Method for establishing nonlinear structural relationship of zero Poisson's ratio accordion honeycomb structure

Abstract

The present invention discloses a method for establishing a nonlinear structural relationship of a zero Poisson's ratio accordion honeycomb structure. First, for the representative cells of the periodic accordion honeycomb structure, a flexible beam model is used to perform elastic analysis and plastic analysis on the bending deformation of the inclined wall plate under large deformation conditions, and the equivalent projection and equivalent load of the inclined wall plate in the elastic stage and the plastic stage are obtained, and then the equivalent stress, equivalent strain, equivalent Poisson's ratio and equivalent Young's modulus of the periodic accordion honeycomb structure in the elastic stage and the plastic stage are calculated. In particular, the accordion honeycomb structure shows an obvious zero Poisson's ratio effect, and the finite element simulation proves the correctness and effectiveness of the present invention. Secondly, for the main structural parameters (angle, yield stress, length, thickness), the influence of each parameter on the nonlinear structural relationship of the accordion honeycomb structure is analyzed, and a method reflecting the nonlinear structural relationship of the same type of accordion honeycomb structure is established.

Description

Technical Field

[0001] The invention relates to the technical field of zero Poisson's ratio accordion honeycomb structures, in particular to a method for establishing a nonlinear structural relationship of a zero Poisson's ratio accordion honeycomb structure. Background Art

[0002] Poisson's ratio refers to the ratio of the absolute value of the transverse normal strain to the axial normal strain when the material is subjected to unidirectional tension or compression, also known as the transverse deformation coefficient. It is an elastic constant that reflects the transverse deformation of the material. Based on the transverse deformation effect of materials when stretched or compressed, materials can be classified into three categories: positive Poisson's ratio materials, negative Poisson's ratio materials, and zero Poisson's ratio materials. Most materials are positive Poisson's ratio materials, which show transverse contraction when stretched longitudinally and transverse expansion when compressed longitudinally; negative Poisson's ratio materials show transverse expansion when stretched longitudinally and transverse contraction when compressed longitudinally; zero Poisson's ratio materials show that the transverse direction remains constant when stretched or compressed longitudinally. The accordion honeycomb structure not only has many advantages of the traditional honeycomb structure, but also has a positive Poisson's ratio deformation characteristic that is different from the traditional structure, reflecting the zero Poisson's ratio effect. Therefore, it has both the characteristics of the honeycomb structure and the deformation characteristics of the zero Poisson's ratio material, which has attracted widespread attention from the academic community and has become a hot topic in current research. Dong Wenjun et al. analyzed and used the classical Euler beam theory to study the calculation method of the equivalent modulus and equivalent Poisson's ratio of the accordion honeycomb material, and obtained two orthogonal equivalent moduli in the plane and the analytical expression of the Poisson's ratio, verifying that the honeycomb material has the property of zero Poisson's ratio; Liu Weidong et al. comprehensively considered the internal force bending moment, axial force and shear force of the accordion honeycomb structure, and derived and verified the analytical formulas of its equivalent elastic modulus, equivalent shear modulus and equivalent shear modulus. The above research mainly focuses on the force analysis of the accordion honeycomb structure in the linear deformation stage, but the plane stiffness and strength of the honeycomb structure are generally low. However, when the stress is large, the structure is prone to nonlinear deformation, which will make the linear analysis method inapplicable. Therefore, it is not enough to perform linear analysis on the accordion honeycomb structure, and nonlinear analysis is also required. Although some scholars have studied the in-plane mechanical properties of accordions, no scholar has studied the nonlinear structural relationship of accordion honeycomb structures. Therefore, the present invention proposes a method, system and device for establishing the nonlinear structural relationship of zero Poisson's ratio accordion honeycomb structures for accordion honeycomb structures. First, a corresponding set of nonlinear algebraic equations is established based on deformation harmonic conditions and equilibrium conditions. Secondly, the sum-difference-product formula, the first kind of complete elliptic integral and the first kind of incomplete elliptic integral are used to solve the wall panels of the accordion honeycomb structure. Finally, the main structural parameters (length, width, depth, angle) are analyzed to analyze the influence of each parameter on the nonlinear structural relationship of the accordion honeycomb structure, and a method for establishing the nonlinear structural relationship that reflects the mechanical properties of the same type of accordion honeycomb structure is proposed. Finally, a system and at least one device are provided through the method for establishing the nonlinear structural relationship of the zero Poisson's ratio accordion honeycomb structure.

[0003] The nonlinear structural relationship of the existing accordion honeycomb structure is mostly processed using the finite element method, which has low calculation accuracy, higher cost and lower efficiency. Summary of the invention

[0004] 1. Technical issues to be resolved

[0005] In view of the deficiencies in the prior art, the present invention provides a method for establishing nonlinear structural relationships of a zero Poisson's ratio accordion honeycomb structure, which has the advantages of higher calculation accuracy and wider application range, and solves the problem of higher cost and lower efficiency.

[0006] (II) Technical solution

[0007] In order to achieve the above-mentioned purpose of higher cost and lower efficiency, the present invention provides the following technical solution: a method for establishing a nonlinear structural relationship of a zero Poisson's ratio accordion honeycomb structure, comprising the following steps:

[0008] S1. Data Analysis

[0009] The horizontal direction is defined as the X direction, and the vertical direction is defined as the Y direction. For the periodic accordion honeycomb structure subjected to horizontal force, the representative cell is intercepted to determine the stress stage (including the compression stage and the tension stage) of the cell. For the representative cell subjected to horizontal force, the deformation stage (including the elastic deformation stage and the plastic deformation stage) of the inclined wall plate is determined and deformation analysis of the corresponding stage is performed.

[0010] S2. Data Projection

[0011] Based on the results of deformation analysis, the equivalent projection and equivalent load of the inclined wall panel are obtained.

[0012] S3. Structural Relationship

[0013] According to the equivalent displacement and equivalent load of the inclined wall plate, the equivalent stress, equivalent strain, equivalent Poisson's ratio and equivalent Young's modulus of the periodic accordion honeycomb structure are obtained, and the nonlinear structural relationship of the accordion honeycomb structure is established.

[0014] like Figure 3 As shown, it represents that the cell is under compression. The inclined wall plate OA is taken as the analysis object. Assuming that the inclined wall plate is in the elastic deformation stage, its force is as follows: Figure 4 As shown, it can be regarded as a slender flexible beam model, in which the O end is fixed and the A end is limited in rotation. Due to the antisymmetry of the deformation of the inclined wall plate OA after being loaded, the half-inclined wall plate OB can be taken for analysis. The deflection curve equation and axial force deformation differential equation of the half-inclined wall plate OB are:

[0015]

[0016]

[0017] make can be transformed into:

[0018]

[0019] △(ds)=-Fcosψds / (E s A)

[0020] Introducing dimensionless force ζ and dimensionless arc length S, using boundary condition M B =0, simplify the deflection curve equation to a dimensionless equation:

[0021]

[0022] in, F cr =π 2 E s I / l 2 ,S=s / l(0≤S≤0.5), β is the rotation angle of point B at the midpoint of the inclined wall panel.

[0023] make Then the dimensionless force ζ can be transformed into the elliptic integral form:

[0024]

[0025] in is the η at point O, i.e. when α = 0 1 value.

[0026] Bending moment at point O M 1 and the ultimate bending moment M max The limit is:

[0027]

[0028]

[0029] A: If M 1 <M max , then the inclined wall plate is in the elastic deformation stage

[0030] The equivalent projection of the inclined wall plate OA is twice that of the half inclined wall plate OB, so the equivalent displacement of the inclined wall plate is and for:

[0031]

[0032]

[0033] Combined formula, decoupling can get the equivalent load F of the cell:

[0034]

[0035] Compressive stress σ of accordion honeycomb structure x for:

[0036]

[0037] In the case of uniaxial force in the X direction, the deformation is mainly borne by the inclined wall plate, and the deformation of the vertical wall plate is too small to be ignored. The deformation in the x direction is twice that of the inclined wall plate OA. Therefore, the deformation in the X direction of the accordion honeycomb structure in the compressive elastic deformation stage is △ x and Y direction deformation △ y for:

[0038]

[0039] △ y =0

[0040] The accordion honeycomb structure is in the stage of elastic deformation under compression, and the strain in the x direction is ε x and the y-direction strain ε y for:

[0041]

[0042] ε y =0

[0043] Equivalent Poisson's ratio v of accordion honeycomb structure under compression and elastic deformation xy and the equivalent Young's modulus E x for:

[0044]

[0045]

[0046] B: If M 1 ≥M max , then the inclined wall plate is in the plastic deformation stage, let M 2 =M max , the bending moment M at point O of the inclined wall 2 Determine the unique plasticity ratio.

[0047] The deflection curve equation of the semi-oblique wall panel OB is:

[0048]

[0049] in θ 0 It is the plastic angle existing in the plastic deformation stage.

[0050] make The formula can be transformed into:

[0051]

[0052] The analysis process is similar to the elastic stage. The bending moment M at point O of the inclined wall is 2 , equivalent displacement for:

[0053]

[0054]

[0055]

[0056] in,

[0057] The equivalent load F on the cell of the inclined wall plate in the plastic deformation stage, the compressive stress σ on the accordion honeycomb structure x , X-direction deformation △ x and Y direction deformation △ y for:

[0058]

[0059]

[0060]

[0061] △ y =0

[0062] The plastic deformation of the accordion honeycomb structure belongs to nonlinear large deformation, so the nonlinear Green strain calculation formula is used for strain calculation. The nonlinear Green strain ε in the x direction is x and the y-direction strain ε y for:

[0063]

[0064] ε y =0

[0065] Equivalent Poisson's ratio v of accordion honeycomb structure under compression and elastic deformation xy and the equivalent Young's modulus E x for:

[0066]

[0067]

[0068] Cell tension stage

[0069] like Figure 7 As shown, the accordion honeycomb structure is under tension. Assuming that the inclined wall panel is in the elastic deformation stage, the deflection curve equation of the semi-inclined wall panel OB is:

[0070]

[0071]

[0072] make The formula can be transformed into:

[0073]

[0074] △(ds)=Fcosψ 3 ds / (E s A)

[0075] The analysis process is similar to the compressive elastic stage. The bending moment M at point O of the inclined wall is 3 for:

[0076]

[0077] in,

[0078] C: If M 3 <M max , then the inclined wall plate is in the elastic deformation stage

[0079] Equivalent displacement of inclined wall Equivalent load F, compressive stress σ of accordion honeycomb structure x , X-direction deformation △ x and Y direction deformation △ y For: For:

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] △ y =0

[0086] The strain ε in the x direction of the accordion honeycomb structure in the tensile elastic stage x , y-direction strain ε y , equivalent Poisson's ratio v xy and the equivalent Young's modulus E x for:

[0087]

[0088] ε y =0

[0089]

[0090]

[0091] D: If M 3 ≥M max , then the inclined wall plate is in the plastic deformation stage, let M 4 =M max , the bending moment M at point O of the inclined wall 2 Determine the unique plasticity ratio.

[0092] The deflection curve equation of the semi-oblique wall panel OB is:

[0093]

[0094] in

[0095] make Then formula (61) can be transformed into:

[0096]

[0097] The analysis process is similar to the elastic stage. The bending moment M at point O of the inclined wall is 4 , equivalent displacement for:

[0098]

[0099]

[0100]

[0101] in,

[0102] The equivalent load F on the cell of the inclined wall plate in the plastic deformation stage, the compressive stress σ on the accordion honeycomb structure x , X-direction deformation △ x and Y direction deformation △ y for:

[0103]

[0104]

[0105]

[0106] △ y =0

[0107] The plastic deformation of the accordion honeycomb structure belongs to nonlinear large deformation, so the nonlinear Green strain calculation formula is used for strain calculation. The nonlinear Green strain ε in the x direction is x , y-direction strain ε y , equivalent Poisson's ratio v in the compression plastic deformation stage xy and the equivalent Young's modulus E x for:

[0108]

[0109] ε y =0

[0110]

[0111]

[0112] The cell stress stage and the oblique wall plate deformation stage are divided into four modules:

[0113] A: Equivalent projection of the inclined wall plate during the cell compression stage and the elastic deformation stage and Accordion honeycomb structure equivalent Poisson's ratio v xy and the equivalent Young's modulus E x for:

[0114]

[0115] B: Equivalent projection of the inclined wall plate during the cell compression stage and the plastic deformation stage and Accordion honeycomb structure equivalent Poisson's ratio v xy and the equivalent Young's modulus E x for::

[0116]

[0117] C: Equivalent projection of the inclined wall plate in the stage of elastic deformation of the inclined wall plate during the cell tension stage and Accordion honeycomb structure equivalent Poisson's ratio v xy and the equivalent Young's modulus E x for:

[0118]

[0119] D: Equivalent projection of the inclined wall plate in the plastic deformation stage of the cell tension stage and Accordion honeycomb structure equivalent Poisson's ratio v xy and the equivalent Young's modulus E x for:

[0120]

[0121] Preferably, the accordion honeycomb structure exhibits obvious nonlinear characteristics and obvious zero Poisson's ratio effect when subjected to force in the X direction.

[0122] Preferably, the elastic-plastic theoretical analysis model of the accordion honeycomb structure is compared and analyzed with a related finite element model, which proves the effectiveness of the present invention.

[0123] Preferably, the verified theoretical analysis model is subjected to parameter analysis to study the influence of structural parameters on the nonlinear mechanical properties of the accordion honeycomb structure. The structural parameters include the wall panel angle Material yield strength σ s , the length of the inclined wall l, the width of the cell wall t, and a method to reflect the nonlinear structural relationship of the same type of accordion honeycomb structure is established.

[0124] Preferably, the method for establishing the nonlinear structural relationship of the zero Poisson's ratio accordion honeycomb structure provides a system, a computer system, and the system includes a program. When the program is executed by a processor, the method for establishing the nonlinear structural relationship of the zero Poisson's ratio accordion honeycomb structure is implemented.

[0125] Preferably, the method for establishing the nonlinear structural relationship of the zero Poisson's ratio accordion honeycomb structure provides at least one device, and the device includes a compressive elastic force analysis module, a compressive plastic force analysis module, a tensile elastic force analysis module, and a tensile plastic force analysis module.

[0126] (III) Beneficial effects

[0127] Compared with the prior art, the present invention provides a method for establishing a nonlinear structural relationship of a zero Poisson's ratio accordion honeycomb structure, which has the following beneficial effects:

[0128] 1. The method for establishing the nonlinear structural relationship of the zero Poisson's ratio accordion honeycomb structure obtains the nonlinear structural relationship of the accordion honeycomb structure by decoupling a series of equations, and fully considers the elastic-plastic deformation of the material in the analysis process. Compared with the finite element method, it has higher calculation accuracy and wider application range; compared with the experimental method, it is less expensive and more efficient. Enterprises with special requirements for materials or structures can quickly and accurately analyze the mechanical properties of the required accordion honeycomb structure through the method of the present invention, shorten the product design cycle and reduce the product design cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0129] Figure 1 It is a three-dimensional diagram of the accordion honeycomb structure of the present invention;

[0130] Figure 2It is a schematic diagram of representative cell sizes of the accordion honeycomb structure;

[0131] Figure 3 This is an analysis diagram of the accordion honeycomb structure under compression;

[0132] Figure 4 It is an analytical diagram of the accordion honeycomb structure representing the compression of the cell;

[0133] Figure 5 This is the analysis diagram of the elastic deformation of the inclined wall plate under compression;

[0134] Figure 6 It is the analysis diagram of the plastic deformation of the inclined wall plate under compression;

[0135] Figure 7 This is an analytical diagram of the accordion honeycomb structure under tension;

[0136] Figure 8 It is an analytical diagram of the accordion honeycomb structure representing the tension of the cell;

[0137] Fig. 9 This is the analysis diagram of the elastic deformation of the inclined wall plate under tension;

[0138] Fig.10 It is the analysis diagram of the plastic deformation of the inclined wall plate under tension;

[0139] Fig.11 is the structural rotation angle β and the x-direction strain ε in the specific embodiment of the present invention x Schematic representation of the results in the finite element model, elastic model, and plastic model;

[0140] Fig.12 At different angles Schematic diagram of the results of equivalent material parameters under ;

[0141] Fig.13 is the yield strength σ at different sizes s Schematic diagram of the results of equivalent material parameters under ;

[0142] Fig.14 It is a schematic diagram of the equivalent material parameters under different lengths of inclined wall panels l;

[0143] Fig.15 It is a schematic diagram of the equivalent material parameters under different wall thickness t. DETAILED DESCRIPTION

[0144] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0145] The method for establishing the nonlinear structural relationship of the zero Poisson's ratio accordion honeycomb structure comprises the following steps:

[0146] S1. Data Analysis

[0147] The horizontal direction is defined as the X direction, and the vertical direction is defined as the Y direction. For the periodic accordion honeycomb structure subjected to horizontal force, the representative cell is intercepted to determine the stress stage (including the compression stage and the tension stage) of the cell. For the representative cell subjected to horizontal force, the deformation stage (including the elastic deformation stage and the plastic deformation stage) of the inclined wall plate is determined and deformation analysis of the corresponding stage is performed.

[0148] S2. Data Projection

[0149] Based on the results of deformation analysis, the equivalent projection and equivalent load of the inclined wall panel are obtained.

[0150] S3. Structural Relationship

[0151] According to the equivalent displacement and equivalent load of the inclined wall plate, the equivalent stress, equivalent strain, equivalent Poisson's ratio and equivalent Young's modulus of the periodic accordion honeycomb structure are obtained, and the nonlinear structural relationship of the accordion honeycomb structure is established.

[0152] like Figure 3 As shown, it represents that the cell is under compression. The inclined wall plate OA is taken as the analysis object. Assuming that the inclined wall plate is in the elastic deformation stage, its force is as follows: Figure 4 As shown, it can be regarded as a slender flexible beam model, in which the O end is fixed and the A end is limited in rotation. Due to the antisymmetry of the deformation of the inclined wall plate OA after being loaded, the half-inclined wall plate OB can be taken for analysis. The deflection curve equation and axial force deformation differential equation of the half-inclined wall plate OB are:

[0153]

[0154]

[0155] make can be transformed into:

[0156]

[0157] △(ds)=-Fcosψds / (E s A)

[0158] Introducing dimensionless force ζ and dimensionless arc length S, using boundary condition M B =0, simplify the deflection curve equation to a dimensionless equation:

[0159]

[0160] in, F cr =π 2 E s I / l 2 ,S=s / l(0≤S≤0.5), β is the rotation angle of point B at the midpoint of the inclined wall panel.

[0161] make Then the dimensionless force ζ can be transformed into the elliptic integral form:

[0162]

[0163] in is the η at point O, i.e. when α = 0 1 value.

[0164] Bending moment at point O M 1 and the ultimate bending moment M max The limit is:

[0165]

[0166]

[0167] A: If M 1 <M max , then the inclined wall plate is in the elastic deformation stage

[0168] The equivalent projection of the inclined wall plate OA is twice that of the half inclined wall plate OB, so the equivalent displacement of the inclined wall plate is and for:

[0169]

[0170]

[0171] Combined formula, decoupling can get the equivalent load F of the cell:

[0172]

[0173] Compressive stress σ of accordion honeycomb structure x for:

[0174]

[0175] In the case of uniaxial force in the X direction, the deformation is mainly borne by the inclined wall plate, and the deformation of the vertical wall plate is too small to be ignored. The deformation in the x direction is twice that of the inclined wall plate OA. Therefore, the deformation in the X direction of the accordion honeycomb structure in the compressive elastic deformation stage is △ x and Y direction deformation △ y for:

[0176]

[0177] △ y =0

[0178] The accordion honeycomb structure is in the stage of elastic deformation under compression, and the strain in the x direction is ε x and the y-direction strain ε y for:

[0179]

[0180] ε y =0

[0181] Equivalent Poisson's ratio v of accordion honeycomb structure under compression and elastic deformation xy and the equivalent Young's modulus E x for:

[0182]

[0183]

[0184] B: If M 1 ≥M max , then the inclined wall plate is in the plastic deformation stage, let M 2 =M max , the bending moment M at point O of the inclined wall 2 Determine the unique plasticity ratio.

[0185] The deflection curve equation of the semi-oblique wall panel OB is:

[0186]

[0187] in θ 0 It is the plastic angle existing in the plastic deformation stage.

[0188] make The formula can be transformed into:

[0189]

[0190] The analysis process is similar to the elastic stage. The bending moment M at point O of the inclined wall is 2 , equivalent displacement for:

[0191]

[0192]

[0193]

[0194] in,

[0195] The equivalent load F on the cell of the inclined wall plate in the plastic deformation stage, the compressive stress σ on the accordion honeycomb structure x , X-direction deformation △ x and Y direction deformation △ y for:

[0196]

[0197]

[0198]

[0199] △ y =0

[0200] The plastic deformation of the accordion honeycomb structure belongs to nonlinear large deformation, so the nonlinear Green strain calculation formula is used for strain calculation. The nonlinear Green strain ε in the x direction is x and the y-direction strain ε y for:

[0201]

[0202] ε y =0

[0203] Equivalent Poisson's ratio v of accordion honeycomb structure under compression and elastic deformation xy and the equivalent Young's modulus E x for:

[0204]

[0205]

[0206] Cell tension stage

[0207] like Figure 7 As shown, the accordion honeycomb structure is under tension. Assuming that the inclined wall panel is in the elastic deformation stage, the deflection curve equation of the semi-inclined wall panel OB is:

[0208]

[0209]

[0210] make The formula can be transformed into:

[0211]

[0212] △(ds)=Fcosψ 3 ds / (E s A)

[0213] The analysis process is similar to the compressive elastic stage. The bending moment M at point O of the inclined wall is 3 for:

[0214]

[0215] in,

[0216] C: If M 3 <M max , then the inclined wall plate is in the elastic deformation stage

[0217] Equivalent displacement of inclined wall Equivalent load F, compressive stress σ of accordion honeycomb structure x , X-direction deformation △ x and Y direction deformation △ y For: For:

[0218]

[0219]

[0220]

[0221]

[0222]

[0223] △ y =0

[0224] The strain ε in the x direction of the accordion honeycomb structure in the tensile elastic stage x , y-direction strain ε y , equivalent Poisson's ratio v xy and the equivalent Young's modulus E x for:

[0225]

[0226] ε y =0

[0227]

[0228]

[0229] D: If M 3 ≥M max , then the inclined wall plate is in the plastic deformation stage, let M 4 =M max , the bending moment M at point O of the inclined wall 2 Determine the unique plasticity ratio.

[0230] The deflection curve equation of the semi-oblique wall panel OB is:

[0231]

[0232] in

[0233] make Then formula (61) can be transformed into:

[0234]

[0235] The analysis process is similar to the elastic stage. The bending moment M at point O of the inclined wall is 4 , equivalent displacement for:

[0236]

[0237]

[0238]

[0239] in,

[0240] The equivalent load F on the cell of the inclined wall plate in the plastic deformation stage, the compressive stress σ on the accordion honeycomb structure x , X-direction deformation △ x and Y direction deformation △ y for:

[0241]

[0242]

[0243]

[0244] △ y =0

[0245] The plastic deformation of the accordion honeycomb structure belongs to nonlinear large deformation, so the nonlinear Green strain calculation formula is used for strain calculation. The nonlinear Green strain ε in the x direction is x , y-direction strain ε y , Equivalent Poisson's ratio v in the compression plastic deformation stage xy and the equivalent Young's modulus E xfor:

[0246]

[0247] ε y =0

[0248]

[0249]

[0250] The cell stress stage and the oblique wall plate deformation stage are divided into four modules:

[0251] A: Equivalent projection of the inclined wall plate during the cell compression stage and the elastic deformation stage and Accordion honeycomb structure equivalent Poisson's ratio v xy and the equivalent Young's modulus E x for:

[0252]

[0253] B: Equivalent projection of the inclined wall plate during the cell compression stage and the plastic deformation stage and Accordion honeycomb structure equivalent Poisson's ratio v xy and the equivalent Young's modulus E x for::

[0254]

[0255] C: Equivalent projection of the inclined wall plate in the stage of elastic deformation of the inclined wall plate during the cell tension stage and Accordion honeycomb structure equivalent Poisson's ratio v xy and the equivalent Young's modulus E x for:

[0256]

[0257] D: Equivalent projection of the inclined wall plate in the plastic deformation stage of the cell tension stage and Accordion honeycomb structure equivalent Poisson's ratio v xy and the equivalent Young's modulus E x for:

[0258] The accordion honeycomb structure exhibits obvious nonlinear characteristics and obvious zero Poisson's ratio effect when subjected to force in the X direction. The elastic-plastic theoretical analysis model of the accordion honeycomb structure is compared with the relevant finite element model to prove the effectiveness of the present invention. The parameter analysis of the verified theoretical analysis model is carried out to study the influence of structural parameters on the nonlinear mechanical properties of the accordion honeycomb structure. The structural parameters include the wall panel angle Material yield strength σ s , the length of the inclined wall panel l, the width of the cell wall panel t, a method for establishing a nonlinear structural relationship that reflects the same type of accordion honeycomb structure, a system is provided through the method for establishing a nonlinear structural relationship of a zero Poisson's ratio accordion honeycomb structure, a computer system, the system includes a program, and when the program is executed by a processor, the method for establishing a nonlinear structural relationship of a zero Poisson's ratio accordion honeycomb structure is implemented, and at least one device is provided through the method for establishing a nonlinear structural relationship of a zero Poisson's ratio accordion honeycomb structure, and the device includes a compressive elastic force analysis module, a compressive plastic force analysis module, a tensile elastic force analysis module, and a tensile plastic force analysis module.

[0259] The present invention obtains the nonlinear structural relationship of the accordion honeycomb structure by decoupling a series of equations, and fully considers the elastic-plastic deformation of the material during the analysis process. Compared with the finite element method, it has higher calculation accuracy and wider application range; compared with the experimental method, it is less expensive and more efficient. For those companies with special requirements for materials or structures, the method in this article can be used to conveniently and quickly design a suitable honeycomb structure, making the design, production and manufacturing process more convenient, and further shortening the product design cycle.

[0260] Fig.11 This is a schematic diagram of the comparative analysis results between the theoretical model and the finite element model, where the structural and material parameters are: Angle l=10mm, h=30mm, t=1mm, b=1mm, σ s =335MPA, Es=200000MPa. The x-axis is the structural rotation angle β of the wall panel point B when the structure is under tension, and the y-axis is the strain in the x direction when the structure is under tension. When the rotation angle β gradually increases, the elastic model maintains the elastic deformation stage, and the finite element model and the elastic-plastic model enter the plastic deformation stage from the elastic deformation stage. Therefore, the inflection point indicates that the accordion honeycomb structure elastic-plastic model and the finite element model begin to enter plastic deformation, that is, the plastic rotation angle appears.

[0261] It can be seen from the slope of the curve that the slope of the elastic model remains unchanged, while the slopes of the elastic-plastic model and the finite element increase with the appearance of the plastic rotation angle, indicating that the increased strain under the same rotation angle increment increases, and the slope of the finite element model is between the elastic deformation and the elastic-plastic deformation, which is consistent with the actual situation, verifying the effectiveness of the nonlinear analysis method for the mechanical properties of the accordion honeycomb structure proposed in this paper.

[0262] Fig.12 It shows the angles of different sizes. The variation of nonlinear equivalent material parameters with the increase of rotation angle β, where the structural and material parameters are: l = 10 mm, h = 30 mm, t = 1 mm, b = 1 mm, σ s =335MPa, Es = 200000MPa, angle They are: 15°, 30°, 45°, 60°, 75° respectively; the increase of the rotation angle β also represents the increase of the degree of cell deformation. It can be seen that:

[0263] 1. With the angle Increase, equivalent Young's modulus E in x direction x Increase.

[0264] 2. As the rotation angle β increases, the equivalent Young's modulus E in the x direction x The equivalent Young's modulus decreases, and there is an obvious inflection point in the equivalent Young's modulus, that is, the structure begins to deform plastically when a plastic hinge appears. It changes linearly before the appearance of the plastic hinge, and shows extremely strong nonlinearity after the appearance of the plastic hinge.

[0265] Fig.13 It represents the yield stress σ at different sizes s The variation of the nonlinear equivalent material parameters under the condition of β as the rotation angle β increases, where the structural and material parameters are: l = 10 mm, h = 30 mm, t = 1 mm, b = 1 mm, Es = 200000 MPa, yield stress σ s They are: 100MPa, 200MPa, 300MPa, 400MPa, and 500MPa respectively; the increase in the angle β also means the increase in the degree of cell deformation.

[0266] It can be seen that:

[0267] 1. With the yield stress σ s Increase, equivalent Young's modulus E in x direction x Reduce.

[0268] 2. In the elastic stage, before the plastic hinge appears, the yield strength σ s There is no effect on structural parameters;

[0269] 3. The greater the yield strength, the greater the degree of structural deformation before the plastic hinge appears. Before the plastic hinge appears, it is a linear change, and after the plastic hinge appears, it shows extremely strong nonlinearity.

[0270] Fig.14 It shows the variation of nonlinear equivalent material parameters under different wall panel lengths l as the rotation angle β increases, where the structural and material parameters are: h=30mm, t=1mm, b=1mm, σ s =335MPA, Es=200000MPa, the wall length l is: 5mm, 7.5mm, 10mm, 12.5mm, 15mm respectively; the increase of the rotation angle β also represents the increase of the degree of cell deformation. It can be seen that:

[0271] 1. As the length l of the wall increases, the equivalent Young's modulus E in the x direction x Reduce.

[0272] 2. The equivalent Young's modulus has an obvious inflection point, that is, a plastic hinge appears in the structure. It changes linearly before the plastic hinge appears, and shows extremely strong nonlinearity after the plastic hinge appears.

[0273] Fig.15 It shows the variation of nonlinear equivalent material parameters with increasing rotation angle β under different wall thickness t, where the structural and material parameters are: l=10mm, h=30mm, b=1mm, σ s =335MPA, Es=200000MPa, the wall thickness t is: 0.5mm, 1mm, 2mm, 3mm, 4mm respectively; the increase of the rotation angle β also represents the increase of the degree of cell deformation. It can be seen that:

[0274] 1. As the thickness t of the wall increases, the equivalent Young's modulus E in the x direction x Increase.

[0275] 2. The thicker the wall panel is, the smaller the degree of structural deformation is, and the plastic hinge will appear. Before the plastic hinge appears, it is a linear change, and after the plastic hinge appears, it shows extremely strong nonlinearity.

[0276] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for establishing a nonlinear structural relationship of a zero Poisson's ratio accordion honeycomb structure, characterized in that: The following steps are involved: S1. Data analysis defines the horizontal direction as the X direction and the vertical direction as the Y direction. For the periodic accordion honeycomb structure subjected to force in the horizontal direction, the representative cell is intercepted to determine the stress stage (including the compression stage and the tension stage) of the cell. For the representative cell subjected to force in the horizontal direction, the deformation stage (including the elastic deformation stage and the plastic deformation stage) of the inclined wall plate is determined and deformation analysis of the corresponding stage is performed; S2. Data Projection According to the results of deformation analysis, the equivalent projection and equivalent load of the inclined wall plate are obtained; S3. Structural Relationship According to the equivalent displacement and equivalent load of the inclined wall plate, the equivalent stress, equivalent strain, equivalent Poisson's ratio and equivalent Young's modulus of the periodic accordion honeycomb structure are obtained, and the nonlinear structural relationship of the accordion honeycomb structure is established; When the accordion honeycomb structure is subjected to force in the horizontal direction, the bending moment M1 at the compression deformation stage, the bending moment M3 at the tension deformation stage, and the ultimate bending moment M max They are: in: E s is the Young's modulus of the structural material, I is the polar moment of inertia of the structural material, b is the wall depth of the structure, t is the wall thickness of the structure, s is the arc length of the semi-oblique wall OB after force deformation, l is the length of the oblique wall OA, α is the rotation angle at the arc coordinate s of the semi-oblique wall after force deformation (the rotation angle at point O is 0, and the rotation angle at point B is β), σ s is the yield stress of the structural material, φ is the angle between the AO wall and the CO wall, F1(β) and F3(β) are the first kind of elliptic integrals, η1 and η3 are new variables generated by the coordinate transformation formula, is the value of η1 at point O, is the value of η3 at point O; When M1 <M max or M2 <M max When M1≥M max Or M2 ≥ M max When , the inclined wall plate is in the plastic deformation stage, the only plastic hinge θ0 can be determined, and the bending moment M2 in the compression plastic deformation stage and the bending moment M4 in the tension plastic deformation stage at point O are respectively: in:

2. The method for establishing a nonlinear structural relationship of a zero Poisson's ratio accordion honeycomb structure according to claim 1, characterized in that: The cell stress stage and the inclined wall plate deformation stage are divided into four modules A: Equivalent projection of the inclined wall plate during the cell compression stage and the elastic deformation stage and for: B: Equivalent projection of the inclined wall plate during the cell compression stage and the plastic deformation stage and for: C: Equivalent projection of the inclined wall plate in the stage of elastic deformation of the inclined wall plate during the cell tension stage and for: D: Equivalent projection of the inclined wall plate in the stage of plastic deformation of the inclined wall plate during the cell tension stage and for:

3. The method for establishing nonlinear structural relationship of zero Poisson's ratio accordion structure according to claim 1, characterized in that: The cell stress stage and the inclined wall plate deformation stage are divided into four modules A: The accordion structure has an equivalent Poisson's ratio v during the stage of cell compression and the stage of elastic deformation of the inclined wall plate. xy and the equivalent Young's modulus E x for: B: The equivalent Poisson's ratio v of the accordion structure during the plastic deformation stage of the inclined wall plate during the cell compression stage xy and the equivalent Young's modulus E x for: C: The accordion structure equivalent Poisson's ratio v in the stage of elastic deformation of the inclined wall plate during the cell tension stage xy and the equivalent Young's modulus E x for: D: Cell tension stage Oblique wall plate plastic deformation stage, accordion structure equivalent Poisson's ratio v xy and the equivalent Young's modulus E x for:

4. The method for establishing nonlinear structural relationship of zero Poisson's ratio accordion honeycomb structure according to claim 1, characterized in that: A system and a computer system are provided by the method for establishing the nonlinear structural relationship of the zero Poisson's ratio accordion honeycomb structure. The system includes a program. When the program is executed by a processor, the method for establishing the nonlinear structural relationship of the zero Poisson's ratio accordion honeycomb structure is implemented.

5. The method for establishing nonlinear structural relationship of zero Poisson's ratio accordion honeycomb structure according to claim 1, characterized in that: At least one device is provided by the method for establishing the nonlinear structural relationship of the zero Poisson's ratio accordion honeycomb structure, and the device includes a compressive elastic force analysis module, a compressive plastic force analysis module, a tensile elastic force analysis module, and a tensile plastic force analysis module.

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