CN107139873B - Automobile rear bumper with function gradient negative Poisson's ratio structure and optimization method - Google Patents
Automobile rear bumper with function gradient negative Poisson's ratio structure and optimization method Download PDFInfo
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- B60R19/00—Wheel guards; Radiator guards, e.g. grilles; Obstruction removers; Fittings damping bouncing force in collisions
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Abstract
The invention discloses an automobile rear bumper with a functional gradient negative Poisson's ratio structure and an optimization method, wherein the automobile rear bumper comprises a bumper front cover, a bumper body and a bumper rear cover; the bumper body is made of a negative Poisson ratio material and is used for absorbing energy when an automobile collides; the front bumper cover and the rear bumper cover are matched with each other to form a shell, the bumper body is fixed in the shell and then connected with the automobile body of the automobile. The invention also discloses an optimization method of the automobile rear bumper, and by the method, under the condition of considering noise factor interference, according to design targets and requirements, the thickness of the front bumper cover, the thickness of the rear bumper cover and the thickness gradient of the negative Poisson ratio structure are designed by using a Taguchi robustness optimization method, so that the energy absorption capacity of the structure is effectively improved, the safety of passengers in an automobile is ensured, and the effect of light weight is achieved.
Description
Technical Field
The invention relates to the field of passive safety of automobiles, in particular to an automobile rear bumper with a functional gradient negative Poisson's ratio structure and an optimization method.
Background
In traffic accidents, the rate of rear-end collisions is the highest, and when a rear-end collision occurs, the safety of passengers in a vehicle subjected to rear-end collision is important. Therefore, the crashworthiness of the rear bumper of the automobile must be given sufficient attention in the automobile design process. At present, most of rear bumpers of automobiles are made of cast iron, so that the crashworthiness is ensured, but the rear bumpers do not meet the lightweight requirement of automobile design; some automobiles adopt foam materials, and although the aim of lightening is achieved, the crashworthiness is obviously insufficient.
Disclosure of Invention
The invention aims to solve the technical problem of providing a functional gradient negative poisson's ratio structure rear bumper and an optimization method aiming at the defects in the background technology.
The invention adopts the following technical scheme for solving the technical problems:
an automobile rear bumper with a functional gradient negative Poisson's ratio structure comprises a bumper front cover, a bumper body and a bumper rear cover;
the bumper body is made of a negative Poisson ratio material and is used for absorbing energy when an automobile is collided;
the front bumper cover and the rear bumper cover are matched with each other to form a shell, and the bumper body is fixed behind the shell and connected with the automobile body of the automobile.
As a further optimization scheme of the automobile rear bumper with the function gradient negative Poisson's ratio structure, the front bumper cover is plate-mounted, and the section of the rear bumper cover along the axial direction of an automobile is U-shaped;
the bumper front cover is 1220mm long in the longitudinal direction of the automobile, 90mm high in the vertical direction of the automobile and 1mm thick;
the lid is followed the ascending 1220mm of length in the automobile longitudinal direction behind the bumper, and the width on the automobile axial direction is 128mm, is 90mm along the ascending height in the automobile vertical direction, and the thickness of self is 1mm.
As a further optimization scheme of the automobile rear bumper with the functional gradient negative Poisson's ratio structure, the bumper body is composed of three layers of negative Poisson's ratio single cells along the longitudinal direction of an automobile, and the thickness gradient value of each layer of negative Poisson's ratio single cell is constant;
the negative Poisson ratio single cell element is an inwards concave hexagon, and the characteristic parameter values are as follows: the length of the bottom edge is 10.5mm, the length of the inclined wall is 6.291mm, the included angle between the bottom edge and the inclined wall is 75.5deg, and the thickness is 1mm.
The invention also discloses an optimization method of the automobile rear bumper based on the functional gradient negative Poisson's ratio structure, which comprises the following steps:
step 1), fitting a response surface model by using a DOE test optimization method, parametric modeling and finite element analysis;
and 2) optimizing the rear bumper by using a Taguchi design robustness method based on the response surface model to obtain the optimal thickness of the front cover of the rear bumper, the optimal thickness of the rear cover of the bumper and the optimal thickness gradient of the single-cell element with the negative Poisson ratio along the longitudinal direction.
As a further optimization scheme of the optimization method of the automobile rear bumper with the function gradient negative Poisson's ratio structure, the method 1) comprises the following detailed steps:
step 1.1), obtaining thickness gradient parameters of N groups of bumper front covers, bumper rear covers and single cell elements of a negative poisson ratio structure of a bumper body by using an optimal Latin hypercube experimental design method in ISIGHT, wherein N is a natural number larger than 1 and is a preset threshold value;
step 1.2), according to the N groups of parameters obtained in the step 1.1), compiling a macro program in the CATIA, and establishing N groups of geometrical models of the automobile rear bumper with a function gradient negative Poisson's ratio structure;
step 1.3), in HYPERMESH, according to the N groups of automobile rear bumper geometrical models with the function gradient negative Poisson's ratio structures in the step 1.2), establishing N groups of automobile rear side collision finite element models, and solving N groups of finite element calculation results through LSDYNA;
step 1.4), establishing two elliptic base neural network proxy models by using an elliptic base neural network proxy model method and taking the thickness of a front cover of a bumper, the thickness of a rear cover of the bumper, the gradient of a single cell element with a negative Poisson ratio along the axial direction and the collision speed as input and respectively taking the maximum collision force and the specific energy absorption as output according to N groups of finite element calculation results in the step 1.3);
step 1.5), by correlation coefficient R 2 And the root mean square error σ RMSE The method evaluates the precision of the two elliptic base neural network proxy models obtained in the step 1.4), if a correlation coefficient R 2 0.9 or more and root mean square error sigma RMSE If the accuracy of the response surface model meets the requirement, the step 1.6) is continuously executed if the accuracy of the response surface model is more than or equal to 0.1; otherwise, the step 1.1) to the step 1.4) are executed again until the precision requirement is met;
the correlation coefficient R 2 And the root mean square error σ RMSE The calculation formulas of (a) and (b) are respectively as follows:
wherein N is the number of sample points, p is the number of polynomial terms, i is the ith sample point, f i Is the finite element analysis value of the ith sample point, f i ' calculating a value of a response surface model for the ith sample point,
mean of finite element analysis for all sample points.
As a further optimization scheme of the optimization method of the automobile rear bumper with the function gradient negative Poisson's ratio structure, 2) comprises the following detailed steps:
step 2.1), in ISIGIT, selecting control factors including the thickness of a front bumper cover, the thickness of a rear bumper cover and the thickness gradient of a negative Poisson ratio single cell element along the longitudinal direction, taking four levels for each factor, and compiling a control factor experiment table L16 with 16 sets of parameter combinations according to an orthogonal experiment optimization method without considering the interaction of parameters;
step 2.2), continuously selecting the noise factor as the speed of the insurance after the rigid wall collides with the automobile, taking four levels for the noise factor, and compiling a noise factor experiment table L4 with 4 sets of parameter combinations;
step 2.3), a combination table is compiled by taking the control factor experiment table L16 in the step 2.1) as an inner table and the noise factor experiment table L4 in the step 2.2) as an outer table, and the experiment times of the combination table is 16 × 4=64 times;
step 2.4), obtaining the maximum impact force and the specific energy absorption value of 64 tests corresponding to the combination table according to the combination table and the two elliptic base neural network proxy models;
step 2.5), calculating the signal-to-noise ratios of the three control factors on each level relative to the maximum impact force and the specific energy absorption according to the expectation-maximization characteristic, and making a maximum impact force response diagram and a specific energy absorption response diagram by taking each level of the control factors as an abscissa and the corresponding signal-to-noise ratio as an ordinate, wherein the calculation formula of the signal-to-noise ratio SN is as follows:
in the formula, y i The objective function value of the ith test is obtained;
and 2.6), calculating to obtain the contribution rate of each control factor, determining the control factor which has the largest influence on the maximum impact force and the specific energy absorption according to the maximum contribution rate, finding out the optimal point of each factor, namely the point with the largest signal-to-noise ratio, from the maximum impact force response diagram and the specific energy absorption response diagram, combining the optimal points to obtain the optimal combination, wherein the thickness gradient of the corresponding front bumper cover, the thickness of the rear bumper cover and the thickness of the single negative poisson ratio cell along the longitudinal direction is the optimal solution.
As a further optimization scheme of the optimization method of the automobile rear bumper with the functional gradient negative poisson's ratio structure, the calculation steps of the contribution rate of each factor in the step 2.6) are as follows:
step 2.6.1), the total average signal-to-noise ratio is calculated according to the following formula
Wherein n is the total number of tests in the test design, (SN) i Signal to noise ratio for the ith experiment;
step 2.6.2), the total sum of squared deviations SS is calculated according to the following formula:
step 2.6.3), the sum of squared deviations SS of the i-th factor is calculated according to the following formula i ：
Wherein k is the number of levels of the factor; t is the number of trials of the ith factor at the ith level;
average signal-to-noise ratio at jth level for ith factor;
step 2.6.4), the contribution rate of each factor is calculated according to the following formula:
in the formula, P i Is the contribution ratio of the ith factor.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
1. the invention discloses an automobile rear bumper with a functional gradient negative Poisson ratio structure, which combines the functional gradient and the negative Poisson ratio structure, and ensures the characteristics of light weight and good energy absorption of the whole automobile rear bumper;
2. the optimization method of the invention sequentially adopts a DOE test optimization method, a parametric modeling method, a response surface model and a stability method of field design to carry out optimization design on the automobile bumper, and finally determines the thickness of the front cover of the bumper, the thickness of the rear cover of the bumper and the thickness gradient of a single cell element of a negative Poisson ratio structure along the longitudinal direction under the optimal state.
Drawings
FIG. 1 is a schematic view of an automobile rear bumper with a functionally graded negative Poisson's ratio structure according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a dimensional structure of a front cover of a rear bumper provided by an embodiment of the invention;
FIG. 3 is a schematic view of a rear cover of a rear bumper provided in accordance with an embodiment of the present invention;
FIG. 4 is a schematic diagram of a gradient distribution of a negative Poisson's ratio structure of a rear bumper of an automobile provided by an embodiment of the invention along the longitudinal direction of the automobile;
FIG. 5 is a schematic diagram of the size of a negative Poisson ratio structural unit cell of a rear bumper of an automobile according to an embodiment of the present invention;
fig. 6 is a flowchart of an automobile rear bumper post optimization method of a functional gradient negative poisson's ratio structure according to an embodiment of the present invention.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
as shown in fig. 1, an automobile rear bumper with a functional gradient negative poisson's ratio structure comprises a bumper front cover, a bumper body and a bumper rear cover; the bumper body is made of a negative Poisson's ratio material and is used for absorbing energy when an automobile collides; the front bumper cover and the rear bumper cover are matched with each other to form a shell, and the bumper body is fixed in the shell and then connected with the automobile body of the automobile.
The front bumper cover is in plate mounting, and the cross section of the rear bumper cover along the axial direction of the automobile is U-shaped.
As shown in fig. 2, the bumper front cover is 1220mm long in the longitudinal direction of the vehicle, 90mm high in the vertical direction of the vehicle, and 1mm thick itself.
As shown in fig. 3, the bumper back cover is 1220mm long in the vehicle longitudinal direction, 128mm wide in the vehicle axial direction, 90mm high in the vehicle vertical direction, and 1mm thick itself.
As shown in fig. 4, the bumper body is constituted by three layers of negative poisson's ratio single cells in the vehicle longitudinal direction, and the thickness gradient value of each layer of negative poisson's ratio single cell is constant.
As shown in fig. 5, the negative poisson ratio single cell is a concave hexagon, and its characteristic parameter values are: the length of the bottom edge is 10.5mm, the length of the inclined wall is 6.291mm, the included angle between the bottom edge and the inclined wall is 75.5deg, and the thickness is 1mm.
The invention also discloses an optimization method of the automobile rear bumper with the functional gradient negative Poisson's ratio structure, which comprises the following specific steps:
step 1), fitting a response surface model by using a DOE (design of element) test optimization method, parametric modeling and finite element analysis;
and 2) optimally designing the rear bumper of the automobile by using a Taguchi design robustness method based on the response surface model to obtain the optimal thickness of the front cover of the rear bumper, the optimal thickness of the rear cover of the bumper and the optimal thickness gradient of the single cell element of the negative Poisson's ratio structure along the longitudinal direction.
The invention also discloses an optimization method of the automobile rear bumper with the functional gradient negative Poisson's ratio structure, which is characterized in that 1) the optimization method comprises the following detailed steps:
step 1.1), obtaining thickness gradient parameters of N groups of bumper front covers, bumper rear covers and single cell elements of a negative poisson ratio structure of a bumper body by using an optimal Latin hypercube experimental design method in ISIGHT, wherein N is a natural number larger than 1 and is a preset threshold value;
step 1.2), according to the N groups of parameters obtained in the step 1.1), compiling a macro program in the CATIA, and establishing N groups of geometrical models of the automobile rear bumper with a function gradient negative Poisson's ratio structure;
step 1.3), in HYPERMESH, according to the N groups of automobile rear bumper geometrical models with the function gradient negative Poisson's ratio structures in the step 1.2), establishing N groups of automobile rear side collision finite element models, and solving N groups of finite element calculation results through LSDYNA;
step 1.4), establishing two elliptic base neural network proxy models by using an elliptic base neural network proxy model method and taking the thickness of a front bumper cover, the thickness of a rear bumper cover, the gradient of a negative Poisson ratio single cell element along the axial direction and the collision vehicle speed as input and respectively taking the maximum collision force (Fmax) and the ratio energy absorption (SEA) as output according to N groups of finite element calculation results in the step 1.3);
step 1.5), by means of a correlation coefficient R 2 And the root mean square error σ RMSE The method evaluates the precision of the two elliptic base neural network proxy models obtained in the step 1.4), if a correlation coefficient R 2 0.9 or more and root mean square error sigma RMSE If the accuracy of the response surface model meets the requirement, the step 1.6) is continuously executed if the accuracy of the response surface model is more than or equal to 0.1; otherwise, re-executing the step 1.1) to the step 1.4) until the precision requirement is met;
the correlation coefficient R 2 And the root mean square error σ RMSE The calculation formulas of (A) and (B) are respectively as follows:
wherein N is the number of sample points, p is the number of polynomial terms, i is the ith sample point, f i Is the finite element analysis value of the ith sample point, f i ' calculating a value of a response surface model for the ith sample point,
mean of finite element analysis for all sample points.
The step 2) comprises the following detailed steps:
step 2.1), in the ISIGIT, selecting control factors including the thickness of a front bumper cover, the thickness of a rear bumper cover and the thickness gradient of a single negative Poisson ratio cell element along the longitudinal direction, and taking four levels for each factor respectively, and compiling a control factor experiment table L16 with 16 groups of parameter combinations according to an orthogonal experiment optimization method without considering the interaction of the parameters;
step 2.2), continuously selecting noise factors as the speed of the safety after the rigid wall collides with the automobile, taking four levels for the noise factors, and compiling a noise factor test table L4 with 4 groups of parameter combinations;
step 2.3), a combination table is compiled by taking the control factor experiment table L16 in the step 2.1) as an inner table and taking the noise factor experiment table L4 in the step 2.2) as an outer table, wherein the experiment times of the combination table are 16 × 4=64 times;
step 2.4), obtaining the maximum impact force (Fmax) and Specific Energy Absorption (SEA) values of 64 tests corresponding to the combination table according to the combination table and the two elliptic base neural network proxy models;
step 2.5), calculating the signal-to-noise ratios of the three control factors on each level relative to the maximum impact force and the specific energy absorption according to the expected characteristics, and making a maximum impact force response diagram and a specific energy absorption response diagram by taking each level of the control factors as an abscissa and the corresponding signal-to-noise ratio as an ordinate, wherein the calculation formula of the signal-to-noise ratio SN is as follows:
in the formula, y i The objective function value of the ith test is obtained;
and 2.6), calculating to obtain the contribution rate of each control factor, determining the control factor which has the largest influence on the maximum impact force (Fmax) and the Specific Energy Absorption (SEA) according to the maximum contribution rate, finding out the optimal point of each factor, namely the point with the largest signal-to-noise ratio, from the maximum impact force response diagram and the specific energy absorption response diagram, combining the optimal points to obtain the optimal combination, wherein the thickness gradient of the corresponding front bumper cover, the thickness of the rear bumper cover and the thickness of the single negative poisson ratio cell along the longitudinal direction is the optimal solution.
The calculation steps of the contribution rate of each factor in the step 2.6) are as follows:
step 2.6.1), the total average signal-to-noise ratio is calculated according to the following formula
Wherein n is the total number of tests in the test design, (SN) i Signal to noise ratio for the ith experiment;
step 2.6.2), the sum of the squared deviations SS is calculated according to the following formula:
step 2.6.3), the sum of squared deviations SS of the ith factor is calculated according to the following formula i ：
Where k is the number of levels of the factor (k =4 for the present invention); t is the ith factor at the ith levelThe number of tests of (a);
average signal-to-noise ratio at jth level for ith factor;
step 2.6.4), calculating the contribution rate of each factor according to the following formula:
in the formula, P i Is the contribution rate of the ith factor.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The above-mentioned embodiments, objects, technical solutions and advantages of the present invention are further described in detail, it should be understood that the above-mentioned embodiments are only illustrative of the present invention and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (4)
1. A method for optimizing an automobile rear bumper with a functional gradient negative Poisson's ratio structure comprises a bumper front cover, a bumper body and a bumper rear cover;
the bumper body is made of a negative Poisson ratio material and is used for absorbing energy when an automobile is collided;
the front bumper cover and the rear bumper cover are matched with each other to form a shell, and the bumper body is fixed in the shell and then connected with the automobile body of the automobile;
the method for optimizing the automobile rear bumper with the functional gradient negative Poisson's ratio structure is characterized by comprising the following steps of:
step 1), fitting a response surface model by using a DOE test optimization method, parametric modeling and finite element analysis;
step 1.1), obtaining thickness gradient parameters of N groups of bumper front covers, bumper rear covers and single cell elements of a negative poisson ratio structure of a bumper body by using an optimal Latin hypercube experimental design method in ISIGHT, wherein N is a natural number larger than 1 and is a preset threshold value;
step 1.2), according to the N groups of parameters obtained in the step 1.1), in a CATIA, compiling a macro program, and establishing N groups of geometrical models of the rear bumper of the automobile with a functional gradient negative Poisson's ratio structure;
step 1.3), in HYPERMESH, according to the N groups of automobile rear bumper geometrical models with the function gradient negative Poisson's ratio structures in the step 1.2), establishing N groups of automobile rear side collision finite element models, and solving N groups of finite element calculation results through LSDYNA;
step 1.4), establishing two elliptic base neural network proxy models by using an elliptic base neural network proxy model method and taking the thickness of a front cover of a bumper, the thickness of a rear cover of the bumper, the gradient of a negative Poisson ratio single cell element along the axial direction and the collision vehicle speed as input and respectively taking the maximum collision force and specific energy absorption as output according to N groups of finite element calculation results in the step 1.3);
step 1.5), by means of a correlation coefficient R 2 And the root mean square error σ RMSE The method evaluates the precision of the two elliptic base neural network proxy models obtained in the step 1.4), if a correlation coefficient R 2 0.9 or more and root mean square error sigma RMSE If the precision of the response surface model meets the requirement, the step 1.6) is continuously executed if the precision of the response surface model is larger than or equal to 0.1); otherwise, re-executing the step 1.1) to the step 1.4) until the precision requirement is met;
the correlation coefficient R 2 And the root mean square error σ RMSE The calculation formulas of (A) and (B) are respectively as follows:
wherein N is the number of sample points, p is the number of polynomial terms, i is the ith sample point, f i Is the finite element analysis value of the ith sample point, f i ' is a response surface model calculation value for the ith sample point,
the mean value of the finite element analysis of all sample points is obtained;
step 2), optimizing the rear bumper of the automobile by using a Taguchi design robustness method based on the response surface model to obtain the optimal thickness of the front cover of the rear bumper, the optimal thickness of the rear cover of the bumper and the optimal thickness gradient of the single-cell element with the negative Poisson ratio along the longitudinal direction;
step 2.1), in the ISIGIT, selecting control factors including the thickness of a front bumper cover, the thickness of a rear bumper cover and the thickness gradient of a single negative Poisson ratio cell element along the longitudinal direction, and taking four levels for each factor respectively, and compiling a control factor experiment table L16 with 16 groups of parameter combinations according to an orthogonal experiment optimization method without considering the interaction of the parameters;
step 2.2), continuously selecting noise factors as the speed of the safety after the rigid wall collides with the automobile, taking four levels for the noise factors, and compiling a noise factor test table L4 with 4 groups of parameter combinations;
step 2.3), a combination table is compiled by taking the control factor experiment table L16 in the step 2.1) as an inner table and the noise factor experiment table L4 in the step 2.2) as an outer table, and the experiment times of the combination table is 16 × 4=64 times;
step 2.4), obtaining the maximum impact force and the specific energy absorption value of 64 tests corresponding to the combination table according to the combination table and the two elliptic base neural network proxy models;
step 2.5), calculating the signal-to-noise ratios of the three control factors on each level relative to the maximum impact force and the specific energy absorption according to the expected characteristics, and making a maximum impact force response diagram and a specific energy absorption response diagram by taking each level of the control factors as an abscissa and the corresponding signal-to-noise ratio as an ordinate, wherein the calculation formula of the signal-to-noise ratio SN is as follows:
in the formula, y i The objective function value of the ith test is obtained;
and 2.6), calculating to obtain the contribution rate of each control factor, determining the control factor which has the largest influence on the maximum impact force and the specific energy absorption according to the maximum contribution rate, finding out the optimal point of each factor, namely the point with the largest signal-to-noise ratio, from the maximum impact force response diagram and the specific energy absorption response diagram, combining the optimal points to obtain the optimal combination, wherein the thickness gradient of the corresponding front bumper cover, the thickness of the rear bumper cover and the thickness of the single negative poisson ratio cell along the longitudinal direction is the optimal solution.
2. The method for optimizing an automobile rear bumper with a functionally graded negative poisson's ratio structure as claimed in claim 1, wherein the front bumper cover is plate-mounted, and the section of the rear bumper cover along the axial direction of the automobile is U-shaped;
the length of the front bumper cover in the longitudinal direction of the automobile is 1220mm, the height of the front bumper cover in the vertical direction of the automobile is 90mm, and the thickness of the front bumper cover is 1mm;
the bumper rear cover is 1220mm long in the longitudinal direction of the automobile, 128mm wide in the axial direction of the automobile, 90mm high in the vertical direction of the automobile and 1mm thick.
3. The method for optimizing an automobile rear bumper with a functionally graded negative poisson's ratio structure as claimed in claim 1, wherein the bumper body is composed of three layers of negative poisson's ratio single cells along the longitudinal direction of the automobile, and the thickness gradient value of each layer of negative poisson's ratio single cell is constant;
the negative Poisson ratio single cell is an inwards concave hexagon, and the characteristic parameter values are respectively as follows: the length of the bottom edge is 10.5mm, the length of the inclined wall is 6.291mm, the included angle between the bottom edge and the inclined wall is 75.5deg, and the thickness is 1mm.
4. The method for optimizing a rear bumper of an automobile with a functionally graded negative poisson's ratio structure as claimed in claim 1, wherein the step 2.6) of calculating the contribution ratio of each factor comprises the following steps:
step 2.6.1), the total average signal-to-noise ratio is calculated according to the following formula
Wherein n is the total number of tests in the test design, (SN) i Signal to noise ratio for the ith experiment;
step 2.6.2), the total sum of squared deviations SS is calculated according to the following formula:
step 2.6.3), the sum of squared deviations SS of the ith factor is calculated according to the following formula i ：
Wherein k is the number of levels of the factor; t is the number of trials of the ith factor at the ith level;
average signal-to-noise ratio at jth level for ith factor;
step 2.6.4), the contribution rate of each factor is calculated according to the following formula:
in the formula, P i Is the contribution ratio of the ith factor.
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| CN108045338A (en) * | 2018-01-12 | 2018-05-18 | 南京航空航天大学 | A kind of three-dimensional negative poisson's ratio construction car energy-absorption box of positive thickness gradient |
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