Multi-node negative Poisson's ratio concave honeycomb structure and design method thereof

Abstract

The invention discloses a multi-node negative Poisson's ratio concave honeycomb structure and a design method thereof, relates to the field of metamaterials and protection structures, and has excellent energy absorption and impact resistance. The multi-node-like negative Poisson's ratio concave honeycomb structure comprises a plurality of equivalent quarter structure cell elements which are periodically arranged. The cell elements can be discretized into a plurality of nodes, and optimal design of the structure can be achieved through optimal arrangement of node coordinates. And the optimization model realizes optimization of the Poisson's ratio by solving node coordinates. By means of the design method, accurate optimization and digital design of the structural cell elements in various complex application scenes can be achieved. And multifunctional and customized design can be realized by regulating and controlling material attributes, vertex coordinates, the number of nodes and the cross section of the rod piece. The optimized negative Poisson's ratio characteristic realized by the invention shows a huge application prospect in the fields of energy absorption buffering and impact protection, and is particularly suitable for the engineering fields of aerospace, traffic transportation, civil engineering and the like.

Description

Technical Field

[0001] The invention relates to the technical field of concave honeycomb structures, and in particular to a concave honeycomb structure with a multi-node negative Poisson's ratio and a design method thereof. Background Art

[0002] Honeycomb structures are widely used in aerospace, transportation and other fields due to their excellent mechanical properties such as specific stiffness, specific strength and high energy absorption. Reasonable design of the microstructure can make the honeycomb structure exhibit special properties such as negative Poisson's ratio, negative thermal expansion, and negative stiffness.

[0003] Negative Poisson's ratio honeycomb structures have received extensive attention in the field of engineering applications due to their unique deformation mode and excellent mechanical properties. On the one hand, structures with negative Poisson's ratio effect have great advantages in energy absorption due to their unique deformation behavior and mechanical properties. On the other hand, negative Poisson's ratio honeycomb structures have the characteristics of materials gathering inward when under pressure, increasing instantaneous density, and thus enhancing stiffness and toughness. When such structures are subjected to impact, materials gather at the damaged part to achieve the effect of filling or reducing the damaged opening, and are therefore widely used in the design of protective structures. In addition, as a typical porous structure, the unit cell of the negative Poisson's ratio honeycomb structure is highly designable, making lightweight and multifunctional integrated design possible. Performance customization and optimization can be achieved by adjusting the geometric parameters of the unit cell. However, the current negative Poisson's ratio honeycomb structure can only achieve mechanical performance improvements in the design space of specific geometric parameters, and there are still challenges in how to achieve mechanical performance optimization in a larger design space.

[0004] In summary, the negative Poisson's ratio honeycomb structure not only has a unique deformation mode, excellent energy absorption and impact resistance, but also shows great potential in multifunctional integration, and has received extensive attention in the field of engineering applications. As the requirements for structural performance in civil structures, mechanical engineering, aerospace and other engineering fields become increasingly complex, through reasonable mechanical design, research and development of negative Poisson's ratio honeycomb structures with larger design space and better performance will better meet the application needs of various scenarios. Summary of the invention

[0005] Technical problem: The present invention applies discretization method and stiffness matrix method to the design of negative Poisson's ratio concave honeycomb structure, and provides a multi-node negative Poisson's ratio concave honeycomb structure and its design method, which has better energy absorption, impact resistance and higher compression stiffness and strength.

[0006] Technical solution:

[0007] The multi-node negative Poisson's ratio concave honeycomb structure of the present invention comprises a plurality of periodically arranged equivalent quarter structural cells, each of which comprises two boundary rod units and a plurality of end-to-end connected internal rod units.

[0008] Furthermore, any equivalent quarter structure cell, including the boundary vertex N A 、N B 、N C 、N D And the discretized internal nodes N1~N n , and its corresponding boundary bar unit is N A N B and N C N D , the internal rod unit is N B N1, N1N2, N2N3 to N n N C ;

[0009] Boundary Vertex N C The coordinates of the vertex N are defined as (0, 0). A and N B The coordinates are expressed as (x A ,y A ) and (x B ,y B ), bar element N A N B and N C N D Parallel and of equal length, vertex N D The coordinates are expressed as (x B -x A , 0), internal nodes N1~N n The coordinates are expressed as (x i ,y i ), where i represents the internal node number, x i The value range is (x A , x B -x A ), y i The value range is (0, y A ).

[0010] Furthermore, the y-coordinate y of the internal node of each equivalent quarter structure cell is i It decreases monotonically as the node number increases.

[0011] Furthermore, by presetting the vertex coordinates (x A ,y A 、x B ,y B), the number of nodes n, and establish a constrained optimization model to solve the optimal Poisson's ratio and the corresponding node coordinates (x i ,y i ), the constrained optimization model is:

[0012] minimize 12 (x1,x2···x n ,y1,y2···y n )

[0013]

[0014] where u B and v B Represents vertex N B The displacement in the x and y directions of the global coordinate system.

[0015] The present invention also provides a design method for a multi-node negative Poisson's ratio concave honeycomb structure, comprising the following steps:

[0016] Step 1: Apply constraints on the boundaries of the equivalent quarter structural cell to keep the unit deformation consistent with the structural deformation;

[0017] Step 2: Using the stiffness matrix method of the Euler beam element, the stiffness matrix of the equivalent quarter structure cell is established with the coordinates of each internal node of the equivalent quarter structure cell;

[0018] Step 3: At the vertex N of the equivalent quarter structure cell B Assuming vertical load, the boundary vertex displacement and equivalent Poisson's ratio are solved according to the stiffness matrix;

[0019] Step 4: According to the relationship between the obtained Poisson's ratio and the node coordinates, a constrained optimization model is established and solved to obtain the optimal negative Poisson's ratio and the corresponding node coordinates.

[0020] Furthermore, in step 1, the equivalent quarter structure cell, including the boundary vertex N A 、N B 、N C 、N D And the discretized internal nodes N1~N n , and its corresponding boundary bar unit is N A N B and N C N D , the internal rod unit is N B N1, N1N2, N2N3 to N n N C ; Vertex N C The x and y displacements of vertex N are constrained to be 0. B and N CThe rotational degrees of freedom are constrained to 0.

[0021] Furthermore, in step 2, given the material properties and member section properties, the local stiffness matrix of each internal member element is expressed as K e It means that by establishing a global coordinate system and introducing the coordinate transformation matrix T, the stiffness matrix K of the unit in the global coordinate system is obtained. g , by calculating the N B N1, N1N2, N2N3 to N n N C The stiffness matrix of the equivalent quarter structure cell is assembled to obtain the total stiffness matrix K total .

[0022] Furthermore, in step 3, the equivalent Poisson's ratio is expressed as

[0023]

[0024] where u B and v B Represents vertex N B The displacement in the x and y directions of the global coordinate system.

[0025] Furthermore, in step 4, the constrained optimization model is recorded as:

[0026] minimize 12 (x1,x2···x n ,y1,y2···y n )

[0027]

[0028] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0029] (1) Efficient structural design: Based on a multi-node concave honeycomb structure, the present invention discretizes node coordinates to achieve accurate prediction of the Poisson's ratio effect. Combined with the constraint optimization model, the efficient design of the maximum negative Poisson's ratio configuration is achieved to meet the application requirements in the engineering field.

[0030] (2) The design method is widely applicable: The design method proposed in the present invention is applicable to various types of concave honeycomb structures and has good applicability to complex multi-node configurations. By adjusting the geometric parameters, the optimization model can be easily reconstructed to achieve digital solution and optimization of honeycomb structures of different sizes, node numbers and rod cross-sections.

[0031] (3) Multi-modal customized design: The method of the present invention can achieve controllable negative Poisson's ratio characteristics by adjusting the distribution of each node, and realize customized reverse design of structural units based on actual scene applications.

[0032] (4) Combination of lightweight and structural performance: The concave honeycomb structure proposed in the present invention is a typical porous structure with the characteristics of light weight and highly designable structural cells, thus achieving lightweight design. By controlling the distribution of cell nodes, the material usage of the structure can be further reduced, which is beneficial to manufacturing and transportation in actual engineering.

[0033] (5) Excellent energy absorption and protection performance: The negative Poisson's ratio structure proposed in the present invention has an optimized negative Poisson's ratio and has good energy absorption and buffering characteristics when deformed. It is an ideal material for preparing the core of a sandwich structure and has broad engineering application prospects, especially suitable for the design requirements of efficient energy absorption and impact protection. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 The present invention provides a discretization process of an equivalent quarter structural cell of the concave honeycomb structure.

[0035] Figure 2 The invention provides the boundary condition setting of the equivalent quarter structure cell and the conversion of the local coordinate system and the global coordinate system in the stiffness matrix method.

[0036] Figure 3 The optimized design result of Example 1 of the present invention and the corresponding optimized Poisson's ratio.

[0037] Figure 4 The figure is the curve of Poisson's ratio changing with strain and the finite element result of structural deformation under tensile load of Example 1 of the present invention.

[0038] Figure 5 The optimized design result of Example 2 of the present invention and the corresponding optimized Poisson's ratio.

[0039] Figure 6 The stress-strain curve and finite element results of the structural deformation of Example 2 of the present invention under compressive load. DETAILED DESCRIPTION

[0040] The present invention will be further described below with reference to specific embodiments and accompanying drawings:

[0041] The multi-node negative Poisson's ratio concave honeycomb structure provided by the present invention is composed of Figure 1 Each equivalent quarter structure cell consists of N boundary vertices. A 、N B 、N C 、N D And the discretized internal nodes N1~N n The corresponding boundary bar unit is N A N Band N C N D , the internal rod element is N B N1, N1N2, N2N3 to N n N C .

[0042] In the present invention, in order to optimize the structure to achieve negative Poisson's ratio, it is necessary to accurately solve the equivalent Poisson's ratio of the multi-node concave honeycomb structure. C The coordinates of the vertex N are defined as (0, 0). A and N B It can be expressed by coordinates as (x A ,y A ) and (x B ,y B ), where, due to N A and N B are on the same level, so

[0043] y A =y B

[0044] Since the member element N A N B and N C N D Parallel and of equal length, with vertex N C and N D On the same horizontal line, vertex N D It can be expressed by coordinates as (x B -x A , 0). Internal nodes N1~N n It can be expressed by coordinates as (x i ,y i ), where i represents the internal node number, x i The value range is (x A , x B -x A ), y i The value range is (0, y A ). The y-coordinate y of the internal node of each equivalent quarter structure cell i It decreases monotonically as the node number increases.

[0045] Furthermore, the stiffness matrix method of the Euler beam element can integrate rigid constraints and consider bending deformation to solve the Poisson's ratio of the structure. The plane beam element has two nodes and six degrees of freedom in the local coordinate system, where each degree of freedom corresponds to a force or moment. The displacement and load equations of the plane beam element at each node are

[0046] K e ·[δxi δ yi θ i δ xj δ yj θ j ] T =[F xi F yi M i F xj F yj M j ] T

[0047] Where K e represents the local stiffness matrix of the plane beam element, F xi represents the load applied to node i in the x direction, F yi represents the load applied to node i in the y direction, M i represents the bending moment applied to node i; δ xi Indicates that in F xi The displacement of node i in the x direction under the action, δ yi Indicates that in F yi The displacement of node i in the y direction under the action, θ i Indicates that in M i The local coordinate system takes the center of the beam element as the origin, the length direction as the x-axis, and the thickness direction as the y-axis. C is the origin, vector The x-axis is the global coordinate system in the positive direction of the x-axis. The angle between the x-axis of the local coordinate system and the x-axis of the global coordinate system is defined as α, and the coordinate transformation matrix is ​​introduced.

[0048]

[0049] The stiffness matrix of the unit in the global coordinate system can be obtained

[0050] K g =T -1 K e T

[0051] The relationship between the local coordinate system and the global coordinate system is as follows Figure 2 shown.

[0052] Furthermore, by combining the units in the global coordinate system, namely N B N1, N1N2, N2N3 to N n N C The stiffness matrix of the equivalent quarter structural cell can be obtained as

[0053] F=K total ·U

[0054] Where F is the load vector, each component of which represents the load applied to each node, K total is the total stiffness matrix of the equivalent quarter structural cell, and U is the displacement vector, where each component represents the displacement of each node.

[0055] Constraints are imposed on the equivalent quarter structure cell to maintain consistency between the equivalent deformation and the lattice structure deformation. Specifically, the vertex N C The x and y displacements of vertex N are constrained to be 0. B and N C The rotational freedom is constrained to 0. At vertex N B Assuming that a load in the y direction is applied at , U can be solved. The equivalent Poisson's ratio of the structure under the condition of small elastic deformation can be expressed as

[0056]

[0057] where u B and v B Represents vertex N B The displacement in the x and y directions of the global coordinate system.

[0058] Based on the above, the equivalent Poisson's ratio v can be established. 12 The dependent variable is the node coordinate (x i ,y i ) is a function of the independent variable, and a constrained optimization model is established to optimize the Poisson's ratio of the structure.

[0059] In summary, the constrained optimization model can be written as:

[0060] minimize 12 (x1,x2···x n ,y1,y2···y n )

[0061]

[0062] Furthermore, the preset material properties (elastic modulus, Poisson's ratio), bar cross section, vertex coordinates (x A ,y A 、x B ,y B ) and the number of nodes n, the optimal Poisson's ratio and the corresponding node coordinates (x i ,y i ).

[0063] Example 1

[0064] Figure 3The elastic modulus of the material is given as 743.9MPa, Poisson's ratio is 0.3, N A 、N B 、N C 、N D The coordinates are (-1.17, 10.83), (2.83, 10.83), (0, 0) and (4, 0) (unit: mm), the number of nodes is 8 and the unit section is 0.8 mm thick and 3 mm wide. In Example 1, the optimization result is that the equivalent Poisson's ratio of the structure is -9.96.

[0065] Figure 4 The simulation results of the change of equivalent Poisson's ratio of Example 1 under tensile load using finite element software are shown in Figure 1. The finite element model uses beam elements, the y-direction displacement is fixed at the bottom of the model, and a vertical tensile load is applied to the top. The numerical results show that the equivalent Poisson's ratio of the structure in the elastic stage is about -9.97, which is consistent with the prediction results of the optimization model. This shows that the proposed design method has the ability of accurate optimization.

[0066] Example 2

[0067] Based on Example 1, Figure 5 The elastic modulus of the material is given as 743.9MPa, Poisson's ratio is 0.3, N A 、N B 、N C 、N D The coordinates are (-1.17, 6.83), (2.83, 6.83), (0, 0) and (4, 0) (unit: mm), the number of nodes is 8 and the unit section is 0.8 mm thick and 3 mm wide. In Example 2, the optimization result is that the equivalent Poisson's ratio of the structure is -3.78.

[0068] Figure 6 The simulation results of the change of Poisson's ratio of the stress-strain curve of Example 2 under compressive load using finite element software are shown in Figure 2. The finite element model uses solid units, and a rigid plate is fixed at the bottom and top of the model respectively. The bottom plate is subject to fixed constraints, and the top plate is subject to vertical compressive load. The numerical results show that under compressive load, the material of the structure shrinks inward, showing an obvious negative Poisson's ratio effect, the compression stiffness and strength are improved, and it has good energy absorption and buffering effects.

[0069] In summary, the multi-node negative Poisson's ratio concave honeycomb structure proposed in the present invention has a negative Poisson's ratio deformation mode. Utilizing the optimized negative Poisson's ratio characteristics, the proposed optimized structure has better energy absorption, impact resistance, and higher compression stiffness and strength.

[0070] The present invention is not limited to the embodiments described above. The above description of the specific embodiments is intended to describe and illustrate the technical solution of the present invention. The above specific embodiments are merely illustrative and not restrictive. Without departing from the scope of the present invention and the scope of protection of the claims, a person of ordinary skill in the art can also make many forms of specific changes under the guidance of the present invention, which all fall within the scope of protection of the present invention.

Claims

1. A multi-node negative Poisson's ratio concave honeycomb structure, characterized in that: The structure includes a plurality of periodically arranged equivalent quarter structural cells, each of which includes two boundary rod units and a plurality of end-to-end connected internal rod units.

2. The multi-node negative Poisson's ratio concave honeycomb structure according to claim 1, characterized in that: Any equivalent quarter structure cell, including the boundary vertex N A 、N B 、N C 、N D And the discretized internal nodes N1~N n , and its corresponding boundary bar unit is N A N B and N C N D , the internal rod unit is N B N1, N1N2, N2N3 to N n N C ; Boundary Vertex N C The coordinates of the vertex N are defined as (0, 0). A and N B The coordinates are expressed as (x A ,y A ) and (x B ,y B ), bar element N A N B and N C N D Parallel and of equal length, vertex N D The coordinates are expressed as (x B -x A , 0), internal nodes N1~N n The coordinates are expressed as (x i ,y i ), where i represents the internal node number, x i The value range is (x A , x B -x A ), y i The value range is (0, y A ).

3. The multi-node negative Poisson's ratio concave honeycomb structure according to claim 2, characterized in that: The y-coordinate y of the internal node of each equivalent quarter structure cell i It decreases monotonically as the node number increases.

4. The multi-node negative Poisson's ratio concave honeycomb structure according to claim 3, characterized in that: By presetting the vertex coordinates (x A ,y A 、x B ,y B ), the number of nodes n, and establish a constrained optimization model to solve the optimal Poisson's ratio and the corresponding node coordinates (x i ,y i ), the constrained optimization model is: where u B and v B Represents vertex N B The displacement in the x and y directions of the global coordinate system.

5. The design method of the multi-node negative Poisson's ratio concave honeycomb structure according to claim 1, characterized in that: The following steps are involved: Step 1: Apply constraints on the boundaries of the equivalent quarter structural cell to keep the unit deformation consistent with the structural deformation; Step 2: Using the stiffness matrix method of the Euler beam element, the stiffness matrix of the equivalent quarter structural cell is established with the coordinates of each internal node of the equivalent quarter structural cell; Step 3: At the vertex N of the equivalent quarter structure cell B Assuming vertical load, the boundary vertex displacement and equivalent Poisson's ratio are solved according to the stiffness matrix; Step 4: According to the relationship between the obtained Poisson's ratio and the node coordinates, a constrained optimization model is established and solved to obtain the optimal negative Poisson's ratio and the corresponding node coordinates.

6. The design method of the multi-node negative Poisson's ratio concave honeycomb structure according to claim 5, characterized in that: In step 1, the equivalent of a quarter structure cell, including the boundary vertex N A 、N B 、N C 、N D And the discretized internal nodes N1~N n , and its corresponding boundary bar unit is N A N B and N C N D , the internal rod unit is N B N1, N1N2, N2N3 to N n N C ; Vertex N C The x and y displacements of vertex N are constrained to be 0. B and N C The rotational degrees of freedom are constrained to 0.

7. The design method of a multi-node negative Poisson's ratio concave honeycomb structure according to claim 6, characterized in that: In step 2, given the material properties and member cross-section properties, the local stiffness matrix of each internal member element is expressed as K e It means that by establishing a global coordinate system and introducing the coordinate transformation matrix T, the stiffness matrix K of the unit in the global coordinate system is obtained. g , by calculating the N B N1, N1N2, N2N3 to N n N C The stiffness matrix of the equivalent quarter structure cell is assembled to obtain the total stiffness matrix K total .

8. The design method of a multi-node negative Poisson's ratio concave honeycomb structure according to claim 7, characterized in that: In step 3, the equivalent Poisson's ratio is expressed as where u B and v B Represents vertex N B The displacement in the x and y directions of the global coordinate system.

9. The design method of a multi-node negative Poisson's ratio concave honeycomb structure according to claim 8, characterized in that: In step 4, the constrained optimization model is recorded as:

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