity and corresponding impact time of the projectile after it breaks through the lth layer of the casing; Then, the impact velocity of the projectile after breaking through the l-th layer of the structure is expressed as: in, The strain energy consumed when the lth layer fails. Energy consumed for layer 1 damage The energy consumed for tensile fracture of the l-th layer is expressed as: in, G II For type II interlayer energy release rate, σ IL e represents the interlaminar shear strength. up This represents the energy density of the innermost layer of the casing structure. Finally, the impact time corresponding to the projectile breaking through the l-th layer of structure is expressed as: Step 4.3: Solve for the energy absorption characteristics of the receiver after the projectile breaks through the first layer of the receiver; The energy absorbed by the receiver after the projectile penetrates the first layer of the receiver is: The specific energy absorbed by the receiver after the projectile penetrates the first layer of the receiver is: Where, m s This refers to the total mass of the casing.

6. The method for calculating the high-speed impact characteristics of a composite cylindrical casing with a negative Poisson's ratio honeycomb core according to claim 5, characterized in that, Step 5 includes the following process: Step 5.1: Calculate the total off-axis stress; Substitute the initial displacement of the projectile into the displacement equation and control equation of the casing at the impact center in step 4.1 to solve for the displacement component w0; substitute the displacement component and material parameters into steps 2.2-2.3 to obtain the total off-axis stress. Step 5.2: Apply failure criteria to determine whether the innermost layer material of the casing has failed; Use the failure criteria in step 3 to determine whether the innermost material of the casing has failed under the total off-axis stress in step 5.1; if it has failed, proceed to step 5.

3. Step 5.3: Determine whether the initial step size meets the accuracy requirements; Determine if the initial step size is less than the initial step size precision; If it is less than, then proceed to step 5.4; Step 5.4: Determine whether the strain rate meets the requirements for accurate calculation in high-speed impact problems; Determine if the ratio of strain rate to initial strain rate is less than the initial strain rate accuracy; if it is less, proceed to step 5.

5. Step 5.5: Output the projectile's impact velocity, impact time, and energy absorption characteristics of the innermost layer of the casing after the innermost layer of the output casing is damaged; Substitute the initial high-speed impact velocity and displacement component w0 of the projectile given in step 1.3 into step 4.2 to obtain the impact velocity and corresponding impact time of the projectile after the innermost layer of the casing is damaged. Further solve for the energy absorption and specific energy absorption of the casing as described in step 4.3; at this point, the solution for the energy absorption characteristics of the innermost layer of the casing is completed. Step 5.6: Solve for the energy absorption characteristics of the l-th layer of the casing; Treat the existing casing as the structure after removing the innermost layer, the initial layer number = initial layer number + 1, repeat steps 5.1-5.5 to obtain the energy absorption characteristics of the innermost layer of the existing casing. The innermost layer of the existing casing is the lth layer of the original casing. Step 5.7: Repeat step 5.6 until the projectile impact velocity, impact time and energy absorption characteristics of the casing structure of all layers of the original casing are obtained.

7. The method for calculating the high-speed impact characteristics of a composite cylindrical casing with a negative Poisson's ratio honeycomb core according to claim 6, characterized in that, In step 7, if the initial step size does not meet the accuracy requirements, the initial step size is reduced so that the initial step size = initial step size / 2, the initial displacement is reset so that the initial displacement = initial displacement - initial step size, and steps 5.2-5.7 are repeated.

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