CN112149260A - Design method of three-dimensional impact-resistant negative Poisson's ratio structure - Google Patents
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Abstract
A design method of a three-dimensional impact-resistant negative Poisson ratio structure belongs to the technical field of negative Poisson ratio materials, and specifically comprises the following steps: step 1: establishing a geometric model and extracting structural parameters; step 2: deducing the relation between the relative density, the equivalent modulus, the Poisson ratio, the failure stress and the structural parameters; and step 3: carrying out compression and impact simulation on the model, and determining the value range of each structural parameter; and 4, step 4: processing the structural parameters to obtain the structural parameters with larger influence on the energy absorption performance, and 5: optimizing the structural parameters by using a multi-objective optimization method; step 6: calculating initial peak stress and specific energy absorption, if the initial peak stress and specific energy absorption do not meet the requirements, entering the step 5 for iterative cycle again, and ending the cycle when the requirements are met; and 7: and taking the optimized structural parameters to construct a model to obtain the three-dimensional impact-resistant negative Poisson's ratio structure. The method can ensure that the obtained structure has lower initial peak stress and higher specific energy absorption.
Description
Technical Field
The invention belongs to the technical field of negative Poisson ratio materials, and particularly relates to a design method of a three-dimensional impact-resistant negative Poisson ratio structure.
Background
Negative poisson's ratio material or structure, also known as auxetic material or structure, contracts laterally as it is compressed axially and expands laterally outward as it is stretched axially.
Compared with a positive poisson ratio material, the negative poisson ratio grid material has better energy absorption performance and impact resistance, particularly, the energy absorption capacity of the negative poisson ratio grid material is obviously improved due to the auxetic effect of a negative poisson ratio structure, and common three-dimensional negative poisson ratio grid materials have a plurality of structures, such as an arrow type structure, a concave hexagonal structure and a star type structure. In addition to the structure, the dimensional parameters of the lattice structure have a significant influence on its impact resistance.
At present, the design of a three-dimensional impact-resistant negative Poisson ratio structure mainly focuses on how to obtain the negative Poisson ratio performance, the total amount of absorbed energy and the like, but in practical application, only the total amount of the absorbed energy cannot be concerned, the attention is also required to the deformation stage of the structure and the corresponding equivalent stress and strain at the moment, and the existing design method cannot give full play to the energy absorption performance of the structure. Therefore, the three-dimensional impact-resistant negative Poisson's ratio structure design method with the general significance is provided, and particularly the method for determining the size parameters has important theoretical and application significance.
Disclosure of Invention
The invention aims to provide a design method of a three-dimensional impact-resistant negative Poisson's ratio structure, and provides a design method of a three-dimensional impact-resistant negative Poisson's ratio structure with low initial peak stress and high specific energy absorption, and the three-dimensional impact-resistant negative Poisson's ratio structure has high practicability and high adaptability.
The purpose of the invention is realized by the following technical scheme:
a design method of a three-dimensional impact-resistant negative Poisson's ratio structure comprises the following steps:
step 1: establishing a geometric model, and extracting structural parameters of the constructed model;
step 2: deducing the relation between the relative density, equivalent elastic modulus, Poisson's ratio and failure stress of the structure and the structure parameters extracted in the step 1;
and step 3: performing compression and impact simulation on the model in the step 1, fitting a stress-strain curve according to a simulation result, calculating the absorption energy of the material with unit mass by using the stress-strain curve, and determining each structural parameter x in the step 1 according to the required energy absorption performancenThe value range of (a);
and 4, step 4: normalizing the structural parameters, determining the relationship between the normalized structural parameters and the absorption energy of the material with unit mass, and obtaining the influence coefficient t of the structural parameters on the absorption energy of the material with unit massiThe structural parameter having a large influence on the energy absorption performance is obtained and is set to [ y ]1,y2,…,ym]T；
And 5: combining the calculation result of the step 2, and aiming at the initial peak stress and the specific energy absorption to the structure parameter [ y ] selected in the step 41,y2,…,ym]TOptimizing;
step 6: calculating initial peak stress and specific energy absorption corresponding to the structural parameters in the step 5, if the initial peak stress and specific energy absorption do not meet the requirements, increasing the optimization times, entering the step 5 again to perform iterative loop, and ending the loop when the initial peak stress and specific energy absorption meet the requirements;
and 7: and (6) carrying out model construction according to the optimized structure parameters obtained in the step (6) to obtain a three-dimensional impact-resistant negative Poisson's ratio structure optimized by the target model.
Further, the specific steps of step 2 are as follows:
step 2.1: establishing a functional relation among relative density, equivalent elastic modulus, Poisson ratio, failure stress and structural parameters;
step 2.2: and analyzing the corresponding relation between the structural parameters and the structural properties, and obtaining the properties of the structures under different structural parameters through calculation.
Further, the specific steps of step 3 are as follows:
step 3.1, performing compression and impact simulation on the model in the step 1, deducing a relation function between stress and strain, and fitting parameters in the relation function by using a simulation result to determine a stress and strain relation;
step 3.2, calculating the relation between the absorption energy of the material with unit mass and the stress according to the stress-strain relation in the step 3.1;
step 3.3, determining each structural parameter x in the step 1 according to the relation between the absorption energy of the material with unit mass and the stress obtained in the step 3.2nThe value range of (a).
Further, the specific steps of step 4 are as follows:
step 4.1, carrying out normalization processing on the structural parameters in the step 1 to obtain:
in the formula: x is the number ofiIs the structural parameter, x, in step 1maxIs a desired maximum value of the structural parameter, xminIs the minimum value of the structural parameter; and then determine qiThe relationship with the energy w absorbed per unit mass of material;
step 4.2, q obtained according to step 4.1iObtaining the relation between the normalized parameters and the absorption energy w of the material with unit massiCoefficient of influence on the energy absorption per unit mass of material:
in the formula: w is a0Is the value of the energy absorbed by the material per unit mass at the starting point of the platform stress enhancement region, qiThe structure parameter after normalization is shown as sigma, and the sigma is the stress of the structure with the negative Poisson ratio when stressed;
step 4.3, according to tiSize of (2)Determining the influence of each structural parameter on the energy absorption performance of the structure, and taking
The parameter(s) of (1) is a main parameter and is marked as [ y1,y2,…,ym]T。
Further, the specific steps of step 5 are as follows:
step 5.1, establishing an optimization model:
minf(y)＝(f1(y),...,fp(y))T
marking the design domain as S, if a feasible solution y ∈ S can be obtained, making the design domain as S
If f (y) < f (y), then y is called the optimal solution of the multi-objective optimization problem, gi(y) is equal to or more than 0 and is inequality constraint, hj0 is equality constraint, the constraint conditions include bar member geometric constraint and structural strength constraint, p is number of optimization targets, k1And k2Respectively the number of inequality constraints and equality constraints;
step 5.2, selecting an optimal Latin square design method, and selecting N groups of sampling points within a variable parameter threshold range, wherein the variable parameter is [ y1,y2,…,ym]T；
Step 5.3, designing and extracting a sample by using an optimal Latin method, and performing polynomial fitting by using a least square method;
step 5.4, select [ y1,y2,…,ym]TThe highest orders of the two-dimensional model are 2 orders, and a 2-order response surface model is established;
and 5.5, performing multi-objective optimization design on the approximate 2-order response surface model by adopting a non-dominated sorting genetic algorithm NSGA-II.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a design method of a three-dimensional impact-resistant negative Poisson's ratio structure with general significance, which can ensure that the initial peak stress of the obtained structure is lower and the specific energy absorption is higher.
Drawings
FIG. 1 is a flow chart of a three-dimensional impact-resistant negative Poisson's ratio structure design;
FIG. 2 is a schematic diagram of an optimal Latin square design sampling pattern;
FIG. 3 is a second order response surface plot of specific energy absorption;
FIG. 4 is a second order response surface plot of initial peak stress.
Detailed Description
The invention is described in further detail below with reference to the accompanying figures 1-4 and the detailed description.
Detailed description of the invention
As shown in fig. 1, a method for designing a three-dimensional impact-resistant negative poisson's ratio structure designs and optimizes a three-dimensional model when different requirements are made on the impact resistance of a target, and the method comprises the following specific steps:
step 1: establishing a geometric model, and extracting structural parameters of the constructed model;
step 2: deducing the relation between the relative density, equivalent elastic modulus, Poisson's ratio and failure stress of the structure and the structure parameters extracted in the step 1;
and step 3: performing compression and impact simulation on the model in the step 1, fitting a stress-strain curve according to a simulation result, calculating the absorption energy of the material with unit mass by using the stress-strain curve, and determining each structural parameter x in the step 1 according to the required energy absorption performancenThe value range of (a);
and 4, step 4: normalizing the structural parameters, determining the relationship between the normalized structural parameters and the absorption energy of the material with unit mass, and obtaining the influence coefficient t of the structural parameters on the absorption energy of the material with unit massiThe structural parameter having a large influence on the energy absorption performance is obtained and is set to [ y ]1,y2,…,ym]T；
And 5: combining the calculation results of the step 2 to obtain the initial peak stress and the specific absorptionCan be targeted to the structural parameter [ y ] selected in step 41,y2,…,ym]TOptimizing;
step 6: calculating initial peak stress and specific energy absorption corresponding to the structural parameters in the step 5, if the initial peak stress and specific energy absorption do not meet the requirements, increasing the optimization times, entering the step 5 again to perform iterative loop, and ending the loop when the initial peak stress and specific energy absorption meet the requirements;
and 7: and (6) carrying out model construction according to the optimized structure parameters obtained in the step (6) to obtain a three-dimensional impact-resistant negative Poisson's ratio structure optimized by the target model.
Detailed description of the invention
This embodiment mode is a further description of the first embodiment mode.
The specific process of the step 2 is as follows:
step 2.1, establishing a functional relation among the relative density, the equivalent elastic modulus, the Poisson ratio, the failure stress and the structural parameters and forming, wherein the relation between the structural parameters and the mechanical properties can be obtained through the following formula:
in the formula: rhoRDRelative density of the lattice structure, pSIs the equivalent density of the lattice structure, i.e. the volume of the contour containing pores in the structural mass ratio, pMDensity of the matrix material used to make the lattice structure;
in the formula: e is the equivalent elastic modulus, F is the acting force exerted on the structural unit, H is the distance between the stress points of the cell element, A is the surface area on the cell element, and Delta is the relative displacement between the two hand points;
in the formula: v is the equivalent poisson's ratio,xfor the deformation of the grid cells in the x-direction,ydeformation of the grid cells in the y-direction;
in the formula: pcrThe failure stress is mu is a length coefficient, E is an equivalent elastic modulus, the minimum moment of inertia of the cross section of the I pressure lever, and L is a structural height;
and 2.2, analyzing the corresponding relation between the structural parameters and the structural properties, and obtaining the properties of the structures under different structural parameters through calculation.
Detailed description of the invention
This embodiment mode is a further description of the first embodiment mode.
The specific process of the step 3 is as follows:
step 3.1, performing compression and impact simulation on the model in the step 1, deducing a relation function between stress and strain, fitting parameters in the relation function by using a simulation result, and determining an expression of the stress and strain relation function;
step 3.2, calculating the relation between the absorption energy of the material with unit mass and the stress according to the stress-strain relation in the step 3.1;
step 3.3, determining each structural parameter x in the step 1 according to the relation between the absorption energy of the material with unit mass and the stress obtained in the step 3.2nThe value range of (a).
Detailed description of the invention
This embodiment mode is a further description of the first embodiment mode.
The specific process of the step 4 is as follows:
step 4.1, carrying out normalization processing on the structural parameters in the step 1 to obtain:
in the formula: x is the number ofiIs the structural parameter, x, in step 1maxIs a desired maximum value of the structural parameter, xminFor the minimum value of the structural parameter, q is determinediThe relationship to the energy absorbed per unit mass of material;
step 4.2, q obtained according to step 4.1iObtaining the relation between the normalized parameters and the absorption energy of the material with unit massiCoefficient of influence on the energy absorption per unit mass of material:
in the formula: w is a0Is the value of the energy absorbed by the material per unit mass at the starting point of the platform stress enhancement region, qiThe structure parameter after normalization is shown as sigma, and the sigma is the stress of the structure with the negative Poisson ratio when stressed;
step 4.3, according to tiDetermining the influence of each structural parameter on the energy absorption performance of the structure, and taking
The parameter(s) of (1) is a main parameter and is marked as [ y1,y2,…,ym]T。
Detailed description of the invention
This embodiment mode is a further description of the first embodiment mode.
The specific process of the step 5 is as follows:
step 5.1, taking the ratio energy absorption and the initial peak stress as optimization targets, and carrying out comparison on main structural parameters [ y1,y2,…,ym]TPerforming multi-objective optimization, and establishing an optimization model:
minf(y)＝(f1(y),...,fp(y))T
marking the design domain as S, if a feasible solution y ∈ S can be obtained, making the design domain as S
If f (y) < f (y), then y is called the optimal solution of the multi-objective optimization problem, gi(y) is equal to or more than 0 and is inequality constraint, hjAnd (y) 0 is an equality constraint, and the constraint conditions comprise a bar member geometric constraint and a structural strength constraint. p is the number of optimization objectives, k1And k2The number of inequality constraints and equality constraints are respectively.
Step 5.2, referring to fig. 2, selecting an optimal latin square design method, and selecting N groups of sampling points within a variable parameter threshold range, wherein the variable parameter is ykAnd yl。
And 5.3, designing and extracting a sample by using an optimal Latin method, and performing polynomial fitting by using a least square method:
by variance R2And root mean square error RMSE as evaluation criteria:
where k is the number of sampling points, and in the example, k is 9, P00、Pi0、PijAre all polynomial coefficients.
Step 5.4, select ykAnd ylThe highest orders of (2) are all 2 orders, so that a 2-order response surface model is established as follows, and a response surface can be drawn, referring to fig. 3-4:
in the formula: SEA is the specific energy absorption of the structure, IPS is the initial peak stress, and m is the number of optimized parameters.
And 5.5, performing multi-objective optimization design on the approximate 2-order response surface model by adopting a non-dominated sorting genetic algorithm NSGA-II.
The above description is not intended to limit the present invention, and the above description is only a preferred embodiment of the present invention, and the present invention is not limited to the above examples, and those skilled in the art can change the embodiments and applications of the present invention according to the idea of the present invention, and the changes made within the spirit and scope of the present invention also belong to the protection scope of the present invention, and the content of the present description should not be interpreted as limiting the present invention.
Claims (5)
1. A design method of a three-dimensional impact-resistant negative Poisson ratio structure is characterized by comprising the following steps:
step 1: establishing a geometric model, and extracting structural parameters of the constructed model;
step 2: deducing the relation between the relative density, equivalent elastic modulus, Poisson's ratio and failure stress of the structure and the structure parameters extracted in the step 1;
and step 3: performing compression and impact simulation on the model in the step 1, fitting a stress-strain curve according to a simulation result, calculating the absorption energy of the material with unit mass by using the stress-strain curve, and determining each structural parameter x in the step 1 according to the required energy absorption performancenThe value range of (a);
and 4, step 4: normalizing the structural parameters, determining the relationship between the normalized structural parameters and the absorption energy of the material with unit mass, and obtaining the influence coefficient t of the structural parameters on the absorption energy of the material with unit massiThe structural parameter having a large influence on the energy absorption performance is obtained and is set to [ y ]1,y2,…,ym]T；
And 5: combining the calculation result of the step 2, and aiming at the initial peak stress and the specific energy absorption to the structure parameter [ y ] selected in the step 41,y2,…,ym]TOptimizing;
step 6: calculating initial peak stress and specific energy absorption corresponding to the structural parameters in the step 5, if the initial peak stress and specific energy absorption do not meet the requirements, increasing the optimization times, entering the step 5 again to perform iterative loop, and ending the loop when the initial peak stress and specific energy absorption meet the requirements;
and 7: and (6) carrying out model construction according to the optimized structure parameters obtained in the step (6) to obtain a three-dimensional impact-resistant negative Poisson's ratio structure optimized by the target model.
2. The method for designing a three-dimensional impact-resistant negative Poisson's ratio structure according to claim 1, wherein the specific steps of the step 2 are as follows:
step 2.1: establishing a functional relation among relative density, equivalent elastic modulus, Poisson ratio, failure stress and structural parameters;
step 2.2: and analyzing the corresponding relation between the structural parameters and the structural properties, and obtaining the properties of the structures under different structural parameters through calculation.
3. The method for designing a three-dimensional impact-resistant negative Poisson's ratio structure according to claim 1, wherein the specific steps of the step 3 are as follows:
step 3.1, performing compression and impact simulation on the model in the step 1, deducing a relation function between stress and strain, and fitting parameters in the relation function by using a simulation result to determine a stress and strain relation;
step 3.2, calculating the relation between the absorption energy of the material with unit mass and the stress according to the stress-strain relation in the step 3.1;
step 3.3, determining each structural parameter x in the step 1 according to the relation between the absorption energy of the material with unit mass and the stress obtained in the step 3.2nThe value range of (a).
4. The method for designing a three-dimensional impact-resistant negative Poisson's ratio structure according to claim 1, wherein the specific steps of the step 4 are as follows:
step 4.1, carrying out normalization processing on the structural parameters in the step 1 to obtain:
in the formula: x is the number ofiIs the structural parameter, x, in step 1maxIs a desired maximum value of the structural parameter, xminIs the minimum value of the structural parameter; and then determine qiThe relationship with the energy w absorbed per unit mass of material;
step 4.2, q obtained according to step 4.1iObtaining the relation between the normalized parameters and the absorption energy w of the material with unit massiCoefficient of influence on the energy absorption per unit mass of material:
in the formula: w is a0Is the value of the energy absorbed by the material per unit mass at the starting point of the platform stress enhancement region, qiThe structure parameter after normalization is shown as sigma, and the sigma is the stress of the structure with the negative Poisson ratio when stressed;
step 4.3, according to tiDetermining the influence of each structural parameter on the energy absorption performance of the structure, and taking
The parameter(s) of (1) is a main parameter and is marked as [ y1,y2,…,ym]T。
5. The method for designing a three-dimensional impact-resistant negative Poisson's ratio structure according to claim 1, wherein the specific steps of the step 5 are as follows:
step 5.1, establishing an optimization model:
min f(y)＝(f1(y),...,fp(y))T
marking the design domain as S, if a feasible solution y ∈ S can be obtained, making the design domain as S
If f (y) < f (y), then y is called the optimal solution of the multi-objective optimization problem, gi(y) is equal to or more than 0 and is inequality constraint, hj0 is equality constraint, the constraint conditions include bar member geometric constraint and structural strength constraint, p is number of optimization targets, k1And k2Respectively the number of inequality constraints and equality constraints;
step 5.2, selecting an optimal Latin square design method, and selecting N groups of sampling points within a variable parameter threshold range, wherein the variable parameter is [ y1,y2,…,ym]T；
Step 5.3, designing and extracting a sample by using an optimal Latin method, and performing polynomial fitting by using a least square method;
step 5.4, select [ y1,y2,…,ym]TThe highest orders of the two-dimensional model are 2 orders, and a 2-order response surface model is established;
and 5.5, performing multi-objective optimization design on the approximate 2-order response surface model by adopting a non-dominated sorting genetic algorithm NSGA-II.
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| CN113343371A (en) * | 2021-01-29 | 2021-09-03 | 北京理工大学重庆创新中心 | Design method of foam-filled negative Poisson's ratio composite structure |
| CN113343371B (en) * | 2021-01-29 | 2022-07-15 | 北京理工大学重庆创新中心 | Design method of foam-filled negative Poisson's ratio composite structure |
| CN114117635A (en) * | 2021-11-24 | 2022-03-01 | 湖南大学 | Design method of multi-dimensional multi-rigidity light energy absorption structure |
| CN114117635B (en) * | 2021-11-24 | 2024-09-03 | 湖南大学 | Design method of multidimensional multi-rigidity light energy absorption structure |
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