CN112149260A - Design method of three-dimensional impact-resistant negative Poisson's ratio structure - Google Patents

Design method of three-dimensional impact-resistant negative Poisson's ratio structure Download PDF

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CN112149260A
CN112149260A CN202011159250.1A CN202011159250A CN112149260A CN 112149260 A CN112149260 A CN 112149260A CN 202011159250 A CN202011159250 A CN 202011159250A CN 112149260 A CN112149260 A CN 112149260A
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孙雅洲
史小全
刘宏瑞
刘海涛
白临奇
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Abstract

一种三维抗冲击负泊松比结构的设计方法,属于负泊松比材料技术领域,具体包括以下步骤:步骤1:建立几何模型,提取结构参数;步骤2:推导相对密度、等效模量、泊松比、失效应力与结构参数的关系;步骤3:对模型进行压缩和冲击仿真,确定各结构参数的取值范围;步骤4:对结构参数进行处理,获得对吸能性能影响较大的结构参数,步骤5:利用多目标优化方法对结构参数进行优化;步骤6:计算初始峰应力和比吸能,若不符合要求则再次进入步骤5迭代循环,当达到要求,结束循环;步骤7:取优化后的结构参数构建模型,得到三维抗冲击负泊松比结构。通过本发明能够使获得的结构初始峰应力更低,比吸能更高。

Figure 202011159250

A design method for a three-dimensional impact-resistant negative Poisson's ratio structure belongs to the technical field of negative Poisson's ratio materials, and specifically includes the following steps: step 1: establishing a geometric model and extracting structural parameters; step 2: deriving relative density and equivalent modulus , Poisson’s ratio, the relationship between failure stress and structural parameters; Step 3: Perform compression and impact simulation on the model to determine the value range of each structural parameter; Step 4: Process the structural parameters to obtain a greater impact on the energy absorption performance Step 5: Use the multi-objective optimization method to optimize the structural parameters; Step 6: Calculate the initial peak stress and specific energy absorption, if it does not meet the requirements, enter the iterative cycle of Step 5 again, when the requirements are met, end the cycle; Step 7: Take the optimized structural parameters to build a model to obtain a three-dimensional impact-resistant negative Poisson's ratio structure. Through the present invention, the initial peak stress of the obtained structure can be lower and the specific energy absorption is higher.

Figure 202011159250

Description

一种三维抗冲击负泊松比结构的设计方法A design method for a three-dimensional impact-resistant structure with negative Poisson's ratio

技术领域technical field

本发明属于负泊松比材料技术领域,具体涉及一种三维抗冲击负泊松比结构的设计方法。The invention belongs to the technical field of negative Poisson's ratio materials, and in particular relates to a design method for a three-dimensional impact-resistant negative Poisson's ratio structure.

背景技术Background technique

负泊松比材料或结构也被称为拉胀材料或结构,当其受轴向压缩时,横向也发生收缩,当其受轴向拉伸时,其横向也向外扩张。Negative Poisson's ratio materials or structures, also known as auxetic materials or structures, shrink laterally when axially compressed, and expand laterally when stretched axially.

负泊松比网格材料与正泊松比材料相比具有更好的吸能性能和抗冲击能力,尤其是负泊松比结构的拉胀效应使其吸收能量的能力得到了显著的提升,常见的三维负泊比松结构有很多,如箭头型、内凹六边型,星型等。除结构外,网格结构的尺寸参数对其抗冲击性能有显著影响。Negative Poisson's ratio mesh materials have better energy absorption performance and impact resistance than positive Poisson's ratio materials. There are many common three-dimensional negative Poisson structures, such as arrow-shaped, concave hexagonal, star-shaped and so on. In addition to the structure, the dimensional parameters of the grid structure have a significant impact on its impact resistance.

目前对于三维抗冲击负泊松比结构的设计,主要集中在如何获得负泊松比性能,以及吸收能量总量等方面,而实际应用中往往不能只关注吸收能量的总量,对于结构所处的变形阶段、以及此时对应等效应力、应变的大小也需要进行关注,而现有的设计方法不能充分发挥结构的吸能性能。因此,提出一种具有普遍意义的三维抗冲击负泊松比结构设计方法,尤其在于尺寸参数的确定方法,具有重要的理论和应用意义。At present, the design of three-dimensional impact-resistant negative Poisson's ratio structures mainly focuses on how to obtain negative Poisson's ratio performance and the total amount of absorbed energy. The deformation stage of the structure and the corresponding equivalent stress and strain also need to be paid attention to, and the existing design methods cannot give full play to the energy absorption performance of the structure. Therefore, it is of great theoretical and practical significance to propose a general design method of three-dimensional impact-resistant negative Poisson's ratio structure, especially the determination method of size parameters.

发明内容SUMMARY OF THE INVENTION

本发明的目的在于提供一种三维抗冲击负泊松比结构的设计方法,针对三维抗冲击负泊松比结构,提供了一种具有初始峰应力低,比吸能高的三维抗冲击负泊松比结构的设计方法,具有高实用性和高适应性。The purpose of the present invention is to provide a design method for a three-dimensional impact-resistant negative Poisson's ratio structure, and for the three-dimensional impact-resistant negative Poisson's ratio structure, a three-dimensional impact-resistant negative Poisson's ratio structure with low initial peak stress and high specific energy absorption is provided. The design method of the loose ratio structure has high practicability and high adaptability.

本发明的目的是通过以下技术方案来实现的:The purpose of this invention is to realize through the following technical solutions:

一种三维抗冲击负泊松比结构的设计方法,包括以下步骤:A design method for a three-dimensional impact-resistant negative Poisson's ratio structure, comprising the following steps:

步骤1:建立几何模型,提取构建模型的结构参数;Step 1: Build a geometric model and extract the structural parameters of the model;

步骤2:推导结构的相对密度、等效弹性模量、泊松比、失效应力与步骤1中提取的结构参数之间的关系;Step 2: Derive the relationship between the relative density, equivalent elastic modulus, Poisson's ratio, failure stress of the structure and the structural parameters extracted in Step 1;

步骤3:对步骤1的模型进行压缩和冲击仿真,根据仿真结果拟合应力应变曲线,利用应力应变曲线计算单位质量材料吸收能量,根据所需能量吸收性能确定步骤1中的各结构参数xn的取值范围;Step 3: Perform compression and impact simulation on the model in Step 1, fit the stress-strain curve according to the simulation results, use the stress-strain curve to calculate the energy absorbed by the material per unit mass, and determine each structural parameter x n in Step 1 according to the required energy absorption performance range of values;

步骤4:对结构参数进行归一化处理,确定归一化后各结构参数与单位质量材料吸收能量之间的关系,获得各结构参数对单位质量材料吸收能量的影响系数ti,获得对能量吸收性能影响较大的结构参数,设为[y1,y2,…,ym]TStep 4: Normalize the structural parameters, determine the relationship between the normalized structural parameters and the energy absorbed by the material per unit mass, obtain the influence coefficient t i of each structural parameter on the energy absorbed by the material per unit mass, and obtain the effect on the energy Structural parameters that have great influence on absorption performance, set as [y 1 ,y 2 ,…,y m ] T ;

步骤5:结合步骤2的计算结果,以初始峰应力和比吸能为目标对步骤4中选取的结构参数[y1,y2,…,ym]T进行优化;Step 5: Based on the calculation results of Step 2, optimize the structural parameters [y 1 , y 2 ,..., y m ] T selected in Step 4 with the initial peak stress and specific energy absorption as the target;

步骤6:计算步骤5结构参数对应的初始峰应力和比吸能,若不符合要求则增加优化次数,再次进入步骤5迭代循环,当初始峰应力和比吸能达到要求时,结束循环;Step 6: Calculate the initial peak stress and specific energy absorption corresponding to the structural parameters in Step 5. If they do not meet the requirements, increase the number of optimizations, and enter the iterative cycle of Step 5 again. When the initial peak stress and specific energy absorption meet the requirements, end the cycle;

步骤7:根据步骤6获得的优化后的结构参数进行模型构建,得到目标模型优化后的三维抗冲击负泊松比结构。Step 7: Build a model according to the optimized structural parameters obtained in Step 6, and obtain a three-dimensional impact-resistant negative Poisson's ratio structure after the optimization of the target model.

进一步的,所述步骤2的具体步骤如下:Further, the specific steps of the step 2 are as follows:

步骤2.1:建立相对密度、等效弹性模量、泊松比、失效应力与结构参数的函数关系;Step 2.1: Establish the functional relationship between relative density, equivalent elastic modulus, Poisson's ratio, failure stress and structural parameters;

步骤2.2:分析结构参数与结构性质的对应关系,通过计算获取不同结构参数下的结构的性质。Step 2.2: Analyze the corresponding relationship between structural parameters and structural properties, and obtain the properties of the structure under different structural parameters through calculation.

进一步的,所述步骤3的具体步骤如下:Further, the specific steps of the step 3 are as follows:

步骤3.1,对步骤1的模型进行压缩和冲击仿真,推导应力应变之间的关系函数,利用仿真结果拟合关系函数中的参数,确定应力应变关系;Step 3.1, perform compression and impact simulation on the model in step 1, derive the relationship function between stress and strain, and use the simulation results to fit the parameters in the relationship function to determine the stress-strain relationship;

步骤3.2,根据步骤3.1中的应力应变关系计算单位质量材料吸收能量与应力之间的关系;Step 3.2, according to the stress-strain relationship in step 3.1, calculate the relationship between the absorbed energy per unit mass of material and the stress;

步骤3.3,根据步骤3.2获得的单位质量材料吸收能量与应力之间关系确定步骤1中的各结构参数xn的取值范围。In step 3.3, the value range of each structural parameter x n in step 1 is determined according to the relationship between the absorbed energy per unit mass of the material and the stress obtained in step 3.2.

进一步的,所述步骤4的具体步骤如下:Further, the specific steps of the step 4 are as follows:

步骤4.1,对步骤1中的结构参数进行归一化处理,得到:Step 4.1, normalize the structural parameters in step 1 to obtain:

Figure BDA0002743725190000021
Figure BDA0002743725190000021

式中:xi为步骤1中的结构参数,xmax为该结构参数可取的最大值,xmin为该结构参数可取的最小值;进而确定qi与单位质量材料吸收能量w之间的关系;In the formula: x i is the structural parameter in step 1, x max is the maximum value that the structural parameter can take, and x min is the minimum value that the structural parameter can take; and then determine the relationship between qi and the absorbed energy w per unit mass of material ;

步骤4.2,根据步骤4.1获得的qi与单位质量材料吸收能量w之间的关系,得到各归一化参数qi对单位质量材料吸收能量的影响系数:In step 4.2, according to the relationship between qi obtained in step 4.1 and the absorbed energy w per unit mass of material, the influence coefficient of each normalized parameter qi on the absorbed energy per unit mass of material is obtained:

Figure BDA0002743725190000022
Figure BDA0002743725190000022

式中:w0为平台应力增强区起始点时的单位质量材料吸收能量值,qi为归一化后的结构参数,σ为负泊松比结构受力时的应力;where w 0 is the energy absorbed per unit mass of the material at the starting point of the stress-enhancing zone of the platform, q i is the normalized structural parameter, and σ is the stress of the negative Poisson’s ratio structure under stress;

步骤4.3,根据ti的大小确定各结构参数对结构能量吸收性能的影响,取

Figure BDA0002743725190000031
的参数为主要参数,记为[y1,y2,…,ym]T。Step 4.3, according to the size of t i to determine the influence of each structural parameter on the energy absorption performance of the structure, take
Figure BDA0002743725190000031
The parameters of are the main parameters, denoted as [y 1 ,y 2 ,…,y m ] T .

进一步的,所述步骤5的具体步骤如下:Further, the specific steps of the step 5 are as follows:

步骤5.1,建立优化模型:Step 5.1, establish an optimization model:

minf(y)=(f1(y),...,fp(y))T minf(y)=(f 1 (y),...,f p (y)) T

Figure BDA0002743725190000032
Figure BDA0002743725190000032

将其设计域记为S,如果能得到一个可行解y*∈S,使得对于

Figure BDA0002743725190000033
,有f(y*)<f(y),则称y*为多目标优化问题的最优解,gi(y)≥0为不等式约束,hj(y)=0为等式约束,约束条件包括杆件几何约束,结构强度约束,p为优化目标的个数,k1和k2分别为不等式约束和等式约束个数;Denote its design domain as S, if a feasible solution y*∈S can be obtained, such that for
Figure BDA0002743725190000033
, if f(y*)<f(y), then y* is the optimal solution of the multi-objective optimization problem, g i (y)≥0 is the inequality constraint, h j (y)=0 is the equality constraint, Constraints include geometric constraints of members, structural strength constraints, p is the number of optimization objectives, k 1 and k 2 are the number of inequality constraints and equality constraints, respectively;

步骤5.2,选取最优拉丁方设计方法,在变量参数阈值范围内选取N组采样点,所述变量参数为[y1,y2,…,ym]TStep 5.2, select the optimal Latin square design method, select N groups of sampling points within the threshold range of variable parameters, and the variable parameters are [y 1 , y 2 ,..., y m ] T ;

步骤5.3,利用最优拉丁方设计提取样本,采用最小二乘法进行多项式拟合;Step 5.3, using the optimal Latin square design to extract samples, and using the least squares method to perform polynomial fitting;

步骤5.4,选取[y1,y2,…,ym]T的最高阶数均为2阶,并建立2阶响应面模型;Step 5.4, select [y 1 , y 2 ,..., y m ] the highest order of T is 2, and establish a 2-order response surface model;

步骤5.5,采用非支配排序遗传算法NSGA-II对近似的2阶响应面模型来进行多目标优化设计。In step 5.5, the non-dominated sorting genetic algorithm NSGA-II is used to perform multi-objective optimization design on the approximate second-order response surface model.

本发明相对于现有技术的有益效果:本发明提供了一种具有普遍意义的三维抗冲击负泊松比结构的设计方法,能够使获得的结构初始峰应力更低,比吸能更高。The beneficial effects of the present invention relative to the prior art: the present invention provides a general design method for a three-dimensional impact-resistant negative Poisson's ratio structure, which can make the initial peak stress of the obtained structure lower and the specific energy absorption higher.

附图说明Description of drawings

图1是三维抗冲击负泊松比结构设计流程图;Figure 1 is a flow chart of the three-dimensional impact-resistant negative Poisson's ratio structure design;

图2是最优拉丁方设计采样方式示意图;Figure 2 is a schematic diagram of the optimal Latin square design sampling method;

图3比吸能的二阶响应面图;Figure 3. Second-order response surface diagram of specific energy absorption;

图4初始峰应力的二阶响应面图。Figure 4. Second-order response surface plot of initial peak stress.

具体实施方式Detailed ways

下面结合附图1-4和具体实施方式对本发明作进一步详细说明。The present invention will be further described in detail below with reference to the accompanying drawings 1-4 and specific embodiments.

具体实施方式一Specific implementation one

如图1所示,一种三维抗冲击负泊松比结构的设计方法,对目标的抗冲击性能有不同要求时,对三维模型进行设计和优化,具体步骤如下:As shown in Figure 1, a design method of a three-dimensional impact-resistant negative Poisson's ratio structure, when there are different requirements for the impact resistance of the target, the three-dimensional model is designed and optimized. The specific steps are as follows:

步骤1:建立几何模型,提取构建模型的结构参数;Step 1: Build a geometric model and extract the structural parameters of the model;

步骤2:推导结构的相对密度、等效弹性模量、泊松比、失效应力与步骤1中提取的结构参数之间的关系;Step 2: Derive the relationship between the relative density, equivalent elastic modulus, Poisson's ratio, failure stress of the structure and the structural parameters extracted in Step 1;

步骤3:对步骤1的模型进行压缩和冲击仿真,根据仿真结果拟合应力应变曲线,利用应力应变曲线计算单位质量材料吸收能量,根据所需能量吸收性能确定步骤1中的各结构参数xn的取值范围;Step 3: Perform compression and impact simulation on the model in Step 1, fit the stress-strain curve according to the simulation results, use the stress-strain curve to calculate the energy absorbed by the material per unit mass, and determine each structural parameter x n in Step 1 according to the required energy absorption performance range of values;

步骤4:对结构参数进行归一化处理,确定归一化后各结构参数与单位质量材料吸收能量之间的关系,获得各结构参数对单位质量材料吸收能量的影响系数ti,获得对能量吸收性能影响较大的结构参数,设为[y1,y2,…,ym]TStep 4: Normalize the structural parameters, determine the relationship between the normalized structural parameters and the energy absorbed by the material per unit mass, obtain the influence coefficient t i of each structural parameter on the energy absorbed by the material per unit mass, and obtain the effect on the energy Structural parameters that have great influence on absorption performance, set as [y 1 ,y 2 ,…,y m ] T ;

步骤5:结合步骤2的计算结果,以初始峰应力和比吸能为目标对步骤4中选取的结构参数[y1,y2,…,ym]T进行优化;Step 5: Based on the calculation results of Step 2, optimize the structural parameters [y 1 , y 2 ,..., y m ] T selected in Step 4 with the initial peak stress and specific energy absorption as the target;

步骤6:计算步骤5结构参数对应的初始峰应力和比吸能,若不符合要求则增加优化次数,再次进入步骤5迭代循环,当初始峰应力和比吸能达到要求时,结束循环;Step 6: Calculate the initial peak stress and specific energy absorption corresponding to the structural parameters in Step 5. If they do not meet the requirements, increase the number of optimizations, and enter the iterative cycle of Step 5 again. When the initial peak stress and specific energy absorption meet the requirements, end the cycle;

步骤7:根据步骤6获得的优化后的结构参数进行模型构建,得到目标模型优化后的三维抗冲击负泊松比结构。Step 7: Build a model according to the optimized structural parameters obtained in Step 6, and obtain a three-dimensional impact-resistant negative Poisson's ratio structure after the optimization of the target model.

具体实施方式二Specific embodiment two

本具体实施方式,是对具体实施方式一的进一步说明。This specific embodiment is a further description of the specific embodiment 1.

所述步骤2的具体流程如下:The specific process of step 2 is as follows:

步骤2.1,建立相对密度、等效弹性模量、泊松比、失效应力与结构参数的函数关系并加以成型,结构参数与各力学性能的关系可以通过以下公式获得:Step 2.1, establish the functional relationship between relative density, equivalent elastic modulus, Poisson's ratio, failure stress and structural parameters and shape them. The relationship between structural parameters and various mechanical properties can be obtained by the following formula:

Figure BDA0002743725190000041
Figure BDA0002743725190000041

式中:ρRD为网格结构的相对密度,ρS为网格结构的等效密度,即结构质量比上包含孔隙的轮廓体积,ρM为制造网格结构所用基体材料的密度;In the formula: ρ RD is the relative density of the grid structure, ρ S is the equivalent density of the grid structure, that is, the contour volume containing pores in the structure-to-mass ratio, ρ M is the density of the matrix material used to manufacture the grid structure;

Figure BDA0002743725190000042
Figure BDA0002743725190000042

式中:E为等效弹性模量,F为在结构单元上施加的作用力,H为胞元受力点之间的距离,A为胞元上表面积,Δ为两手点之间的相对位移;where E is the equivalent elastic modulus, F is the force exerted on the structural unit, H is the distance between the force points of the cell, A is the surface area of the cell, and Δ is the relative displacement between the two hand points ;

Figure BDA0002743725190000043
Figure BDA0002743725190000043

式中:v为等效泊松比,εx为网格单元在x方向的变形,εy为网格单元在y方向的变形;where v is the equivalent Poisson's ratio, ε x is the deformation of the grid element in the x direction, ε y is the deformation of the grid element in the y direction;

Figure BDA0002743725190000051
Figure BDA0002743725190000051

式中:Pcr失效应力,μ为长度系数,E为等效弹性模量,I压杆横截面的最小惯性矩,L为结构高度;where: P cr failure stress, μ is the length coefficient, E is the equivalent elastic modulus, I is the minimum moment of inertia of the cross section of the compression rod, and L is the height of the structure;

步骤2.2,分析结构参数与结构性质的对应关系,通过计算获取不同结构参数下的结构的性质。In step 2.2, the corresponding relationship between the structural parameters and the structural properties is analyzed, and the properties of the structures under different structural parameters are obtained through calculation.

具体实施方式三Specific embodiment three

本具体实施方式,是对具体实施方式一的进一步说明。This specific embodiment is a further description of the specific embodiment 1.

所述步骤3的具体流程如下:The specific process of step 3 is as follows:

步骤3.1,对步骤1的模型进行压缩和冲击仿真,推导应力应变之间的关系函数,利用仿真结果拟合关系函数中的参数,确定应力应变关系函数的表达式;Step 3.1, perform compression and impact simulation on the model in step 1, deduce the relationship function between stress and strain, use the simulation results to fit the parameters in the relationship function, and determine the expression of the stress-strain relationship function;

步骤3.2,根据步骤3.1中的应力应变关系计算单位质量材料吸收能量与应力之间的关系;Step 3.2, according to the stress-strain relationship in step 3.1, calculate the relationship between the absorbed energy per unit mass of material and the stress;

步骤3.3,根据步骤3.2获得的单位质量材料吸收能量与应力之间关系确定步骤1中的各结构参数xn的取值范围。In step 3.3, the value range of each structural parameter x n in step 1 is determined according to the relationship between the absorbed energy per unit mass of the material and the stress obtained in step 3.2.

具体实施方式四Specific embodiment four

本具体实施方式,是对具体实施方式一的进一步说明。This specific embodiment is a further description of the specific embodiment 1.

所述步骤4的具体流程如下:The specific process of step 4 is as follows:

步骤4.1,对步骤1中的结构参数进行归一化处理,得到:Step 4.1, normalize the structural parameters in step 1 to obtain:

Figure BDA0002743725190000052
Figure BDA0002743725190000052

式中:xi为步骤1中的结构参数,xmax为该结构参数可取的最大值,xmin为该结构参数可取的最小值,进而确定qi与单位质量材料吸收能量之间的关系;In the formula: x i is the structural parameter in step 1, x max is the maximum value that the structural parameter can take, and x min is the minimum value that the structural parameter can take, and then determine the relationship between qi and the energy absorbed by the material per unit mass;

步骤4.2,根据步骤4.1获得的qi与单位质量材料吸收能量之间的关系,得到各归一化参数qi对单位质量材料吸收能量的影响系数:In step 4.2, according to the relationship between qi obtained in step 4.1 and the absorbed energy per unit mass of material, the influence coefficient of each normalized parameter qi on the absorbed energy per unit mass of material is obtained:

Figure BDA0002743725190000053
Figure BDA0002743725190000053

式中:w0为平台应力增强区起始点时的单位质量材料吸收能量值,qi为归一化后的结构参数,σ为负泊松比结构受力时的应力;where w 0 is the energy absorbed per unit mass of the material at the starting point of the stress-enhancing zone of the platform, q i is the normalized structural parameter, and σ is the stress of the negative Poisson’s ratio structure under stress;

步骤4.3,根据ti的大小确定各结构参数对结构能量吸收性能的影响,取

Figure BDA0002743725190000061
的参数为主要参数,记为[y1,y2,…,ym]T。Step 4.3, according to the size of t i to determine the influence of each structural parameter on the energy absorption performance of the structure, take
Figure BDA0002743725190000061
The parameters of are the main parameters, denoted as [y 1 ,y 2 ,…,y m ] T .

具体实施方式五Specific embodiment five

本具体实施方式,是对具体实施方式一的进一步说明。This specific embodiment is a further description of the specific embodiment 1.

所述步骤5的具体流程如下:The specific process of step 5 is as follows:

步骤5.1,取比吸能和初始峰应力为优化目标,对主要结构参数[y1,y2,…,ym]T进行多目标优化,建立优化模型:Step 5.1, take the specific energy absorption and initial peak stress as the optimization objectives, perform multi-objective optimization on the main structural parameters [y 1 , y 2 ,..., y m ] T , and establish the optimization model:

minf(y)=(f1(y),...,fp(y))T minf(y)=(f 1 (y),...,f p (y)) T

Figure BDA0002743725190000062
Figure BDA0002743725190000062

将其设计域记为S,如果能得到一个可行解y*∈S,使得对于

Figure BDA0002743725190000068
,有f(y*)<f(y),则称y*为多目标优化问题的最优解,gi(y)≥0为不等式约束,hj(y)=0为等式约束,约束条件包括杆件几何约束,结构强度约束。p为优化目标的个数,k1和k2分别为不等式约束和等式约束个数。Denote its design domain as S, if a feasible solution y*∈S can be obtained, such that for
Figure BDA0002743725190000068
, if f(y*)<f(y), then y* is the optimal solution of the multi-objective optimization problem, g i (y)≥0 is the inequality constraint, h j (y)=0 is the equality constraint, Constraints include member geometry constraints and structural strength constraints. p is the number of optimization objectives, and k 1 and k 2 are the number of inequality constraints and equality constraints, respectively.

步骤5.2,参见图2,选取最优拉丁方设计方法,在变量参数阈值范围内选取N组采样点,所述变量参数为yk和ylStep 5.2, referring to Fig. 2, select the optimal Latin square design method, select N groups of sampling points within the threshold range of variable parameters, and the variable parameters are y k and y l .

步骤5.3,利用最优拉丁方设计提取样本,采用最小二乘法进行多项式拟合:Step 5.3, use the optimal Latin square design to extract samples, and use the least squares method to perform polynomial fitting:

Figure BDA0002743725190000063
Figure BDA0002743725190000063

以方差R2和均方根误差RMSE做评价标准:Take the variance R 2 and the root mean square error RMSE as the evaluation criteria:

Figure BDA0002743725190000064
Figure BDA0002743725190000064

Figure BDA0002743725190000065
Figure BDA0002743725190000065

Figure BDA0002743725190000066
Figure BDA0002743725190000066

Figure BDA0002743725190000067
Figure BDA0002743725190000067

式中k为采样点的个数,所述实例中k的取值为9,P00、Pi0、Pij均为多项式系数。In the formula, k is the number of sampling points, and in the example, the value of k is 9, and P 00 , P i0 , and P ij are all polynomial coefficients.

步骤5.4,选取yk和yl的最高阶数均为2阶,从而建立2阶响应面模型如下,并可绘制响应面,参考图3-4:Step 5.4, select the highest order of y k and y l to be 2 order, so as to establish the 2 order response surface model as follows, and the response surface can be drawn, refer to Figure 3-4:

Figure BDA0002743725190000071
Figure BDA0002743725190000071

Figure BDA0002743725190000072
Figure BDA0002743725190000072

式中:SEA为结构的比吸能,IPS为初始峰应力,m为被优化的参数个数。where SEA is the specific energy absorption of the structure, IPS is the initial peak stress, and m is the number of parameters to be optimized.

步骤5.5采用非支配排序遗传算法NSGA-II对近似的2阶响应面模型来进行多目标优化设计。Step 5.5 uses the non-dominated sorting genetic algorithm NSGA-II to perform multi-objective optimization design on the approximate second-order response surface model.

上述说明并非对本发明的限制,以上内容仅为本发明的较佳实施案例,本发明也不仅限于上述举例,本技术领域的技术人员,依据本发明的思想,在具体实施方式及应用范围上均有可变之处,在本发明的实质范围内所做出的变化,也属于本发明的保护范围,本说明书内容不应理解为对本发明的限制。The above description is not a limitation of the present invention, the above content is only a preferred embodiment of the present invention, and the present invention is not limited to the above examples. Those skilled in the art, according to the idea of the present invention, are all in the specific embodiment and application scope. There are changes, and changes made within the essential scope of the present invention also belong to the protection scope of the present invention, and the contents of this specification should not be construed as limiting the present invention.

Claims (5)

1.一种三维抗冲击负泊松比结构的设计方法,其特征在于,包括以下步骤:1. a design method of three-dimensional impact-resistant negative Poisson's ratio structure, is characterized in that, comprises the following steps: 步骤1:建立几何模型,提取构建模型的结构参数;Step 1: Build a geometric model and extract the structural parameters of the model; 步骤2:推导结构的相对密度、等效弹性模量、泊松比、失效应力与步骤1中提取的结构参数之间的关系;Step 2: Derive the relationship between the relative density, equivalent elastic modulus, Poisson's ratio, failure stress of the structure and the structural parameters extracted in Step 1; 步骤3:对步骤1的模型进行压缩和冲击仿真,根据仿真结果拟合应力应变曲线,利用应力应变曲线计算单位质量材料吸收能量,根据所需能量吸收性能确定步骤1中的各结构参数xn的取值范围;Step 3: Perform compression and impact simulation on the model in Step 1, fit the stress-strain curve according to the simulation results, use the stress-strain curve to calculate the energy absorbed by the material per unit mass, and determine each structural parameter x n in Step 1 according to the required energy absorption performance range of values; 步骤4:对结构参数进行归一化处理,确定归一化后各结构参数与单位质量材料吸收能量之间的关系,获得各结构参数对单位质量材料吸收能量的影响系数ti,获得对能量吸收性能影响较大的结构参数,设为[y1,y2,…,ym]TStep 4: Normalize the structural parameters, determine the relationship between the normalized structural parameters and the energy absorbed by the material per unit mass, obtain the influence coefficient t i of each structural parameter on the energy absorbed by the material per unit mass, and obtain the effect on the energy Structural parameters that have great influence on absorption performance, set as [y 1 ,y 2 ,…,y m ] T ; 步骤5:结合步骤2的计算结果,以初始峰应力和比吸能为目标对步骤4中选取的结构参数[y1,y2,…,ym]T进行优化;Step 5: Based on the calculation results of Step 2, optimize the structural parameters [y 1 , y 2 ,..., y m ] T selected in Step 4 with the initial peak stress and specific energy absorption as the target; 步骤6:计算步骤5结构参数对应的初始峰应力和比吸能,若不符合要求则增加优化次数,再次进入步骤5迭代循环,当初始峰应力和比吸能达到要求时,结束循环;Step 6: Calculate the initial peak stress and specific energy absorption corresponding to the structural parameters in Step 5. If they do not meet the requirements, increase the number of optimizations, and enter the iterative cycle of Step 5 again. When the initial peak stress and specific energy absorption meet the requirements, end the cycle; 步骤7:根据步骤6获得的优化后的结构参数进行模型构建,得到目标模型优化后的三维抗冲击负泊松比结构。Step 7: Build a model according to the optimized structural parameters obtained in Step 6, and obtain a three-dimensional impact-resistant negative Poisson's ratio structure after the optimization of the target model. 2.根据权利要求1所述的一种三维抗冲击负泊松比结构的设计方法,其特征在于,所述步骤2的具体步骤如下:2. the design method of a kind of three-dimensional impact-resistant negative Poisson's ratio structure according to claim 1, is characterized in that, the concrete steps of described step 2 are as follows: 步骤2.1:建立相对密度、等效弹性模量、泊松比、失效应力与结构参数的函数关系;Step 2.1: Establish the functional relationship between relative density, equivalent elastic modulus, Poisson's ratio, failure stress and structural parameters; 步骤2.2:分析结构参数与结构性质的对应关系,通过计算获取不同结构参数下的结构的性质。Step 2.2: Analyze the corresponding relationship between structural parameters and structural properties, and obtain the properties of the structure under different structural parameters through calculation. 3.根据权利要求1所述的一种三维抗冲击负泊松比结构的设计方法,其特征在于,所述步骤3的具体步骤如下:3. the design method of a kind of three-dimensional impact-resistant negative Poisson's ratio structure according to claim 1, is characterized in that, the concrete steps of described step 3 are as follows: 步骤3.1,对步骤1的模型进行压缩和冲击仿真,推导应力应变之间的关系函数,利用仿真结果拟合关系函数中的参数,确定应力应变关系;Step 3.1, perform compression and impact simulation on the model in step 1, derive the relationship function between stress and strain, and use the simulation results to fit the parameters in the relationship function to determine the stress-strain relationship; 步骤3.2,根据步骤3.1中的应力应变关系计算单位质量材料吸收能量与应力之间的关系;Step 3.2, according to the stress-strain relationship in step 3.1, calculate the relationship between the absorbed energy per unit mass of material and the stress; 步骤3.3,根据步骤3.2获得的单位质量材料吸收能量与应力之间关系确定步骤1中的各结构参数xn的取值范围。In step 3.3, the value range of each structural parameter x n in step 1 is determined according to the relationship between the absorbed energy per unit mass of the material and the stress obtained in step 3.2. 4.根据权利要求1所述的一种三维抗冲击负泊松比结构的设计方法,其特征在于,所述步骤4的具体步骤如下:4. the design method of a kind of three-dimensional impact-resistant negative Poisson's ratio structure according to claim 1, is characterized in that, the concrete steps of described step 4 are as follows: 步骤4.1,对步骤1中的结构参数进行归一化处理,得到:Step 4.1, normalize the structural parameters in step 1 to obtain:
Figure FDA0002743725180000021
Figure FDA0002743725180000021
式中:xi为步骤1中的结构参数,xmax为该结构参数可取的最大值,xmin为该结构参数可取的最小值;进而确定qi与单位质量材料吸收能量w之间的关系;In the formula: x i is the structural parameter in step 1, x max is the maximum value that the structural parameter can take, and x min is the minimum value that the structural parameter can take; and then determine the relationship between qi and the absorbed energy w per unit mass of material ; 步骤4.2,根据步骤4.1获得的qi与单位质量材料吸收能量w之间的关系,得到各归一化参数qi对单位质量材料吸收能量的影响系数:In step 4.2, according to the relationship between qi obtained in step 4.1 and the absorbed energy w per unit mass of material, the influence coefficient of each normalized parameter qi on the absorbed energy per unit mass of material is obtained:
Figure FDA0002743725180000022
Figure FDA0002743725180000022
式中:w0为平台应力增强区起始点时的单位质量材料吸收能量值,qi为归一化后的结构参数,σ为负泊松比结构受力时的应力;where w 0 is the energy absorbed per unit mass of the material at the starting point of the stress-enhancing zone of the platform, q i is the normalized structural parameter, and σ is the stress of the negative Poisson’s ratio structure under stress; 步骤4.3,根据ti的大小确定各结构参数对结构能量吸收性能的影响,取
Figure FDA0002743725180000023
的参数为主要参数,记为[y1,y2,…,ym]T
Step 4.3, according to the size of t i to determine the influence of each structural parameter on the energy absorption performance of the structure, take
Figure FDA0002743725180000023
The parameters of are the main parameters, denoted as [y 1 ,y 2 ,…,y m ] T .
5.根据权利要求1所述的一种三维抗冲击负泊松比结构的设计方法,其特征在于,所述步骤5的具体步骤如下:5. the design method of a kind of three-dimensional impact-resistant negative Poisson's ratio structure according to claim 1, is characterized in that, the concrete steps of described step 5 are as follows: 步骤5.1,建立优化模型:Step 5.1, establish an optimization model: min f(y)=(f1(y),...,fp(y))T min f(y)=(f 1 (y),...,f p (y)) T
Figure FDA0002743725180000024
Figure FDA0002743725180000024
将其设计域记为S,如果能得到一个可行解y*∈S,使得对于
Figure FDA0002743725180000025
有f(y*)<f(y),则称y*为多目标优化问题的最优解,gi(y)≥0为不等式约束,hj(y)=0为等式约束,约束条件包括杆件几何约束,结构强度约束,p为优化目标的个数,k1和k2分别为不等式约束和等式约束个数;
Denote its design domain as S, if a feasible solution y*∈S can be obtained, such that for
Figure FDA0002743725180000025
If f(y*)<f(y), then y* is called the optimal solution of the multi-objective optimization problem, g i (y) ≥ 0 is an inequality constraint, h j (y)=0 is an equality constraint, and the constraint The conditions include geometric constraints of members and structural strength constraints, p is the number of optimization objectives, and k 1 and k 2 are the numbers of inequality constraints and equality constraints, respectively;
步骤5.2,选取最优拉丁方设计方法,在变量参数阈值范围内选取N组采样点,所述变量参数为[y1,y2,…,ym]TStep 5.2, select the optimal Latin square design method, select N groups of sampling points within the threshold range of variable parameters, and the variable parameters are [y 1 , y 2 ,..., y m ] T ; 步骤5.3,利用最优拉丁方设计提取样本,采用最小二乘法进行多项式拟合;Step 5.3, using the optimal Latin square design to extract samples, and using the least squares method to perform polynomial fitting; 步骤5.4,选取[y1,y2,…,ym]T的最高阶数均为2阶,并建立2阶响应面模型;Step 5.4, select [y 1 , y 2 ,..., y m ] the highest order of T is 2, and establish a 2-order response surface model; 步骤5.5,采用非支配排序遗传算法NSGA-II对近似的2阶响应面模型来进行多目标优化设计。In step 5.5, the non-dominated sorting genetic algorithm NSGA-II is used to perform multi-objective optimization design on the approximate second-order response surface model.
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