Design method of high-resilience honeycomb structure based on TPU

Abstract

The application discloses a design method of a high-rebound-performance honeycomb structure based on TPU, and is characterized by comprising the following steps: S1, adopting a topological optimization method to perform structure design, the size of a topological optimization design domain is consistent with the size of the honeycomb structure, the design domain is divided into a limited number of microstructure units, and the attribute of each unit is described by the position and relative density thereof; S2, taking the relative density of the unit as a design variable, introducing an equivalent elastic modulus model into the topological optimization model, thereby connecting the design variable with the in-plane mechanical performance as a target function; S3, finally, obtaining the numerical form of the optimization result, namely, the relative density matrix of the unit, through an optimization solving algorithm; and S4, on the basis of the discretization of the design space, performing finite element analysis on the honeycomb structure.

Description

Technical Field

[0001] This invention belongs to the field of honeycomb structure optimization design and additive manufacturing technology, specifically relating to a design method for a high-resilience honeycomb structure based on TPU. Background Technology

[0002] Honeycomb structures are widely used in various energy-absorbing components due to their excellent energy absorption capacity. Honeycomb structures made of ordinary engineering plastics are characterized by high stiffness and strong resistance to deformation, but their resilience is poor, making them prone to damage. Using TPU material to manufacture honeycomb structures can enhance resilience, but stiffness will decrease, and resistance to deformation will weaken. Topology optimization is frequently used in structural design to enhance certain structural properties; for honeycomb structures, stiffness is often used as the objective function.

[0003] Topology optimization, as a mature structural design method, optimizes material distribution within a given region based on load conditions, constraints, and performance indicators to arrive at the optimal material distribution scheme. Compared to traditional structural design methods, topology optimization designs the structure according to requirements, and the results are initially verified during the design process, usually yielding better structural design results. The patent "A Method, Device, and Storage Medium for Optimizing Intra-Shape Self-Similar Cellular Structures, Application No.: CN201910691240.3" designs the individual cells of a cellular structure using topology optimization, resulting in an intra-shape self-similar cellular structure and optimizing specific stiffness. However, because this optimization design only targets the individual cells, the overall structure directly uses combinations of identical cells, making it difficult to say that the overall performance of the cellular structure is optimal. Furthermore, most topology optimization designs for cellular structures focus only on a single performance characteristic, neglecting other excellent mechanical properties of cellular structures, such as resilience. In practical applications, greater stiffness means stronger resistance to deformation, and a higher resilience modulus means more reuse and cost savings. Summary of the Invention

[0004] The purpose of this invention is to solve the above-mentioned problems and provide a honeycomb structure with both high stiffness and high resilience. The design method is based on TPU and uses TPU as the material to design the honeycomb structure, which is designed using a topology optimization method.

[0005] To solve the above-mentioned technical problems, the technical solution of the present invention is: 1. A design method for a high-resilience honeycomb structure based on TPU, comprising the following steps:

[0006] S1. The topology optimization method is used for structural design. The size of the topology optimization design domain is consistent with the size of the cellular structure. The design domain is divided into a finite number of micro-structural units. The properties of each unit are described by its position and relative density.

[0007] S2. Using the relative density of the elements as the design variable, the equivalent elastic modulus model is introduced into the topology optimization model, thereby linking the design variables with the in-plane mechanical properties as the objective function.

[0008] S3. Finally, the numerical form of the optimization result, namely the relative density matrix of the elements, is obtained through the optimization solution algorithm.

[0009] S4. Based on the spatial discretization of the design, perform finite element analysis on the honeycomb structure.

[0010] Furthermore, the topology optimization model in step S2 is as follows:

[0011]

[0012] Where C represents the structural compliance, which is the reciprocal of the stiffness and also the objective function; K represents the overall stiffness matrix of the structure; F represents the load vector; is the overall displacement vector corresponding to F; V represents the total volume of the structure; f represents the expected volume reduction percentage; V0 is the design area volume; x e v e u e With k e These represent the relative density of the element, the volume of the element, the displacement vector of the element, and the stiffness matrix of the element, respectively.

[0013] Furthermore, the calculation method of the mechanical performance equivalent model is as follows: reinforcing nodes are introduced into the uniform honeycomb structure, and the equivalent elastic modulus model is obtained by fitting the finite element simulation analysis results and data of the in-plane mechanical properties of the node-reinforced honeycomb to obtain a model that is more suitable for non-uniform honeycomb structures than the traditional equivalent model.

[0014] Further, based on the correction value of the concentric circle radius of the cell, it is determined whether the microstructure unit in step S1 is located inside the cell; the average value of the relative density of the cells in the cell is taken, the relative density matrix of the cells is transformed into the relative density matrix of the cells, and CAD parametric modeling is performed using the relative density of the cells to obtain a variable density cell structure model.

[0015] Furthermore, the variable density honeycomb structure is manufactured using TPU material through fused deposition modeling technology.

[0016] Furthermore, based on the molding accuracy of the equipment, the minimum allowable feature size in the honeycomb structure is calculated, and the minimum feature size is mapped to the value range of the design variables in step S2 to ensure the manufacturability of the design results.

[0017] Furthermore, step S4 also includes the following sub-steps:

[0018] S41. Apply load and displacement constraints to the unit nodes according to the actual working conditions of the problem and the optimization effect to be achieved.

[0019] S42. Input material properties, calculate the shape function matrix, and establish the element stiffness matrix;

[0020] S43. Assemble the element stiffness matrices into a global stiffness matrix;

[0021] S44. Solve the system of linear equations based on the equilibrium equations and physical equations to obtain the displacement matrix of the nodes;

[0022] S45. Calculate the overall displacement and compliance through the displacement field.

[0023] The beneficial effects of this invention are:

[0024] 1. The design method for a high-resilience honeycomb structure based on TPU provided by this invention is more suitable for calculating the equivalent elastic modulus model of non-uniform honeycomb structures. In non-uniform honeycomb structures, some cells have relatively large nodes, and the effect of these nodes cannot be ignored. To incorporate the influence of node size on the mechanical properties of the honeycomb structure, the nodes of the uniform honeycomb are enlarged by different ratios to obtain multiple node-reinforced honeycombs with different node sizes. Finite element analysis is performed on these node-reinforced honeycombs to calculate their equivalent elastic modulus, determining the relationship between the equivalent elastic modulus and node size and relative density.

[0025] 2. This invention establishes a circle with a size close to that of the honeycomb cell, using the center of the honeycomb cell as the center, and considers the cells inside the circle as being inside the honeycomb cell. Compared to determining whether a cell is inside a cell by its envelope, this method has the advantages of simple operation, significantly improved computational efficiency, and accurate results at low relative densities.

[0026] 3. This invention proposes to use TPU material in the manufacture of variable density honeycomb structures to enhance the resilience of the honeycomb structures.

[0027] 4. The topology optimization model of this invention uses structural stiffness as the objective function to reduce deformation under load while limiting structural weight or material usage to a lower standard. TPU material is one of the most elastic materials in additive manufacturing, and this invention uses TPU to improve the springback after load unloading. The additive manufacturing method used in this invention is suitable for manufacturing complex structures such as variable-density honeycomb structures and can also accelerate product design and manufacturing cycles. The high-resilience honeycomb structure based on TPU proposed in this invention enhances stiffness and resilience by addressing both deformation under load and springback after unloading, thereby improving its resistance to deformation. Attached Figure Description

[0028] Figure 1This is a manufacturing result diagram of the design method of a high-resilience honeycomb structure based on TPU according to the present invention;

[0029] Figure 2 This is a schematic diagram of the cell element of the node-enhanced honeycomb of the present invention;

[0030] Figure 3 These are the loads and boundary constraints applied to the initial uniform honeycomb structure in this embodiment of the invention;

[0031] Figure 4 This refers to the compliance change process during the topology optimization iteration process of this invention;

[0032] Figure 5 This is the relative density distribution of the cells as a result of the topology optimization of this invention, represented by a grayscale image. Detailed Implementation

[0033] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0034] like Figures 1 to 5 As shown, the present invention provides a design method for a high-resilience honeycomb structure based on TPU, comprising the following steps:

[0035] S1. The topology optimization method is used for structural design. The size of the topology optimization design domain is consistent with the size of the cellular structure. The design domain is divided into a finite number of micro-structural units. The properties of each unit are described by its position and relative density.

[0036] Based on the correction value of the concentric circle radius of the honeycomb cell, it is determined whether the microstructure unit in step S1 is located inside the honeycomb cell. The average value of the relative density of the cells within the honeycomb cell is taken, and the relative density matrix of the cells is transformed into the relative density matrix of the cells. CAD parametric modeling is performed using the relative density of the cells to obtain a variable density honeycomb structure model. The variable density honeycomb structure is manufactured using TPU material through fused deposition modeling technology.

[0037] In this step, the structural design process involves first calculating the equivalent elastic modulus model, and then using topology optimization and numerical mapping to obtain a variable density honeycomb structure.

[0038] The equivalent elastic modulus model for this step is obtained through the following steps:

[0039] S11. Model a uniform hexagonal honeycomb structure with a length of 90mm, a height of 60mm, a thickness of 15mm, an inscribed circle diameter of 7.5mm, and a relative density of v = 0.35.

[0040] S12. Perform static compression simulation on a uniform honeycomb in finite element simulation software to obtain the relationship between external force and in-plane axial deformation, and calculate the equivalent elastic modulus E.

[0041] S13. Change the value of v and repeat steps (a) and (b) until more than 5 sets of data are obtained;

[0042] S14. Obtain the equivalent elastic modulus model of the uniform honeycomb through numerical fitting.

[0043] S15. Enlarge the node size of the honeycomb to r to obtain a node-reinforced honeycomb. The cell shape varies depending on the size of r. Figure 2 As shown.

[0044] S16. Based on the structural characteristics of the node-reinforced honeycomb, obtain the relationship between relative density v and cell wall length l, cell wall thickness t, and node size r:

[0045] S17. Perform static compression simulation on the nodal reinforced honeycomb in finite element simulation software to obtain the relationship between external force and in-plane axial deformation, and calculate the equivalent elastic modulus E.

[0046] S18. Calculate the equivalent elastic modulus model of the nodal-reinforced honeycomb structure using numerical fitting:

[0047] E = f(v, r).

[0048] The steps to obtain a variable-density honeycomb structure using topology optimization and numerical mapping are as follows:

[0049] S21. Establish a topology optimization model based on the SIMP interpolation model:

[0050]

[0051] stKU=F

[0052]

[0053] 0 < x min ≤x e ≤x max e = 1, 2, ..., n

[0054] Where C represents the structural compliance, which is the reciprocal of the stiffness and also the objective function; K represents the overall stiffness matrix of the structure; F represents the load vector; is the overall displacement vector corresponding to F; V represents the total volume of the structure; f represents the expected volume reduction percentage; V0 is the design area volume; x e v e u e ke and ke represent the element relative density, element volume, element displacement vector, and element stiffness matrix, respectively; ρ is the penalty factor.

[0055] S22. Discretize the design space into 90×60 microstructure units. The properties of each unit are described by its position in the design space and the relative density x of the units.

[0056] S23. Apply nodal forces to the unit nodes of the first layer at the top of the cellular structure design domain, and apply fixed constraints to the unit nodes at the bottom.

[0057] S24. Finite element analysis is used to obtain the displacement matrix of the nodes. The overall displacement U and compliance C are calculated through the displacement field.

[0058] S25. Using the OC optimization criterion method, iteratively design the variable v and compare the value of the flexibility C until the value of the flexibility C no longer decreases. At this point, the relative density matrix of the elements is the result of the topology optimization.

[0059] S26. Based on the positional relationship between cells and units, convert the relative density of units to the relative density of cells. Assign weights of 1 and 0 to units based on the distance between the cell center and the unit center:

[0060]

[0061] Then, based on the distance weights, the mean relative density of cells within the cell is calculated to obtain the cell relative density:

[0062]

[0063] In the formula, wk(m) is the distance weight of element m with respect to cell k; Dk is the distance between element m and cell k; R is the radius of the concentric circle of the cell; h is the correction factor of the radius of the concentric circle, which is to ensure that the elements contained in the circle with radius h·R can correctly reflect the size and shape of the cell; ρc(k) is the relative density of cell k; x(m) is the relative density of element m; ne is the total number of microstructure elements in the design space.

[0064] S27. Import the cell relative density data into the modeling software UG and parametrically model the variable density honeycomb structure.

[0065] The variable density honeycomb structure in this step is manufactured using the FDM method, and the steps are as follows:

[0066] S31. Based on the molding accuracy of the FDM equipment, test and calculate the minimum feature dimensions, including the minimum wall thickness tmin and the minimum pore size dmin for variable density honeycomb structures.

[0067] S32. The allowable range of relative element density is determined by the minimum feature size:

[0068]

[0069] In the formula, xmin and xmax represent the minimum and maximum relative densities of cells allowed in manufacturing, respectively; ρc(max) and ρc(min) represent the minimum and maximum relative densities of cells allowed, respectively; tmin is the minimum allowable wall thickness; dmin is the minimum allowable pore size; and l is the cell wall length.

[0070] S33. Introduce the allowable range of relative unit densities as a manufacturing constraint into the topology optimization model.

[0071] S34. Set the printing temperature to 220°C, which is slightly higher than the melting temperature of TPU. Then slice the variable density honeycomb structure model to complete the manufacturing process.

[0072] The mechanical properties of the variable-density honeycomb structure were evaluated through mechanical tests, which consisted of two parts: a uniaxial compression test to assess its resistance to deformation under load, and a uniaxial compression followed by unloading to assess its resilience. The test speed for both tests was 2 mm / min.

[0073] Based on the results of uniaxial compression tests, the compressive stiffness of the variable-density honeycomb structure increased from 60.43 N / mm in the initial uniform honeycomb structure to 89.63 N / mm, an improvement of 48.32% compared to before optimization. In the springback test, the variable-density honeycomb structure was 1.178 mm short of fully springing back to its initial height, with a springback rate of 92.15%. The results indicate that this invention significantly improves the mechanical properties of the honeycomb structure, and due to the good coordination of each component, the overall design and manufacturing process is highly efficient.

[0074] S2. Using the relative density of the elements as the design variable, the equivalent elastic modulus model is introduced into the topology optimization model, thereby linking the design variables with the in-plane mechanical properties as the objective function.

[0075] Based on the molding accuracy of the equipment, the minimum allowable feature size in the honeycomb structure is calculated, and the minimum feature size is mapped to the value range of the design variables in step S2 to ensure the manufacturability of the design results.

[0076] The topology optimization model in step S2 is as follows:

[0077]

[0078] stKU=F

[0079]

[0080] 0 < x min ≤x e ≤x max e = 1, 2, ..., n;

[0081] Where C represents the structural compliance, which is the reciprocal of the stiffness and also the objective function; K represents the overall stiffness matrix of the structure; F represents the load vector; is the overall displacement vector corresponding to F; V represents the total volume of the structure; f represents the expected volume reduction percentage; V0 is the design area volume; x e v e u e With k e These represent the relative density of the element, the volume of the element, the displacement vector of the element, and the stiffness matrix of the element, respectively.

[0082] S3. Finally, the numerical form of the optimization result, namely the relative density matrix of the elements, is obtained through the optimization solution algorithm.

[0083] S4. Based on the spatial discretization of the design, perform finite element analysis on the honeycomb structure.

[0084] Step S4 further includes the following sub-steps:

[0085] S41. Apply load and displacement constraints to the unit nodes according to the actual working conditions of the problem and the optimization effect to be achieved.

[0086] S42. Input material properties, calculate the shape function matrix, and establish the element stiffness matrix;

[0087] S43. Assemble the element stiffness matrices into a global stiffness matrix;

[0088] S44. Solve the system of linear equations based on the equilibrium equations and physical equations to obtain the displacement matrix of the nodes;

[0089] S45. Calculate the overall displacement and compliance through the displacement field.

[0090] The optimization model is solved using the OC optimization criterion method. The iteration direction and termination condition are determined by the finite element analysis results corresponding to each iteration. Specifically, the iteration direction is determined by the first derivative of the compliance with respect to the relative density of the elements, i.e., the sensitivity. The iteration terminates when the difference in the compliance between two consecutive iterations is less than a given value, and the relative density matrix of the elements at this point is the result of topology optimization.

[0091] The calculation method of the mechanical property equivalent model is as follows: reinforcing nodes are introduced into the uniform honeycomb structure, and the equivalent elastic modulus model is obtained by fitting the finite element simulation analysis results and data of the in-plane mechanical properties of the node-reinforced honeycomb to obtain a model that is more suitable for non-uniform honeycomb structures than the traditional equivalent model.

[0092] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A design method for a high-resilience honeycomb structure based on TPU, characterized in that, Includes the following steps: S1. The topology optimization method is used for structural design. The size of the topology optimization design domain is consistent with the size of the cellular structure. The design domain is divided into a finite number of micro-structural units. The properties of each unit are described by its position and relative density. S2. Using the relative density of the elements as the design variable, the equivalent elastic modulus model is introduced into the topology optimization model, thereby linking the design variables with the in-plane mechanical properties as the objective function. S3. Finally, the numerical form of the optimization result, namely the relative density matrix of the elements, is obtained through the optimization solution algorithm. Based on the correction value of the concentric circle radius of the cell, determine whether the microstructure unit in step S1 is located inside the cell; take the average value of the relative density of the cells in the cell, convert the relative density matrix of the cells into the relative density matrix of the cells, and use the relative density of the cells to perform CAD parametric modeling to obtain the variable density cell structure model. S4. Based on the spatial discretization of the design, perform finite element analysis on the honeycomb structure; The calculation method of the equivalent elastic modulus model is as follows: reinforcing nodes are introduced into the uniform honeycomb structure, and the equivalent elastic modulus model is obtained by fitting the finite element simulation analysis results and data of the in-plane mechanical properties of the node-reinforced honeycomb to obtain an equivalent elastic modulus model that is more suitable for non-uniform honeycomb structures than the traditional equivalent model.

2. The design method of a high-resilience honeycomb structure based on TPU according to claim 1, characterized in that: The topology optimization model in step S2 is as follows: ； Where C represents the structural compliance, which is the reciprocal of the stiffness and also the objective function; K represents the overall stiffness matrix of the structure; F represents the load vector; U is the overall displacement vector corresponding to F; V represents the total volume of the structure; f represents the expected volume reduction percentage; V0 is the design area volume; x e v e u e With k e These represent the relative density of the element, the volume of the element, the displacement vector of the element, and the stiffness matrix of the element, respectively.

3. The design method of a high-resilience honeycomb structure based on TPU according to claim 1, characterized in that: A variable-density honeycomb structure manufactured using TPU material through fused deposition modeling (FDM) technology.

4. The design method of a high-resilience honeycomb structure based on TPU according to claim 1, characterized in that: Based on the molding accuracy of the equipment, the minimum allowable feature size in the honeycomb structure is calculated, and the minimum feature size is mapped to the value range of the design variables in step S2 to ensure the manufacturability of the design results.

5. The design method of a high-resilience honeycomb structure based on TPU according to claim 1, characterized in that, Step S4 further includes the following sub-steps: S41. Apply load and displacement constraints to the unit nodes according to the actual working conditions of the problem and the optimization effect to be achieved. S42. Input material properties, calculate the shape function matrix, and establish the element stiffness matrix; S43. Assemble the element stiffness matrices into a global stiffness matrix; S44. Solve the system of linear equations based on the equilibrium equations and physical equations to obtain the displacement matrix of the nodes; S45. Calculate the overall displacement and compliance through the displacement field.

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