Adjustable poisson ratio hole structure and design method thereof

Abstract

The present application relates to the technical field of hole structure design, and solves the problem of adjusting Poisson's ratio of hole structure, and relates to a hole structure with adjustable Poisson's ratio and a design method thereof, wherein the hole structure is composed of an outer hexagonal structure and an inner hexagonal structure, the outer hexagonal structure is composed of six vertices OCO1O2C1O3 connected in sequence, and the first two vertices are connected; the inner hexagonal structure is composed of six vertices OBO1O2B1O3 connected in sequence, and the first and last two vertices are connected; the outer hexagonal structure and the inner hexagonal structure have two common edges OO3 and O1O2; in the hole structure with adjustable Poisson's ratio, the other four edges of the outer hexagonal structure are equal except the two common edges OO3 and O1O2; and the other four edges of the inner hexagonal structure are equal except the two common edges OO3 and O1O2.The hole structure can change the overall Poisson's ratio between positive and negative values by adjusting the structure parameters, and has a larger adjustment range.

Description

Technical Field

[0001] This invention relates to the field of cavity structure design technology, and in particular to a cavity structure with an adjustable Poisson's ratio and its design method. Background Technology

[0002] Hollow structures possess excellent mechanical and thermodynamic properties, offering significant advantages in vibration damping and energy absorption, noise reduction, heat conduction and dissipation, fracture resistance, and lightweight design. A positive Poisson's ratio structure exhibits outward deformation in the orthogonal direction under compression; a negative Poisson's ratio structure exhibits inward deformation in the orthogonal direction under compression; and a zero Poisson's ratio structure exhibits no deformation in the orthogonal direction under compression. Different hollow structure parameters result in different Poisson's ratios. In practical engineering, the appropriate Poisson's ratio needs to be determined based on the application scenario.

[0003] The patent application CN115163717A, entitled "A Novel Composite Metamaterial Capable of Achieving Poisson Ratio Positive-Negative Conversion and Its Design Method," utilizes a combination of multiple materials to adjust the Poisson ratio of a structure. However, this method has the following problems in practical applications: First, designing connections between dissimilar materials is difficult, economical, and hard to promote; second, this design method cannot quantitatively adjust the Poisson ratio of the structure.

[0004] To address the aforementioned shortcomings, this invention proposes an adjustable Poisson's ratio cavity structure and its design method. By changing the parameters of the cavity structure, a target Poisson's ratio can be obtained to meet the needs of practical scenarios. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide an adjustable Poisson's ratio cavity structure and its design method.

[0006] One of the above-mentioned objectives of the present invention is achieved through the following technical solution:

[0007] An adjustable Poisson's ratio cavity structure is composed of an outer hexagonal structure and an inner hexagonal structure. The outer hexagon is formed by connecting six vertices OCO1O2C1O3 sequentially, with the first and last vertices connected. The inner hexagon is formed by connecting six vertices OBO1O2B1O3 sequentially, with the first and last vertices connected. The outer and inner hexagons share two common sides, OO3 and O1O2. In this adjustable Poisson's ratio cavity structure, the outer hexagon has four equal sides except for the two common sides OO3 and O1O2. The inner hexagon also has four equal sides except for the two common sides OO3 and O1O2.

[0008] The second objective of this invention is achieved through the following technical solution.

[0009] A method for designing a cavity structure with an adjustable Poisson's ratio includes the following steps:

[0010] S1: Parametric modeling of the cavity structure;

[0011] S2: Establish a mechanical analysis model for the cavity structure, and simplify the mechanical analysis model for the cavity structure based on symmetry;

[0012] S3: Based on the simplified mechanical analysis model of the cavity structure, determine the optimization parameters of the cavity structure, the constraints on the values ​​of the optimization parameters, and the number of particle swarms, and initialize the particle swarms of the cavity structure parameters using the hypercubic Latin sampling method;

[0013] S4: Determine the number of redundant constraint forces and equivalent systems in the simplified mechanical analysis model, and solve the nodal forces of the cavity structure using the force method;

[0014] S5: Calculate the bending moment of each segment of the cavity structure;

[0015] S6: Calculate the displacement of the cavity structure in the x-axis and y-axis directions under a unit load using the unit load method, where the x-axis direction is the direction of the line connecting O to O1, and the y-axis direction is the direction of the line connecting O3 to O.

[0016] S7: Calculate the Poisson's ratio of the cavity structure under the current parameters;

[0017] S8: Calculate the fitness of each particle for each cavity structure parameter based on the target Poisson's ratio and the current cavity structure Poisson's ratio;

[0018] S9: Calculate the individual historical best position and the group historical best position of each particle with structural parameters of the cavity.

[0019] S10: Determine whether the historical optimal value of the swarm of cavity structure parameter particles satisfies the convergence condition; if the convergence condition is satisfied, output the cavity structure parameters; if the convergence condition is not satisfied, update the cavity structure parameter particle swarm and return to step S4 until the convergence condition is satisfied.

[0020] Furthermore, in step S1, the parameterized model of the cavity structure mainly includes three parameters: the lengths a of the cavity structures OO3 and O1O2, the length a0 of the cavity structure along the x-axis, and the angles θ1 and θ2 between the outer hexagon OC and the horizontal plane; the lengths a1 of the four sides of the inner hexagon are determined by the following formula:

[0021]

[0022] In the formula, a0 is the length of the cavity structure along the x-axis; θ1 is the angle between the side of the outer hexagon OC and the horizontal; θ2 is the angle between the side of the inner hexagon OB and the horizontal.

[0023] The lengths a2 of the four sides of the outer hexagon are determined by the following formula:

[0024]

[0025] Furthermore, in step S2, the mechanical analysis model of the cavity structure is as follows: a unit load is applied downward along the y-axis at point C, and a unit load is applied upward along the y-axis at point C1. Based on symmetry, the force model can be simplified to: retaining 1 / 4 of the cavity structure model, and replacing the original rigid connection with a sliding fixed support at points C, B, and the midpoint A of OO3; the sliding fixed supports at points C and B can slide along the y-axis, and the sliding fixed support at point A can slide along the x-axis; point C is subjected to a load of 1 / 2 in the negative y-axis direction.

[0026] Furthermore, in step S3, the optimization parameters for the cavity structure are the angle θ1 between the outer hexagon OC and the horizontal and the angle θ2 between the inner hexagon OB and the horizontal. The values ​​of θ1 and θ2 need to satisfy the following constraints:

[0027] 0≤θ1<90°

[0028]

[0029] In the formula, θ1 is the angle between the outer hexagon OC and the horizontal; θ2 is the angle between the inner hexagon OB and the horizontal; a0 is the length of the cavity structure along the x-axis; and a1 is the length of the four sides of the inner hexagon.

[0030] During the optimization process, the number of particles in the swarm is set to 200; during the sampling process using the hypercubic Latin sampling method, the number of samples is set to 200.

[0031] Furthermore, in step S4, the number of redundant constraint forces in the simplified mechanical analysis model is determined by the following formula:

[0032] N = mn

[0033] In the formula, N is the number of redundant constraints in the simplified mechanical analysis model, m is the total number of constraints in the simplified mechanical analysis model, and n is the number of equilibrium equations;

[0034] In step S4, the simplified mechanical analysis model is equivalent to the analysis system after removing redundant constraints in the simplified mechanical analysis model;

[0035] In step S4, the redundant constraint forces in the simplified mechanical analysis model can be solved according to the force method canonical equation. The force method canonical equation for this cavity structure is:

[0036]

[0037] In the formula, [X1,X2,...,X] N] represents redundant constraint force; δ ij To simplify the mechanical analysis model and retain only X in the equivalent system j And let X j =1, in X i Along X at the point of application i Displacement in the direction; Δ iF To simplify the mechanical analysis model of a relatively system, all redundant unknown forces are removed, retaining only the original known loads, in X... i Point of application along X i Displacement caused by direction.

[0038] Furthermore, in step S5, the bending moment of segment OA of the cavity structure under load is:

[0039]

[0040] In the formula, M OA (x) represents the bending moment of segment OA of the cavity structure under load; X i M is the i-th redundant constraint force; OAi (x) represents the cavity structure only in X. i The bending moment of segment OA when a unit load is applied; M′ OA (x) represents the bending moment of segment OA in the simplified mechanical analysis model of the equivalent system under the original load only;

[0041] The bending moment of segment OB of the cavity structure under load is:

[0042]

[0043] In the formula, M OB (x) represents the bending moment of segment OB of the cavity structure under load; X i M is the i-th redundant constraint force; OBi (x) represents the cavity structure only in X. i The bending moment of segment OB when a unit load is applied at point M′; OB (x) represents the bending moment of segment OB in the simplified mechanical analysis model of the equivalent system under the original load only;

[0044] The bending moment of the cavity structure in segment OC under load is:

[0045]

[0046] In the formula, M OC (x) represents the bending moment of the cavity structure in segment OC under load; X i M is the i-th redundant constraint force; OCi (x) represents the cavity structure only in X. i The bending moment of segment OC when a unit load is applied; M′ OC(x) represents the bending moment of segment OC in the simplified mechanical analysis model of the equivalent system under the original load.

[0047] Furthermore, in step S6, the displacement of the cavity structure in the x-axis direction under load is:

[0048]

[0049] In the formula, M OA (x) represents the bending moment of segment OA of the cavity structure under load; M OB (x) represents the bending moment of segment OB of the cavity structure under load; M OC (x) represents the bending moment of the cavity structure in segment OC under load; M OAx (x) represents the bending moment of segment OA when a horizontal unit load is applied only at point A in the cavity structure; M OBx (x) represents the bending moment of segment OB when a horizontal unit load is applied only at point A in the cavity structure; M OCx (x) represents the bending moment of segment OC when a horizontal unit load is applied only at point A in the cavity structure; a represents the lengths of OO3 and O1O2 in the cavity structure; a1 represents the lengths of the remaining four sides of the inner hexagon; a2 represents the lengths of the remaining four sides of the outer hexagon.

[0050] The displacement of the cavity structure in the y-axis direction under load is:

[0051]

[0052] In the formula, M OA (x) represents the bending moment of segment OA of the cavity structure under load; M OB (x) represents the bending moment of segment OB of the cavity structure under load; M OC (x) represents the bending moment of the cavity structure in segment OC under load; M OAy (x) represents the bending moment of segment OA when a vertical unit load is applied only at point C in the cavity structure; M OBx (x) represents the bending moment of segment OB when a vertical unit load is applied only at point C in the cavity structure; M OCx (x) is the bending moment of segment OC when a vertical unit load is applied only at point C in the cavity structure; a is the length of cavity structures OO3 and O1O2; a1 is the length of the four sides of the inner hexagon; a2 is the length of the four sides of the outer hexagon.

[0053] Furthermore, in step S7, the Poisson's ratio of the cavity structure under the current parameters is:

[0054]

[0055] In the formula, Δx represents the displacement of the cavity structure in the x-direction under load; L xL represents the width of the cavity structure in the x-direction; Δy represents the displacement of the cavity structure in the y-direction under load; y ε represents the width of the cavity structure in the y-direction; ε is the Poisson's ratio of the cavity structure under the current parameters.

[0056] Furthermore, in step S8, the fitness of the pore structure parameter particles is:

[0057] ε fit =|ε obj -ε|

[0058] In the formula, ε fit The fitness of particles for pore structure parameters; ε obj ε represents the target Poisson's ratio; ε is the Poisson's ratio of the cavity structure under the current parameters.

[0059] Furthermore, in step 9, the individual historical optimal position of each cavity structure parameter particle refers to the optimal solution experienced by each particle during the iteration process. Each iteration will produce i individual historical optimal positions, that is, in the k-th iteration, the individual historical optimal position of the i-th particle can be determined by the following expression:

[0060]

[0061] In the formula, The historical optimal value of the i-th cavity structure parameter particle in the k-th iteration; The historical optimal value of the particle for the i-th cavity structure parameter in the (k-1)th iteration;

[0062] The collective historical optimal position of particles for each cavity structure parameter refers to the optimal solution experienced by all particles during the iteration process. Each iteration yields only one collective historical optimal position. That is, in the k-th iteration, the collective historical optimal position can be determined by the following expression:

[0063]

[0064] In the formula, The historical optimal value of the i-th cavity structure parameter particle in the k-th iteration; The particle swarm is the historical best for the cavity structure parameters in the k-th iteration.

[0065] Furthermore, in step S10, the criteria for determining convergence are:

[0066]

[0067] In the formula, The particle swarm is the historical best for the cavity structure parameters in the k-th iteration; The particle population has historically optimal parameters for the cavity structure in the (k-1)th iteration; χ is the convergence threshold, typically ranging from 0.01 to 0.05.

[0068] In step 10, the particle swarm optimization of the pore structure parameters is updated using the following formula:

[0069]

[0070] In the formula, Let be the flight speed of the i-th parameter particle in the (k+1)-th iteration step; ω represents the flight velocity of the i-th parameter particle in the k-th iteration step. max ω represents the upper limit of the inertia weight values. min This is the lower bound for the inertia weight values; inter max `inter` is the maximum number of iterations; `inter` is the current number of iterations; `c1` is the individual learning factor; `r1` is the individual random factor. is the historical optimal value of the i-th cavity structure parameter particle in the k-th iteration; c2 is the global learning factor; r2 is the global random variable; The particle swarm is the historical best for the cavity structure parameters in the k-th iteration; This represents the position of the i-th particle in the k-th iteration; It represents the position of the i-th particle in the (k+1)-th iteration.

[0071] The advantages of this invention are:

[0072] 1. This invention proposes an adjustable Poisson's ratio cavity structure, which can achieve a structure meeting the desired Poisson's ratio requirements by adjusting the parameters of the cavity structure. The Poisson's ratio of traditional honeycomb structures can only be adjusted within the range greater than 0, while the Poisson's ratio of a concave hexagonal structure can only be adjusted within the range less than 0. The cavity structure proposed in this invention allows the overall Poisson's ratio to vary between positive and negative values ​​by adjusting the structural parameters, providing a wider adjustment range and making it more suitable for widespread application.

[0073] 2. Currently, achieving a target Poisson's ratio structure through a combination of multiple materials is challenging due to the difficulty in connecting the different materials, resulting in high costs. However, the adjustable Poisson's ratio cavity structure design method proposed in this invention adjusts the overall Poisson's ratio by changing the parameters of the cavity structure. This method is simple, practical, and economical.

[0074] 3. This invention employs a mechanical analytical method to calculate the Poisson's ratio of the cavity structure, which significantly improves computational efficiency and saves computational resources compared to the finite element method.

[0075] 4. This invention employs an improved particle swarm optimization (PSO) algorithm when determining the specific parameters of the cavity. By introducing the hypercubic Latin sampling method to initialize the particle swarm, the local convergence problem of the traditional PSO algorithm can be effectively improved, accelerating convergence. Attached Figure Description

[0076] Figure 1 This is a schematic diagram of the adjustable cavity structure proposed in this invention;

[0077] Figure 2 A flowchart illustrating a method for designing a cavity structure with an adjustable Poisson's ratio;

[0078] Figure 3 A mechanical analysis model for adjustable Poisson's ratio cavity structures;

[0079] Figure 4 A simplified model of the forces acting on an adjustable Poisson's ratio cavity structure;

[0080] Figure 5 The simplified model for mechanical analysis is quite systematic;

[0081] Figure 6 To simplify the mechanical analysis model, the force analysis diagram of the system is equivalent to only the original load acting on it.

[0082] Figure 7 The force analysis diagram of the cavity structure when a unit load is applied only at X1;

[0083] Figure 8 The force analysis diagram of the cavity structure when a unit load is applied only at X2;

[0084] Figure 9 The force analysis diagram of the cavity structure when a unit load is applied only at X3;

[0085] Figure 10 The force analysis diagram of the cavity structure when a horizontal unit load is applied only at point A;

[0086] Figure 11 This is a force analysis diagram of the cavity structure when a vertical unit load is applied only at point C. Detailed Implementation

[0087] The structure of the present invention will be further described below with reference to the accompanying drawings and through embodiments. It should be noted that these embodiments are descriptive and not limiting.

[0088] As attached Figure 1 As shown, the adjustable Poisson's ratio cavity structure is composed of an outer hexagonal structure and an inner hexagonal structure. The outer hexagon OCO1O2C1O3 and the inner hexagon OBO1O2B1O3 share two common sides, OO3 and O1O2. Except for the two common sides OO3 and O1O2, the other four sides of the outer hexagon are equal; similarly, except for the two common sides OO3 and O1O2, the other four sides of the inner hexagon are equal.

[0089] As attached Figure 2As shown, an adjustable Poisson's ratio cavity structure and its design method include the following steps:

[0090] S1: Parametric modeling of the cavity structure;

[0091] S2: Simplify the mechanical analysis model of the cavity structure based on symmetry;

[0092] S3: Based on the simplified mechanical analysis model of the cavity structure, determine the optimization parameters of the cavity structure, the constraints on the values ​​of the optimization parameters, and the number of particle swarms, and initialize the particle swarms of the cavity structure parameters using the hypercubic Latin sampling method;

[0093] S4: Determine the number of redundant constraint forces and equivalent systems in the simplified mechanical analysis model, and solve the nodal forces of the cavity structure using the force method;

[0094] S5: Calculate the bending moment of each segment of the cavity structure;

[0095] S6: Calculate the displacement of the cavity structure in the x-axis and y-axis directions under a unit load using the unit load method;

[0096] S7: Calculate the Poisson's ratio of the cavity structure under the current parameters;

[0097] S8: Calculate the fitness of each particle for each cavity structure parameter based on the target Poisson's ratio and the current cavity structure Poisson's ratio;

[0098] S9: Calculate the individual historical best position and the group historical best position of each particle with structural parameters of the cavity.

[0099] S10: Determine whether the swarm's historical best value for the cavity structure parameter particles satisfies the convergence condition. If the convergence condition is met, output the cavity structure parameters; if the convergence condition is not met, update the cavity structure parameter particle swarm and return to step S4 until the convergence condition is met.

[0100] In step S1, the parameterized model of the cavity structure mainly includes three parameters: the lengths a of the cavity structures OO3 and O1O2, the length a0 of the cavity structure along the x-axis, and the angles θ1 and θ2 between the outer hexagon OC and the horizontal plane, and the inner hexagon OB and the horizontal plane. The lengths a1 of the four sides of the inner hexagon are determined by the following formula:

[0101]

[0102] In the formula, a0 is the length of the cavity structure along the x-axis; θ1 is the angle between the side of the outer hexagon OC and the horizontal; θ2 is the angle between the side of the inner hexagon OB and the horizontal.

[0103] The lengths a2 of the four sides of the outer hexagon are determined by the following formula:

[0104]

[0105] In the formula, a0 is the length of the cavity structure along the x-axis; θ1 is the angle between the side of the outer hexagon OC and the horizontal; θ2 is the angle between the side of the inner hexagon OB and the horizontal.

[0106] Parameters a and a0 are input parameters, which are determined according to the actual required cavity structure size.

[0107] In step 2, the mechanical analysis model of the cavity structure is as follows: a unit load is applied downward along the y-axis at point C, and a unit load is applied upward along the y-axis at point C1. Due to symmetry, this force model can be simplified to: retaining 1 / 4 of the cavity structure model, and replacing the original rigid connections at points C, B, and the midpoint A of OO3 with sliding fixed supports. The sliding fixed supports at points C and B can slide along the y-axis, and the sliding fixed support at point A can slide along the x-axis. Point C is subjected to a load of 1 / 2 in the negative y-axis direction.

[0108] In step 3, the optimization parameters for the cavity structure are the angle θ1 between the outer hexagon OC and the horizontal and the angle θ2 between the inner hexagon OB and the horizontal; the values ​​of θ1 and θ2 need to satisfy the following constraints:

[0109] 0≤θ1<90°

[0110]

[0111] In the formula, θ1 is the angle between the outer hexagon OC and the horizontal; θ2 is the angle between the inner hexagon OB and the horizontal; a0 is the length of the cavity structure along the x-axis; and a1 is the length of the four sides of the inner hexagon.

[0112] During the optimization process, the number of particles in the swarm is set to 200; during the sampling process using the hypercubic Latin sampling method, the number of samples is set to 200, and the sampling range of optimization parameters θ1 and θ2 is determined by the above formula.

[0113] In step 4, the number of redundant constraint forces in the simplified mechanical analysis model is determined by the following formula:

[0114] N = mn

[0115] In the formula, N is the number of redundant constraints in the simplified mechanical analysis model, m is the total number of constraints in the simplified mechanical analysis model, and n is the number of equilibrium equations.

[0116] In step 4, the simplified mechanical analysis model is equivalent to the analysis system after removing redundant constraints in the simplified mechanical analysis model.

[0117] In step 4, the redundant constraint forces in the simplified mechanical analysis model can be solved using the force method canonical equations. The force method canonical equations for this cavity structure are:

[0118]

[0119] In the formula, [X1,X2,...,X] N ] represents redundant constraint force; δ ij To simplify the mechanical analysis model and retain only X in the equivalent system j And let X j =1, in X i Along X at the point of application i Displacement in the direction; Δ iF To simplify the mechanical analysis model of a relatively system, all redundant unknown forces are removed, retaining only the original known loads, in X... i Point of application along X i Displacement caused by direction.

[0120] In step 5, the bending moment of segment OA (where A refers to point A in OO3 above) of the cavity structure under load is:

[0121]

[0122] In the formula, M OA (x) represents the bending moment of segment OA of the cavity structure under load; X i M is the i-th redundant constraint force; OAi (x) represents the cavity structure only in X. i The bending moment of segment OA when a unit load is applied; M′ OA (x) represents the bending moment of segment OA in the simplified mechanical analysis model of the equivalent system under the original load.

[0123] The bending moment of segment OB of the cavity structure under load is:

[0124]

[0125] In the formula, M OB (x) represents the bending moment of segment OB of the cavity structure under load; X i M is the i-th redundant constraint force; OBi (x) represents the cavity structure only in X. i The bending moment of segment OB when a unit load is applied at point M′; OB (x) represents the bending moment of segment OB in the simplified mechanical analysis model of the equivalent system under the original load.

[0126] The bending moment of the cavity structure in segment OC under load is:

[0127]

[0128] In the formula, M OC (x) represents the bending moment of the cavity structure in segment OC under load; X i M is the i-th redundant constraint force; OCi (x) represents the cavity structure only in X. i The bending moment of segment OC when a unit load is applied; M′ OC (x) represents the bending moment of segment OC in the simplified mechanical analysis model of the equivalent system under the original load.

[0129] Furthermore, in step 6, the displacement of the cavity structure in the x-axis direction under load is:

[0130]

[0131] In the formula, M OA (x) represents the bending moment of segment OA of the cavity structure under load; M OB (x) represents the bending moment of segment OB of the cavity structure under load; M OC (x) represents the bending moment of the cavity structure in segment OC under load; M OAx (x) represents the bending moment of segment OA when a horizontal unit load is applied only at point A in the cavity structure; M OBx (x) represents the bending moment of segment OB when a horizontal unit load is applied only at point A in the cavity structure; M OCx (x) represents the bending moment of segment OC when a horizontal unit load is applied only at point A in the cavity structure; a represents the lengths of OO3 and O1O2 in the cavity structure; a1 represents the lengths of the four sides of the inner hexagon; a2 represents the lengths of the four sides of the outer hexagon.

[0132] The displacement of the cavity structure in the y-axis direction under load is:

[0133]

[0134] In the formula, M OA (x) represents the bending moment of segment OA of the cavity structure under load; M OB (x) represents the bending moment of segment OB of the cavity structure under load; M OC (x) represents the bending moment of the cavity structure in segment OC under load; M OAy (x) represents the bending moment of segment OA when a vertical unit load is applied only at point C in the cavity structure; M OBy (x) represents the bending moment of segment OB when a vertical unit load is applied only at point C in the cavity structure; M OCy (x) is the bending moment of segment OC when a vertical unit load is applied only at point C in the cavity structure; a is the length of cavity structures OO3 and O1O2; a1 is the length of the four sides of the inner hexagon; a2 is the length of the four sides of the outer hexagon.

[0135] In step 7, the Poisson's ratio of the cavity structure under the current parameters is:

[0136]

[0137] In the formula, Δx represents the displacement of the cavity structure in the x-direction under load; L x L represents the width of the cavity structure in the x-direction; Δy represents the displacement of the cavity structure in the y-direction under load; y ε represents the width of the cavity structure in the y-direction; ε is the Poisson's ratio of the cavity structure under the current parameters.

[0138] In step 8, the fitness of the pore structure parameter particles is:

[0139] ε fit =|ε obj -ε

[0140] In the formula, ε fit The fitness of particles for pore structure parameters; ε obj ε represents the target Poisson's ratio; ε is the Poisson's ratio of the cavity structure under the current parameters.

[0141] In step 9, the individual historical optimal position of each cavity structure parameter particle refers to the optimal solution experienced by each particle during the iteration process. Each iteration will produce i individual historical optimal positions. That is, in the k-th iteration, the individual historical optimal position of the i-th particle can be determined by the following expression:

[0142]

[0143] In the formula, The historical optimal value of the i-th cavity structure parameter particle in the k-th iteration; The historical optimal value of the i-th cavity structure parameter particle in the (k-1)-th iteration is given.

[0144] The collective historical optimal position of particles for each cavity structure parameter refers to the optimal solution experienced by all particles during the iteration process. Each iteration yields only one collective historical optimal position. That is, in the k-th iteration, the collective historical optimal position can be determined by the following expression:

[0145]

[0146] In the formula, The historical optimal value of the i-th cavity structure parameter particle in the k-th iteration; The particle swarm is the historical best for the cavity structure parameters in the k-th iteration.

[0147] In step 10, the criteria for determining convergence are:

[0148]

[0149] In the formula, The particle swarm is the historical best for the cavity structure parameters in the k-th iteration; χ represents the historical optimal value of the particle swarm for the cavity structure parameters in the (k-1)th iteration; χ is the convergence threshold, typically ranging from 0.01 to 0.05.

[0150] Furthermore, in step 10, the pore structure parameter particle swarm is updated using the following formula:

[0151]

[0152]

[0153] In the formula, Let be the flight speed of the i-th parameter particle in the (k+1)-th iteration step; ω represents the flight velocity of the i-th parameter particle in the k-th iteration step. max ω represents the upper limit of the inertia weight values. min This is the lower bound for the inertia weight values; inter max `inter` is the maximum number of iterations; `inter` is the current number of iterations; `c1` is the individual learning factor; `r1` is the individual random factor. is the historical optimal value of the i-th cavity structure parameter particle in the k-th iteration; c2 is the global learning factor; r2 is the global random variable; The particle swarm is the historical best for the cavity structure parameters in the k-th iteration; This represents the position of the i-th particle in the k-th iteration; It represents the position of the i-th particle in the (k+1)-th iteration.

[0154] Specifically, this invention is illustrated by a concrete example of an adjustable Poisson's ratio cavity structure and its design method.

[0155] In this example, the length a and the length a0 in the x-axis direction of the cavity structures OO3 and O1O2 are both 10 mm, and the target Poisson's ratio is 0.18.

[0156] The adjustable Poisson's ratio cavity structure mechanical analysis model is attached. Figure 3 As shown in the attached simplified force model. Figure 4 As shown, a 1 / 4 model of the cavity structure is retained, and the original rigid connections are replaced with sliding fixed supports at points C, B, and the midpoint A of OO3. The sliding fixed supports at points C and B can slide along the y-axis, and the sliding fixed support at point A can slide along the x-axis. Point C is subjected to a load of 1 / 2 magnitude along the negative y-axis.

[0157] The number of redundant constraint forces in this adjustable Poisson's ratio cavity structure is:

[0158] N = mn = 6 - 3 = 3

[0159] In the formula, N is the number of redundant constraints in the simplified mechanical analysis model, m is the total number of constraints in the simplified mechanical analysis model, and n is the number of equilibrium equations.

[0160] The simplified mechanical analysis model is quite systematic, as shown in the attached figure. Figure 5 As shown, the sliding fixed support at point C is replaced by a horizontal force X1 and a torque X2, the sliding fixed support at point A is replaced by a hinge constraint, and a torque X3 is applied at point A.

[0161] The canonical equation for the force method of the cavity structure is:

[0162]

[0163] In the formula, [X1,X2,X3] represent redundant constraint forces; δ ij To simplify the mechanical analysis model and retain only X in the equivalent system j And let X j =1, in X i Along X at the point of application i Displacement in the direction; Δ iF To simplify the mechanical analysis model of a relatively system, all redundant unknown forces are removed, retaining only the original known loads, in X... i Point of application along X i Displacement caused by direction.

[0164] The simplified mechanical analysis model is equivalent to the force analysis diagram of the system under the original load only, as shown in the attached figure. Figure 6 As shown. The simplified mechanical analysis model is equivalent to the bending moment of segment OA under the original load only:

[0165] M′ OA (x)=0

[0166] The simplified mechanical analysis model is equivalent to the bending moment of segment OB under the original load only:

[0167]

[0168] The simplified mechanical analysis model is equivalent to the bending moment of segment OC under the original load only:

[0169]

[0170] The force analysis diagram of the cavity structure when a unit load is applied only at point X1 is attached. Figure 7 As shown. When a unit load is applied only at X1 to the cavity structure, the bending moment of segment OA is:

[0171] M OA1(x)=0

[0172] When a unit load is applied only at X1 to the cavity structure, the bending moment of segment OB is:

[0173] M OB1 (x)=-xsinθ2+a2sinθ1+a1sinθ2

[0174] When a unit load is applied only at X1 to the cavity structure, the bending moment in segment OC is:

[0175] M OC1 (x)=-xsinθ1

[0176] The force analysis diagram of the cavity structure when a unit load is applied only at X2 is attached. Figure 8 As shown. When a unit load is applied only at X2 to the cavity structure, the bending moment of segment OA is:

[0177] M OA2 (x)=0

[0178] When a unit load is applied only at X2 to the cavity structure, the bending moment of segment OB is:

[0179] M OB2 (x)=1

[0180] When a unit load is applied only at X2 to the cavity structure, the bending moment in segment OC is:

[0181] M OC2 (x)=-1

[0182] The force analysis diagram of the cavity structure when a unit load is applied only at X3 is attached. Figure 9 As shown. When a unit load is applied only at X3 to the cavity structure, the bending moment of segment OA is:

[0183] M OA3 (x)=-1

[0184] When a unit load is applied only at X3 to the cavity structure, the bending moment of segment OB is:

[0185] M OB3 (x)=1

[0186] When a unit load is applied only at X3 to the cavity structure, the bending moment in segment OC is:

[0187] M OC3 (x)=0

[0188] The coefficients in the canonical equations of the force method for cavity structures are obtained using the following formula:

[0189]

[0190]

[0191]

[0192]

[0193]

[0194]

[0195]

[0196]

[0197]

[0198] The unknown force X = [X1, X2, X3] is obtained using the following formula:

[0199]

[0200]

[0201]

[0202] The force analysis diagram of the cavity structure when a horizontal unit load is applied only at point A is attached. Figure 10 As shown. When a horizontal unit load is applied only at point A to the cavity structure, the bending moment of segment OA is:

[0203] M OAx (x)=-x

[0204] When a horizontal unit load is applied only at point A to the cavity structure, the bending moment of segment OB is:

[0205]

[0206] When a horizontal unit load is applied only at point A to the cavity structure, the bending moment in segment OC is:

[0207] M OCx (x)=0

[0208] The force analysis diagram of the cavity structure when a vertical unit load is applied only at point C is attached. Figure 11 As shown. When a vertical unit load is applied only at point C to the cavity structure, the bending moment of segment OA is:

[0209] M OAy (x)=0

[0210] When a vertical unit load is applied only at point C to the cavity structure, the bending moment of segment OB is:

[0211] M OBy(x)=-a2cosθ1

[0212] When a vertical unit load is applied only at point C to the cavity structure, the bending moment in segment OC is:

[0213] M OCy (x)=xcosθ1

[0214] The displacement of the cavity structure in the x-axis direction under load is calculated using the following formula:

[0215]

[0216] The displacement of the cavity structure in the y-axis direction under load is calculated using the following formula:

[0217]

[0218] The width L of the cavity structure in the x-direction x It can be obtained using the following formula:

[0219] L x =a0

[0220] The width L of the cavity structure in the y-direction y It can be obtained using the following formula:

[0221] L y =a+2a2sinθ1

[0222] The Poisson's ratio for a cavity structure is calculated using the following formula:

[0223]

[0224] Since the target Poisson ratio for this example is 0.18, i.e. ε obj =0.18, the fitness of the particle for the cavity structure parameter is:

[0225] ε fit =|0.18-ε|

[0226] In this example, the particle swarm optimization convergence threshold χ is set to 0.00001. There are two optimization parameters in this example: the angle θ1 between the outer hexagon OC and the horizontal plane, and the angle θ2 between the inner hexagon OB and the horizontal plane. Therefore, the particle swarm optimization is two-dimensional, i.e., z1 = θ1, z2 = θ2.

[0227] After 107 iterations, the optimization objective converged. When θ1 = 25.35° and θ2 = 19.49°, the Poisson's ratio of the cavity structure was closest to 0.18.

[0228] This invention is not limited to the specific embodiments described above. Those skilled in the art can implement this invention using various other specific embodiments based on the disclosed content of the embodiments and accompanying drawings. Therefore, any design that adopts the design structure and concept of this invention and makes some simple changes or modifications falls within the protection scope of this invention.

Claims

1. A method for designing a cavity structure with an adjustable Poisson's ratio, characterized in that: The adjustable Poisson's ratio cavity structure is composed of an outer hexagonal structure and an inner hexagonal structure, with the outer hexagon consisting of six vertices. It is formed by connecting the first and last vertices in sequence; An inner hexagon consists of six vertices. It is formed by sequential connection, with the first and last vertices connected; the outer hexagon and the inner hexagon have two common edges. and ; The outer hexagon in the adjustable Poisson's ratio cavity structure, except for the two common sides and The outer hexagon has four equal sides; the inner hexagon has two common sides. and Apart from the other four edges, which are equal, the design method includes the following steps: S1: Parametric modeling of the cavity structure; S2: Establish a mechanical analysis model for the cavity structure, and simplify the mechanical analysis model for the cavity structure based on symmetry; S3: Based on the simplified mechanical analysis model of the cavity structure, determine the optimization parameters of the cavity structure, the constraints on the values ​​of the optimization parameters, and the number of particle swarms, and initialize the particle swarms of the cavity structure parameters using the hypercubic Latin sampling method; S4: Determine the number of redundant constraint forces and equivalent systems in the simplified mechanical analysis model, and solve the nodal forces of the cavity structure using the force method; S5: Calculate the bending moment of each segment of the cavity structure; S6: Calculate the displacement of the cavity structure in the x-axis and y-axis directions under a unit load using the unit load method, where the x-axis direction is... O to O 1. The direction of the connecting line, the y-axis direction is... O 3 to O Direction of the line; S7: Calculate the Poisson's ratio of the cavity structure under the current parameters; S8: Calculate the fitness of each particle for each cavity structure parameter based on the target Poisson's ratio and the current cavity structure Poisson's ratio; S9: Calculate the individual historical best position and the group historical best position of each particle with structural parameters of the cavity. S10: Determine whether the historical optimal value of the swarm of cavity structure parameter particles satisfies the convergence condition; if the convergence condition is satisfied, output the cavity structure parameters; if the convergence condition is not satisfied, update the cavity structure parameter particle swarm and return to step S4 until the convergence condition is satisfied.

2. The design method for the adjustable Poisson's ratio cavity structure according to claim 1, characterized in that: In step S1, the parameterized model of the cavity structure mainly includes three parameters: cavity structure. and length Length of the cavity structure along the x-axis outer hexagon Angle between the side and the horizontal and inner hexagon Angle between the side and the horizontal The lengths of the four sides of an inner hexagon Determined by the following formula: ； In the formula, The length of the cavity structure along the x-axis; It is an outer hexagon The angle between the side and the horizontal; It is an inner hexagon The angle between the side and the horizontal; The lengths of the four sides of an outer hexagon Determined by the following formula: ； In the formula, The length of the cavity structure along the x-axis; It is an outer hexagon The angle between the side and the horizontal; It is an inner hexagon The angle between the side and the horizontal.

3. The design method for the adjustable Poisson's ratio cavity structure according to claim 1, characterized in that: In step S2, the mechanical analysis model of the cavity structure is as follows: A unit load is applied downward along the y-axis at point [point], A unit load is applied upwards along the y-axis at the point; due to symmetry, the force model can be simplified to: retaining a 1 / 4 model of the cavity structure, and in... point, Dot and midpoint At the point, a sliding fixed support is used to replace the original rigid connection; Dot and The sliding fixed support at the point can slide along the y-axis. The sliding fixed support at the point can slide along the x-axis; Point C is subjected to a load of 1 / 2 in the negative y-axis direction.

4. The design method for the adjustable Poisson's ratio cavity structure according to claim 1, characterized in that: In step S3, the optimization parameters for the cavity structure are: outer hexagon Angle between the side and the horizontal and inner hexagon Angle between the side and the horizontal , and The value of needs to satisfy the following constraints: ； In the formula, It is an outer hexagon The angle between the side and the horizontal; It is an inner hexagon The angle between the side and the horizontal; The length of the cavity structure along the x-axis; Let be the lengths of the four sides of the inner hexagon; During the optimization process, the number of particles in the swarm is set to 200; during the sampling process using the hypercubic Latin sampling method, the number of samples is set to 200.

5. The design method for the adjustable Poisson's ratio cavity structure according to claim 1, characterized in that: In step S4: The number of redundant constraint forces in the simplified mechanical analysis model is determined by the following formula: ； In the formula, To simplify the mechanical analysis model, the number of redundant constraint forces is reduced. To simplify the mechanical analysis model, the total number of constraints is reduced. The number of equilibrium equations; In step 4, the simplified mechanical analysis model is equivalent to the analysis system after removing redundant constraints in the simplified mechanical analysis model; In step S4, the redundant constraint forces in the simplified mechanical analysis model can be solved according to the force method canonical equation. The force method canonical equation for this cavity structure is: ； In the formula, For redundant constraints; To simplify the mechanical analysis model, only retain the following in a relatively systematic manner: And let ,exist Along the point of application Displacement in the direction; To simplify the mechanical analysis model of a relatively system, all redundant unknown forces are removed, retaining only the original known loads. Point of application along Displacement caused by direction.

6. The design method for the adjustable Poisson's ratio cavity structure according to claim 3, characterized in that: In step S5, the bending moment of segment OA of the cavity structure under load is: ； In the formula, The bending moment of segment OA of the cavity structure under load; This is the i-th redundant constraint force; For the cavity structure only The bending moment of segment OA when a unit load is applied; To simplify the mechanical analysis model, the bending moment of segment OA of the equivalent system is calculated only under the original load. The bending moment of segment OB of the cavity structure under load is: ； In the formula, The bending moment of segment OB of the cavity structure under load; This is the i-th redundant constraint force; For the cavity structure only The bending moment of segment OB when a unit load is applied at point OB; To simplify the model for mechanical analysis, the bending moment of segment OB is equivalent to the system under the original load only. The bending moment of the cavity structure in segment OC under load is: ； In the formula, The bending moment of the cavity structure in segment OC under load; This is the i-th redundant constraint force; For the cavity structure only The bending moment of segment OC when a unit load is applied at point OC; To simplify the mechanical analysis model, the bending moment of the system is calculated only in segment OC under the original load.

7. The design method for the adjustable Poisson's ratio cavity structure according to claim 3, characterized in that: In step S6, the displacement of the cavity structure in the x-axis direction under load is: ； In the formula, The bending moment of segment OA of the cavity structure under load; The bending moment of segment OB of the cavity structure under load; The bending moment of the cavity structure in segment OC under load; The bending moment of segment OA when a horizontal unit load is applied only at point A to the cavity structure; The bending moment of segment OB when a horizontal unit load is applied only at point A to the cavity structure; The bending moment of segment OC when a horizontal unit load is applied only at point A to the cavity structure; Hole structure and Length; The lengths of the remaining four sides of the inner hexagon; The lengths of the remaining four sides of the outer hexagon; The displacement of the cavity structure in the y-axis direction under load is: ； In the formula, The bending moment of segment OA of the cavity structure under load; The bending moment of segment OB of the cavity structure under load; The bending moment of the cavity structure in segment OC under load; The bending moment of segment OA when a vertical unit load is applied only at point C to the cavity structure; The bending moment of segment OB when a vertical unit load is applied only at point C to the cavity structure; The bending moment of segment OC when a vertical unit load is applied only at point C to the cavity structure; Hole structure and Length; Let be the lengths of the four sides of the inner hexagon; Let be the lengths of the four sides of the outer hexagon.

8. The design method for the adjustable Poisson's ratio cavity structure according to claim 1, characterized in that: In step S7, the Poisson's ratio of the cavity structure under the current parameters is: ； In the formula, The displacement of the cavity structure in the x-direction under load; The width of the cavity structure in the x-direction; The displacement of the cavity structure in the y-direction under load; The width of the cavity structure in the y-direction; This represents the Poisson's ratio of the cavity structure under the current parameters.

9. The design method for the adjustable Poisson's ratio cavity structure according to claim 1, characterized in that: In step S8, the fitness of the pore structure parameter particles is: ； In the formula, Fitness of particles for pore structure parameters; The target Poisson's ratio; This represents the Poisson's ratio of the cavity structure under the current parameters.

10. The design method for the adjustable Poisson's ratio cavity structure according to claim 1, characterized in that: In step 9, the individual historical optimal position of each cavity structure parameter particle refers to the optimal solution experienced by each particle during the iteration process. Each iteration will produce i individual historical optimal positions. That is, in the k-th iteration, the individual historical optimal position of the i-th particle can be determined by the following expression: ； In the formula, The historical optimal value of the i-th cavity structure parameter particle in the k-th iteration; The historical optimal value of the particle for the i-th cavity structure parameter in the (k-1)th iteration; The collective historical optimal position of particles for each cavity structure parameter refers to the optimal solution experienced by all particles during the iteration process. Each iteration yields only one collective historical optimal position. That is, in the k-th iteration, the collective historical optimal position can be determined by the following expression: ； In the formula, The historical optimal value of the i-th cavity structure parameter particle in the k-th iteration; The particle swarm is the historical best for the cavity structure parameters in the k-th iteration.

11. The design method for the adjustable Poisson's ratio cavity structure according to claim 1, characterized in that, In step S10, the criteria for determining convergence are: ； In the formula, The particle swarm is the historical best for the cavity structure parameters in the k-th iteration; The particle swarm is the historical best for the cavity structure parameters in the (k-1)th iteration. The convergence threshold is typically set between 0.01 and 0.

05. In step 10, the particle swarm optimization of the pore structure parameters is updated using the following formula: ； In the formula, Let be the flight speed of the i-th parameter particle in the (k+1)-th iteration step; Let be the flight velocity of the i-th parameter particle in the k-th iteration step; This represents the upper limit of the inertia weight value; This is the lower limit for the inertia weight value; This represents the maximum number of iterations. This represents the current iteration number; For individual learning factors; For individual random factors; The historical optimal value of the i-th cavity structure parameter particle in the k-th iteration; As a global learning factor; It is a global random variable; The particle swarm is the historical best for the cavity structure parameters in the k-th iteration; This represents the position of the i-th particle in the k-th iteration; It represents the position of the i-th particle in the (k+1)-th iteration.

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