A method for enhancing stiffness of lattice structures based on multi-scale topology optimization

Abstract

The present invention provides a method for enhancing the stiffness of a lattice structure based on multi-scale topological optimization, and belongs to the technical field of structural design. First, a macroscopic model of the lattice structure is established, a unit cell model of the lattice structure is established, and the unit cell as a whole is divided into an optimized area and a non-optimized area; secondly, a displacement coupling relationship between the macroscopic model and the unit cell model is established to complete the establishment of the multi-scale model of the lattice structure; finally, an optimization solver is used to optimize the multi-scale model of the lattice structure, and the optimization result is reconstructed to obtain a full-size lattice structure model. The present invention can realize the rapid optimization of the lattice structure by establishing a multi-scale model of the lattice structure, and effectively improve the optimization efficiency of the lattice structure; by dividing the unit cell as a whole into an optimized area and a non-optimized area, any lattice structure can be designed for stiffness enhancement without establishing a theoretical model of the lattice structure, which is easy to implement.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural design, and relates to a lattice structure stiffness enhancement design method, in particular to a lattice structure stiffness enhancement method based on multi-scale topology optimization. Background Art

[0002] With the development of science and technology, the fields of aerospace, machinery, and construction have put forward higher and higher requirements for lightweight design of structures. In order to meet the needs of lightweight design of the new generation of industrial equipment, people have developed a variety of new structures, among which the lattice structure has been widely used. The lattice structure is a periodic porous structure with high design flexibility. It has high specific strength and specific stiffness, is suitable for low-density structures, and can reduce weight by more than 70%.

[0003] Lattice structures are widely used, for example, in aerospace, automotive, medical, energy and other fields. They can be used as lightweight and high-strength materials in the manufacture of aircraft, automobiles and other vehicles to improve fuel efficiency and reduce environmental pollution. At the same time, lattice structures can also be used as biomaterials in artificial joints, implants and other medical devices to improve biocompatibility and mechanical properties. In addition, lattice structures can also be used in the energy field, such as in fuel cells, supercapacitors and other energy storage devices to improve energy storage density and release efficiency. Lattice structures can also be used in building materials, such as in building exterior walls, roofs and other structural parts to improve the thermal performance and wind and earthquake resistance of buildings.

[0004] Lattice structure is a new type of multifunctional material with advantages such as light weight, high strength, good thermal insulation and energy absorption properties. It has high application value and development potential in aerospace, automotive industry and bioengineering, and has received extensive attention. However, there are also some challenges in the design of lattice structures, such as how to design and optimize the topological shape and material composition of the lattice structure to obtain the best performance. Therefore, researchers and engineers need to continuously research and develop new lattice structure design technologies to meet the needs of different industries.

[0005] For a lattice structure with a single topological configuration, its mechanical properties are mainly related to the relative density. Therefore, in order to improve the mechanical properties of the lattice structure, its stress conditions must be comprehensively considered during design, and the lattice structure must be optimally laid out. The design of the lattice structure is mainly to design its unit cell, which refers to a small, repeated, representative volume element that captures the microstructural characteristics of the material. It is a basic unit that can be repeated periodically to build a larger structure or model.

[0006] The existing lattice structure design methods mainly use parametric modeling and theoretical derivation for unit cells. This design method requires modeling and analysis for different lattice structures and stress conditions, so the optimization efficiency is low, which is not conducive to the wide application of lattice structures. At the same time, due to the complexity of the lattice structure model, the optimization method based on direct numerical simulation (DNS) faces the problem of high computational cost. The literature Layout and material gradation in topology optimization of functionally graded structures: a global–local approach uses direct numerical simulation to design lattice structures. However, the method based on direct numerical simulation has the problems of large computational complexity and slow optimization speed in the optimization process. At the same time, due to its lightweight characteristics, the lattice structure often leads to insufficient stiffness. It is necessary to repeatedly optimize on the basis of the initial design to improve the stiffness of the lattice structure, which further reduces the design efficiency of the lattice structure. Therefore, it is necessary to establish a general and efficient optimization design method for lattice structures, enhance the stiffness of lattice structures, and further expand the application scope of lattice structures. Summary of the invention

[0007] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a design method for enhancing the stiffness of a lattice structure based on multi-scale topological optimization. The present invention can effectively improve the stiffness of the lattice structure, improve the mechanical properties of the lattice structure, and perform stiffness enhancement design for any lattice structure without establishing a theoretical model of the lattice structure, thereby achieving efficient design of the lattice structure.

[0008] In order to achieve the above object, the technical solution adopted by the present invention is:

[0009] A method for enhancing the stiffness of a lattice structure based on multi-scale topology optimization, wherein the method flow is as follows: Figure 1 As shown, the following steps are included:

[0010] Step (1) establishing a macroscopic model of the lattice structure;

[0011] Step (2) establishing a unit cell model of the lattice structure;

[0012] Step (3) divide the unit cell into an optimized area and a non-optimized area;

[0013] Step (4) establishing the displacement coupling relationship between the macro model and the unit cell model;

[0014] Step (5) optimizing the multi-scale model of the lattice structure using an optimization solver;

[0015] Step (6) Optimize the result reconstruction.

[0016] The specific implementation steps are as follows:

[0017] Furthermore, the step (1) establishes a macroscopic model of the lattice structure, specifically:

[0018] The overall model of the lattice structure is modeled. At this time, there is no need to establish the details of the lattice structure, only a homogenized macro model is needed. The macro model of the lattice structure is discretized by finite element method to obtain a macro unit. According to the force condition of the lattice structure, the boundary conditions of the macro model are established, including displacement boundary conditions and external force boundary conditions. Material parameters are assigned to the macro model.

[0019] Furthermore, the step (2) establishes a unit cell model of the lattice structure, specifically:

[0020] A unit cell model of the lattice structure is established at the integration point of the macro unit. In order to realize the topological optimization design of the lattice structure, the unit cell is modeled as a whole. It should be noted that in this step, the unit cell is also modeled except for the lattice structure. Therefore, the unit cell as a whole here refers to the square, rectangle, etc. in the two-dimensional model, and the cube, cuboid, etc. in the three-dimensional model. Then the unit cell model is discretized to obtain the micro unit, and the material parameters of the lattice structure are assigned to the unit cell model. The volume of the lattice structure before optimization can be obtained by summing the volumes of all unit cells.

[0021] Furthermore, the step (3) divides the unit cell into an optimized area and a non-optimized area, specifically:

[0022] The unit cell model in step (2) is divided into an optimized region and a non-optimized region, where the non-optimized region is a lattice structure. By defining the lattice structure in the unit cell as a non-optimized region, it is ensured that the region will not be deleted during the optimization process, thereby ensuring that the optimized structure contains the defined lattice structure. At the same time, the optimized region is the region other than the lattice structure in the unit cell. By defining this region as an optimized region, the material in this region can be selected during the optimization process, thereby enhancing the stiffness on the basis of the lattice structure.

[0023] Furthermore, the step (4) establishes a displacement coupling relationship between the macro model and the unit cell model, specifically:

[0024] Establish the displacement coupling relationship between the macro unit in step (1) and the micro unit in step (2), that is, the periodic boundary condition. The formula is as follows:

[0025] (1)

[0026] in, represents the node displacement of the unit cell, The nodal displacement of the macro unit, superscript , , and denote the node displacements on the right, left, top, and bottom sides of the unit cell, respectively. , are the horizontal and vertical coordinates in the plane rectangular coordinate system. and Respectively represent the unit cell in Direction and The length of the direction.

[0027] Based on step (1), step (2), step (3) and step (4), the establishment of the multi-scale model of the lattice structure is completed.

[0028] Furthermore, the step (5) uses an optimization solver to optimize the multi-scale model of the lattice structure, specifically:

[0029] The finite element method is used to solve the multi-scale model of the lattice structure and obtain the node displacement of the unit cell. , the sensitivity of the objective function is calculated by formula (2), and then the sensitivity of the lattice structure volume is calculated by formula (3), which are as follows:

[0030] (2)

[0031] (3)

[0032] in is the objective function for optimization, specifically the flexibility of the structure, Microscopic unit The relative density, is the penalty factor, is the stiffness matrix of the microelement, The relative density is The volume of the lattice structure, is the volume of the microscopic unit.

[0033] According to the calculated sensitivity information, a gradient-based optimization solver is used to obtain the optimized structure.

[0034] Furthermore, the gradient-based optimization solver in step (5) includes an optimal criterion method, a moving asymptote method, etc.

[0035] Furthermore, the optimization result reconstruction of step (6) is specifically as follows:

[0036] Since the optimized model only contains the lattice unit cell structure at the macro unit integration point, in order to obtain the optimized lattice model, the optimized result of step (5) is reconstructed to obtain the full-size lattice structure model.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] 1) The present invention establishes a multi-scale model of the lattice structure through steps (1) to (4), which can achieve rapid optimization of the lattice structure and effectively improve the optimization efficiency of the lattice structure;

[0039] 2) The present invention divides the unit cell into an optimized region and a non-optimized region through step (3), and can perform stiffness enhancement design on any lattice structure without establishing a theoretical model of the lattice structure, which is easy to implement. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 The figure is a flow chart of the method of the present invention.

[0041] Figure 2 It is a multi-scale model of the honeycomb lattice structure, where (a) is the macroscopic model of the honeycomb lattice structure; (b) is the unit cell model of the honeycomb lattice structure.

[0042] Figure 3 Optimization results of the method of the present invention and the traditional method, where (a) is the optimization result of the multi-scale model of the honeycomb lattice structure; (b) is the optimization result of the traditional direct numerical simulation.

[0043] Figure 4 The reconstruction results of the honeycomb lattice structure and the unoptimized honeycomb lattice structure, where (a) is the reconstruction result of the honeycomb lattice structure; (b) is the unoptimized honeycomb lattice structure.

[0044] Figure 5 The stress-strain curves and stiffness comparisons of different optimization results of the honeycomb lattice structure, where (a) is the stress-strain curves of different optimization results of the honeycomb lattice structure; (b) is the stiffness comparison of different optimization results of the honeycomb lattice structure.

[0045] Figure 6 It is a multi-scale model of the X-shaped lattice structure, where (a) is the macroscopic model of the X-shaped lattice structure; (b) is the X-1 shaped unit cell model of the lattice structure; (c) is the X-2 shaped unit cell model of the lattice structure; (d) is the X-3 shaped unit cell model of the lattice structure; and (e) is the X-4 shaped unit cell model of the lattice structure.

[0046] Figure 7These are the multi-scale model optimization results of the X-shaped lattice structure, where (a) is the multi-scale optimization result of the X-1 shaped unit cell model; (b) is the multi-scale optimization result of the X-2 shaped unit cell model; (c) is the multi-scale optimization result of the X-3 shaped unit cell model; and (d) is the multi-scale optimization result of the X-4 shaped unit cell model.

[0047] Figure 8 Force-displacement curves of different optimization results, where (a) is the force-displacement curve of different optimization results of the X-shaped lattice structure; (b) is the force-displacement curve of four optimization results of the X-shaped lattice structure. DETAILED DESCRIPTION

[0048] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0049] Embodiment 1: Rigidity enhancement design of honeycomb lattice structure.

[0050] The honeycomb lattice structure has a high energy absorption capacity under compressive load conditions and has been widely used in the industrial field. The figure below shows a two-dimensional model of a honeycomb lattice structure. The length, height and thickness of the model are W=56.4mm, H=80.4mm and T=25mm respectively. A uniformly distributed load of F=1N / m is applied to the top edge, and the bottom edge constrains the displacement in the y direction. At the same time, the node in the lower left corner is fixed along the x direction to avoid rigid body displacement in the horizontal direction.

[0051] The elastic modulus and Poisson's ratio of the material are taken as 1600MPa and 0.3 respectively. The macro model and the unit cell model are meshed using plane stress units, where the macro model is discretized into 2*2 macro units. The unit cell is a representative periodic distribution structure of the honeycomb structure, such as Figure 2 As shown. In order to retain the honeycomb structure during the optimization process, the dark green area in the figure is frozen, that is, the dark green area is not optimized. Taking the minimization of strain energy as the optimization goal, the retained volume fraction is 60%, and the optimization problem is solved by the optimal criterion method. When the strain energy change is less than 0.1%, the iteration is stopped and the optimization result is obtained.

[0052] The topology optimization results are as follows: Figure 3 As shown in (a), Figure 3(b) in the figure is the optimization result using the traditional direct numerical simulation (DNS) method. Since the optimization result is discretized, there are only 4 unit cells at the Gaussian point of a macro unit. Therefore, a reconstruction method is used to obtain a continuous geometric model, and a "copy" method is used to expand the unit cell to the entire model. A macro unit is divided into four parts, and then the density of each unit cell at the Gaussian integration point is extracted to fully fill a quarter of the area of ​​a macro unit. The reconstruction result is shown in Figure 4 In order to verify the improvement of structural stiffness after optimization, an unoptimized honeycomb lattice structure of the same volume is established, as shown in (a). Figure 4 As shown in (b) in .

[0053] Figure 5 (a) in the figure shows the compression results of three honeycomb structures, which can be divided into three stages: elastic stage, post-yield stage and densification stage. The honeycomb optimized by multi-scale topology optimization method and direct numerical simulation has higher elastic modulus and yield stress, which are greater than the unoptimized honeycomb lattice structure. Furthermore, the stiffness calculated by simulation and experiment is shown in Figure 5 As shown in (b) in the figure. The results of the structural stiffness designed by the method proposed in this patent are close to those by the direct numerical simulation method. However, the calculation time of the method proposed in this patent is only about 9% of that of the direct numerical simulation method. At the same time, the stiffness is increased by about 119% compared with the unoptimized honeycomb lattice structure.

[0054] Embodiment 2: Stiffness enhancement design of X-shaped lattice structure.

[0055] The multi-scale topology optimization method is used to enhance the stiffness of four X-shaped lattice structures. The geometric model before optimization and the four X-shaped lattice structures are shown in the figure. The overall height of the model is H=240mm, and the overall width is W=120mm. The macro structure is discretized into 4*8 macro units. The bottom of the model is simply supported, and the midpoint of the top is subjected to a vertical upward concentrated force of F=1N. The side length of the unit cell is w=h=5mm, and the internal dimensions of the unit cell l1 and l2 are 0.6mm and 0.3mm respectively. Similarly, the dark green area is frozen to produce an X-shaped lattice structure after structural topology optimization. With minimizing strain energy as the optimization goal, the retained volume fraction is 60%, and the optimal criterion method is used to solve the optimization problem. When the strain energy change is less than 0.1%, the iteration is stopped, and the optimization results of the four X-shaped lattice structures are obtained, as shown below. Figure 7 shown.

[0056] In order to verify the improvement effect of structural stiffness after optimization, direct numerical simulation was used to optimize the X-shaped lattice structure, and an unoptimized X-shaped lattice structure of the same volume was established. The tensile results of the lattice structures designed by the three methods are shown in Figure 2. Figure 8As shown in (a) in the figure. It can be seen from the figure that the stiffness results of the structure designed by the method proposed in this patent are close to those of the direct numerical simulation method, but the calculation time of the method proposed in this patent is only about 11% of that of the direct numerical simulation method. At the same time, the stiffness is improved by about 25% compared with the unoptimized X-shaped lattice structure.

[0057] Figure 8 (b) in Figure 1 compares four different X-shaped lattice structures, among which the X-3 structure has the best performance and the X-1 structure has the worst performance. When the displacement is 1 mm, the stiffness is X-3, X-4, X-2, and X-1 in descending order. Figure 8 The experimental results shown in (b) are highly consistent with the simulation results, indicating that the multi-scale topology optimization method proposed in this patent has high reliability and accuracy. This method can also be extended to the stiffness enhancement design of other lattice structures.

[0058] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for enhancing the stiffness of a lattice structure based on multi-scale topology optimization, characterized in that: The method for enhancing the rigidity of the lattice structure comprises the following steps: Step (1) establishing a macroscopic model of the lattice structure; Step (2) establishing a unit cell model of the lattice structure; Step (3) divides the unit cell into an optimized area and a non-optimized area; Step (4) establishes the displacement coupling relationship between the macro model and the unit cell model to complete the establishment of the multi-scale model of the lattice structure; specifically: The displacement coupling relationship between the macro unit in step (1) and the micro unit in step (2) is established, and the formula is as follows: Among them, u mic represents the node displacement of the unit cell, u mac The nodal displacement of the macro unit, the superscripts R, L, T and B represent the nodal displacements of the right, left, top and bottom sides of the unit cell, respectively; x and y are the horizontal and vertical coordinates in the plane rectangular coordinate system; L1 and L2 represent the length of the unit cell in the x and y directions, respectively; Step (5) optimizing the multi-scale model of the lattice structure using an optimization solver; Step (6) reconstructs the optimization result obtained in step (5) to obtain a full-size lattice structure model.

2. The method for enhancing the stiffness of a lattice structure based on multi-scale topology optimization according to claim 1, characterized in that: The step (1) establishes a macroscopic model of the lattice structure, specifically: The overall model of the lattice structure is modeled to establish a homogenized macroscopic model; the macroscopic model of the lattice structure is discretized by finite element method to obtain macroscopic units; according to the stress conditions of the lattice structure, the boundary conditions of the macroscopic model are established, including displacement boundary conditions and external force boundary conditions; and material parameters are assigned to the macroscopic model.

3. The method for enhancing stiffness of a lattice structure based on multi-scale topology optimization according to claim 2, characterized in that: The step (2) establishes a unit cell model of the lattice structure, specifically: A unit cell model of the lattice structure is established at the integration point of the macro unit. In order to realize the topological optimization design of the lattice structure, the unit cell is modeled as a whole. During the modeling, the parts of the unit cell except the lattice structure are also modeled to obtain the overall model of the unit cell. The overall model of the unit cell is discretized to obtain micro units, and the material parameters of the lattice structure are assigned to the overall model of the unit cell. The volume of all unit cells is summed to obtain the volume of the lattice structure before optimization.

4. The method for enhancing stiffness of a lattice structure based on multi-scale topology optimization according to claim 3 is characterized in that: The step (3) divides the unit cell into an optimized area and a non-optimized area, specifically: The unit cell model in step (2) is divided into an optimized region and a non-optimized region, wherein the non-optimized region is a lattice structure. By defining the lattice structure in the unit cell as a non-optimized region, it is ensured that the region where the lattice structure is located will not be deleted during the optimization process, thereby ensuring that the optimized structure contains the defined lattice structure. At the same time, the optimized region is the region other than the lattice structure in the unit cell. By defining the region other than the lattice structure as the optimized region, the material in the optimized region can be selected during the optimization process.

5. The method for enhancing stiffness of a lattice structure based on multi-scale topology optimization according to claim 1, characterized in that: In the step (5), an optimization solver is used to optimize the multi-scale model of the lattice structure, specifically: The finite element method is used to solve the multi-scale model of the lattice structure and obtain the node displacement u of the unit cell. mic , the sensitivity of the objective function is calculated by formula (2), and then the sensitivity of the lattice structure volume is calculated by formula (3), which are as follows: Among them, C is the optimization objective function, specifically the flexibility of the lattice structure, ρ e is the relative density of micro-unit e, p is the penalty factor, is the stiffness matrix of the micro-element, V ρ is the volume of the lattice structure when the relative density is ρ, V e is the volume of the microscopic unit; According to the calculated sensitivity information, a gradient-based optimization solver is used to obtain the optimized structure.

6. The method for enhancing the stiffness of a lattice structure based on multi-scale topology optimization according to claim 5, characterized in that: The gradient-based optimization solver in step (5) includes an optimal criterion method and a moving asymptote method.

Images