CN107145626B - Negative poisson ratio structure energy-absorbing box and multidisciplinary collaborative optimization method thereof - Google Patents
Negative poisson ratio structure energy-absorbing box and multidisciplinary collaborative optimization method thereof Download PDFInfo
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Abstract
The invention discloses a negative poisson ratio structure energy-absorbing box and a multidisciplinary collaborative optimization method thereof. Because the two-dimensional negative poisson ratio structure inner core is composed of a large number of negative poisson ratio unit cell structures, parameters of the negative poisson ratio unit cell structures have great influence on energy absorption performance of the energy absorption boxes, the invention provides a multidisciplinary collaborative optimization method based on the negative poisson ratio structure energy absorption boxes, a multidisciplinary collaborative optimization calculation model of the negative poisson ratio structure energy absorption boxes taking mass as a main system, peak collision force, compression displacement and total energy absorption as sub-systems is constructed, a multidisciplinary collaborative optimization is carried out on the main system by adopting a multidisciplinary genetic algorithm, and the sub-systems adopt a sequence quadratic programming algorithm to carry out multidisciplinary collaborative optimization.
Description
Technical Field
The invention belongs to the field of passive safety protection of automobiles, and particularly relates to a negative poisson ratio structure energy-absorbing box and a multidisciplinary collaborative optimization method thereof.
Background
The common energy-absorbing box is of a hollow square structure, when a vehicle collides, the energy-absorbing box often has the problems of unstable deformation and insufficient deformation, so that the effect of absorbing collision energy by the energy-absorbing box is poor, and only a small amount of collision energy can be absorbed. The energy absorption buffer effect of the energy absorption box is not obvious, and most of the rest energy needs to be absorbed by other vehicle components except the energy absorption box, so that the energy absorption box has high maintenance cost, and serious injury to passengers is caused.
The negative poisson ratio structural material shows special deformation performance different from that of the common material when the negative poisson ratio structural material is subjected to load, so that the negative poisson ratio structural material shows more excellent performance than the common material in energy absorption, and therefore the negative poisson ratio structural material can be filled in the conventional energy absorption box to form the negative poisson ratio structural energy absorption box, and the defects of unstable deformation, poor energy absorption effect and the like of the common energy absorption box when a vehicle collides are well overcome.
The energy absorption performance of the energy-absorbing box with the negative poisson ratio structure is closely related to the parameters of the negative poisson ratio unit cell structure, and the energy absorption performance of the energy-absorbing box formed by the unit cell structures with different geometric parameters is also different, so that the energy-absorbing effect of the energy-absorbing box is further improved by optimally designing the negative poisson ratio unit cell structure.
Disclosure of Invention
The invention aims to overcome the defects of the background technology and provides a negative poisson ratio structure energy-absorbing box and a multidisciplinary collaborative optimization method thereof.
The invention solves the technical problems by the following technical proposal:
the negative poisson ratio unit cell structure comprises two symmetrically parallel bottom edges, wherein the same sides of the two bottom edges are connected through a first inclined edge and a second inclined edge which are connected, the lengths of the first inclined edge and the second inclined edge are equal, and the first inclined edge and the second inclined edge of the same side are inclined inwards; the thicknesses of the first inclined edge, the second inclined edge and the bottom edge are t, and t is more than or equal to 0.6mm and less than or equal to 1.2mm; the widths of the first bevel edge, the second bevel edge and the bottom edge are b, and b is more than or equal to 2.2mm and less than or equal to 3mm; the included angle between each bevel edge and the adjacent bottom edge is d, and d is more than or equal to 55 degrees and less than or equal to 75 degrees; the length of the two bottom edges is a, and a is more than or equal to 12mm and less than or equal to 16mm; the vertical distance between the two bottom edges is h, and h is more than or equal to 8mm and less than or equal to 13mm.
Further, the thicknesses t of the first bevel edge, the second bevel edge and the bottom edge are 1.1575mm; the width b of the first bevel edge, the second bevel edge and the bottom edge is 2.2009mm; the included angle d between each bevel edge and the adjacent bottom edge is 74.684 degrees; the length a of the two bottom edges is 13.764mm; the vertical distance h between the two bottom edges was 12.877mm.
The two-dimensional negative poisson ratio structure inner core based on the negative poisson ratio unit cell structure comprises more than one negative poisson ratio unit cell structure, wherein the negative poisson ratio unit cell structures are arranged in an array manner along the extending direction of the width b, the negative poisson ratio unit cell structures are arranged in an array manner along the extending directions of the two ends of the vertical distance h between the two bottom edges, and the negative poisson ratio unit cell structures are arranged in an array manner along the extending directions of the two ends of the length a of the two bottom edges; in the extending direction of the width b, the negative poisson ratio unit cell structures are stacked symmetrically; in the extending direction of the length a, the first inclined edge of the negative poisson ratio unit cell structure is overlapped with the second inclined edge of the adjacent negative poisson ratio unit cell structure; in the extending direction of the distance h, the bottom edges of the adjacent negative poisson ratio unit cell structures are mutually overlapped.
The energy-absorbing box with the negative poisson ratio structure comprises an energy-absorbing box body (1), a front mounting plate (2) and a rear mounting plate (5), wherein one end of the energy-absorbing box body (1) is connected with the front mounting plate (2), and the other end of the energy-absorbing box body (1) is connected with the rear mounting plate (5); the front mounting plate (2) is used for being connected with the automobile bumper beam through bolts, and the rear mounting plate (5) is used for being connected with the longitudinal beam of the automobile body through bolts.
Further, the energy-absorbing box body (1) is of a hollow prismatic structure with a trapezoid cross section, the whole surface of the energy-absorbing box body (1) comprises an upper surface, a lower surface, a left side surface and a right side surface, the upper surface corresponds to the upper bottom of the trapezoid energy-absorbing box body (1), the lower surface corresponds to the lower bottom of the trapezoid energy-absorbing box body (1), and the left side surface and the right side surface correspond to two side edges of the trapezoid energy-absorbing box body (1);
two first induction grooves (41) are symmetrically formed in the left side surface and the right side surface, the first induction grooves (41) are positioned at the trisection point of the axial length of the energy-absorbing box body (1), the first induction grooves far away from the front mounting plate (2) are the first induction grooves, the first induction grooves far away from the rear mounting plate (5) are the second induction grooves, and the first induction grooves (41) extend to the upper surface; three second induction grooves (42) are symmetrically formed in the upper surface and the lower surface, the first second induction groove (42) in the upper surface is positioned in the middle of the upper surface projection of the front mounting plate (2) and the second induction groove (42), the second induction groove (42) in the upper surface is positioned in the middle of the upper surface projection of the first induction groove and the second induction groove (42), and the third induction groove (42) in the upper surface is positioned in the middle of the upper surface projection of the first induction groove and the rear mounting plate (5); the second induction groove (42) and the first induction groove (41) are concave, and the depth of the second induction groove (42) is larger than that of the first induction groove (41); in the direction from the front mounting plate (2) to the rear mounting plate (5), the depths of the three second induction grooves (42) are gradually reduced, and the depths of the two first induction grooves (41) are also gradually reduced.
The multidisciplinary collaborative optimization method of a negative poisson ratio structure energy-absorbing box is characterized in that a two-dimensional negative poisson ratio structure inner core based on a negative poisson ratio unit cell structure is arranged in the negative poisson ratio structure energy-absorbing box, the negative poisson ratio unit cell structure comprises two bottom edges which are symmetrically parallel, the same side of the two bottom edges is connected through a first oblique edge and a second oblique edge which are connected, and the first oblique edge and the second oblique edge of the same side are inclined inwards; the thicknesses of the first inclined edge, the second inclined edge and the bottom edge are t, the widths of the first inclined edge, the second inclined edge and the bottom edge are b, the included angle d between each inclined edge and the adjacent bottom edge is a, the lengths of the two bottom edges are a, and the vertical distance between the two bottom edges is h; the two-dimensional negative poisson ratio structure inner core comprises more than one negative poisson ratio unit cell structure, the negative poisson ratio unit cell structures are arranged in an array along the extending direction of the width b, the negative poisson ratio unit cell structures are arranged in an array along the extending direction of the two ends of the vertical distance h between the two bottom edges, and the negative poisson ratio unit cell structures are arranged in an array along the extending direction of the two ends of the length a of the two bottom edges; in the extending direction of the width b, the negative poisson ratio unit cell structures are stacked symmetrically; in the extending direction of the length a, the first inclined edge of the negative poisson ratio unit cell structure is overlapped with the second inclined edge of the adjacent negative poisson ratio unit cell structure; in the extending direction of the distance h, the bottom edges of adjacent negative poisson ratio unit cell structures are mutually overlapped, and the method comprises the following steps:
step 1), firstly, selecting an orthogonal test design method in ISIGHT optimization software, and uniformly selecting N groups of design sample points in the variation range of each design variable, wherein the design variables are respectively the length a of the bottom edge of a negative Poisson ratio unit cell structure, the included angle d between each inclined edge and the adjacent bottom edge, the vertical distance h between the two bottom edges, the thickness t of the negative Poisson ratio unit cell structure and the width b of the negative Poisson ratio unit cell structure;
step 2), establishing CAD models of inner cores of the N groups of two-dimensional negative poisson ratio structures in PROE software according to the selected N groups of design sample points;
the specific forming process of the CAD model of the two-dimensional negative poisson ratio structure inner core comprises the following steps: firstly, carrying out array change in the X direction on the basis of a negative Poisson ratio unit cell structure to form a negative Poisson ratio multicellular structure; then, carrying out array change in the Y direction and the Z direction on the negative Poisson ratio multicell structure to form an inner core of the two-dimensional negative Poisson ratio structure;
step 3), importing a CAD model of the two-dimensional negative poisson ratio structure inner core into HYPERMESH software, performing geometric cleaning and grid division on the CAD model, and setting the material and thickness of the two-dimensional negative poisson ratio structure inner core;
step 4), a traditional energy-absorbing box shell model without an inner core of a two-dimensional negative poisson ratio structure and a rigid wall model for testing collision are led into HYPERMESH, the inner core of the two-dimensional negative poisson ratio structure is filled in the traditional energy-absorbing box shell, the collision speed between the rigid wall and the energy-absorbing box of the negative poisson ratio structure is set, 6 degrees of freedom of a node which is not contacted with the rigid wall when the energy-absorbing box of the negative poisson ratio structure collides are restrained, and meanwhile contact and output between the rigid wall and the energy-absorbing box of the negative poisson ratio structure are defined;
step 5), importing the finite element simulation model of the energy-absorbing box with the N groups of negative poisson ratio structures into dynamics analysis software LS-DYNA to carry out solving calculation, and collecting data such as mass m, peak collision force P, compression displacement S, total energy absorption W and the like in the collision process of the energy-absorbing box in HYPERGRAPH and HYPERVIEW;
step 6), selecting a high-order response surface model in ISIGHT software, and constructing a response surface model of the mass m, a response surface model of the peak impact force P, a response surface model of the compression displacement S and a response surface model of the total energy absorption W by taking a bottom edge length a, an included angle d between a bevel edge and a bottom edge, a vertical distance h between two bottom edges, a thickness t of the negative poisson ratio unit structure and a width b of the negative poisson ratio unit structure corresponding to N groups of negative poisson ratio unit structures as inputs and taking a mass m, a peak impact force P, a compression displacement S and a total energy absorption W corresponding to N groups of negative poisson ratio unit structures as output parameters;
step 7), performing error check on the four fitted response surface models, namely respectively calculating the correlation coefficients R of the four fitted response surface models 2 And root mean square error sigma RMSE Comparing the correlation coefficient value with a preset correlation coefficient value and a preset root mean square error value; the preset correlation coefficient value is 0.93, and the preset root mean square error value is 0.1.
Step 8), if the correlation coefficient R of the four response surface models 2 All are greater than or equal to the preset correlation coefficient value and root mean square error sigma RMSE And (3) executing the step (9) if the root mean square error value is smaller than or equal to the preset root mean square error value; otherwise re-executeStep 1) to step 7) up to the correlation coefficient R of the four response surface models 2 All are greater than or equal to the preset correlation coefficient value and root mean square error sigma RMSE All are smaller than or equal to preset root mean square error values;
step 9), constructing a multidisciplinary collaborative optimization calculation model of the negative poisson ratio structure energy absorption box taking the mass m as a main system, and taking the peak collision force P, the compression displacement S and the total energy absorption W as subsystems in the ISIGHT;
step 10), according to the established multidisciplinary collaborative optimization calculation model, a multidisciplinary genetic algorithm is adopted for a main system, a sequence quadratic programming algorithm is adopted for a subsystem, multidisciplinary collaborative optimization is carried out on the length a of the bottom edge of a negative poisson ratio unit cell structure, the included angle d between the inclined edge and the bottom edge, the height h between the two bottom edges, the thickness t of the negative poisson ratio unit cell structure and the width b of the negative poisson ratio unit cell structure, an optimized Pareto solution set is obtained, and finally a group of optimal solutions is selected from the Pareto solution set; the parameters of the multi-island genetic algorithm are set as follows: the sub population size is 10, the island number is 10, the genetic algebra is 10, the crossover rate is 1, and the mutation rate and the mobility are 0.01.
Further, the N values in the N sets of design sample points in step 1) are 128, and the orthogonal table of the orthogonal test in step 1) is L128 (45), i.e. 128 tests at a 5-factor 4 level, and the ranges of variation of the design variables are respectively: a epsilon [12,16], b epsilon [2.2,3], h epsilon [8,13], d epsilon [55 DEG, 75 DEG ], t epsilon [0.6,1.2].
Further, the collision speed between the rigid wall and the negative poisson ratio structure energy absorption box in the step 4) is 16km/h.
Further, the order of the high-order response surface model in step 6) is four, and the response surface model of the mass m, the response surface model of the peak collision force P, the response surface model of the compression displacement S, and the response surface model of the total energy absorption W are respectively:
1) Response surface model of mass m:
m＝211.3606+49.6045a+24.1501b+5.3261h+0.6283d+21.2653t-5.3558a 2 -12.2847b 2 -0.7646h 2 -0.0202d 2 -32.3845t 2 -0.0408ab-0.005471ah+0.004664ad-0.1212at-0.004321bh-0.005127bd+0.2367bt-0.001471hd+0.01352ht-0.01615dt+0.25515a 3 +2.8967b 3 +0.05h 3 +0.0002531d 3 +25.1231t 3 -0.004538a 4 -0.2558b 4 -0.001219h 4 -1.1354d 4 -7.2777t 4
2) Response surface model of peak impact force P:
P＝4668216.0363-524643.9041a-7708169.0354b+180530.2357h+116513.3631d+676777.0333t+53084.1734a 2 +4440679.005b 2 -27221.9961h 2 -2741.6867d 2 -1112772.4445t 2 -764.2867ab+92.2161ah+2.71103ad-3377.2085at-887.0286bh+0.6144bd+8016.8117bt-13.102hd-2325.5156ht-166.4317dt-2366.5567a 3 -1130853.1258b 3 +1820.4986h 3 +28.5245d 3 +888866.9604t 3 +39.4309a 4 +107640.8348b 4 -44.8933h 4 -0.1104d 4 -257318.5951t 4
3) Response surface model of compression displacement S:
S＝3164.2166-2619.5605a-3295.4876b-1502.5493h+753.841d+1092.6702t+269.7967a 2 +1835.7762b 2 +219.7779h 2 -17.4459d 2 -1698.359t 2 +1.6865ab+0.7515ah+0.0458ad-5.3776at-0.5554bh-0.3566bd+14.0272bt-0.06261hd-1.1016ht-0.1667dt-12.3464a 3 -452.8848b 3 -14.1708h 3 +0.1794d 3 +1199.2214t 3 +0.211a 4 +41.6366b 4 +0.3391h 4 -0.0006909d 4 -308.9682t 4
4) Response surface model of total energy absorption W:
W＝34302933.709+644211.1649a-50669721.7989b+2764796.5129h-344895.9615d+7488596.9982t-77930.7763a 2 +30603398.0454b 2 -417962.829h 2 +7361.5903d 2 -12384142.8218t 2 -5224.2092ab+1267.0536ah-161.2317ad+24530.8658at-1716.4935bh+1638.7714bd-117348.4422bt+30.2318hd+2382.9861ht-4541.5054dt+4175.07a 3 -8154173.7925b 3 +27621.0081h 3 -68.1648d 3 +9091335.913t 3 -83.9117a 4 +809729.5918b 4 -677.5896h 4 +0.2309d 4 -2449116.2989t 4 。
further, in the step 9), the multi-disciplinary collaborative optimization calculation model of the negative poisson ratio structure energy absorption box with the mass m as a main system, the peak collision force P, the compression displacement S and the total energy absorption W as subsystems is respectively as follows:
1) Mass m main system calculation model:
wherein: a is more than or equal to 12 and less than or equal to 16,2.2, b is more than or equal to 3, h is more than or equal to 8 and less than or equal to 13,55 degrees, d is more than or equal to 75 degrees, t is more than or equal to 0.6 and less than or equal to 1.2, and the relaxation factor epsilon=0.001
2) Peak collision force P subsystem calculation model:
3) Compression displacement S subsystem calculation model:
4) Total energy absorption W subsystem calculation model:
。
the beneficial effects of the invention are as follows:
1. the two-dimensional negative poisson ratio structure inner core with a good energy absorption effect is filled in the two-dimensional negative poisson ratio structure inner core on the basis of the common energy absorption box to form the energy absorption box with the negative poisson ratio structure, so that the defects of unstable deformation, poor energy absorption effect and the like of the common energy absorption box when a vehicle collides are well overcome.
2. The energy absorption performance of the energy-absorbing box with the negative poisson ratio structure is closely related to the parameters of the negative poisson ratio unit structure, and the energy-absorbing effect of the energy-absorbing box can be further improved after the parameters of the negative poisson ratio unit structure are optimally designed.
Drawings
FIG. 1 is a schematic diagram of a negative poisson's ratio structural crash box of the present invention;
FIG. 2 is a schematic diagram of a CAD model of the inner core of the two-dimensional negative Poisson's ratio structure of the present invention;
FIG. 3 is a schematic diagram of a negative Poisson's ratio cell structure;
FIG. 4 is a schematic flow diagram of a multidisciplinary collaborative optimization method for a negative poisson's ratio structure crash box of the present invention.
Reference numerals illustrate:
the energy-absorbing box comprises a 1-energy-absorbing box body, a 2-front mounting plate, a 3-two-dimensional inner core with a negative poisson ratio structure, a 41-induction groove I, a 42-induction groove II and a 5-rear mounting plate.
Detailed Description
The invention is further illustrated by the following examples, which are intended to be illustrative only and not limiting in any way.
It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. 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.
A negative poisson ratio unit cell structure is shown in figure 3, and comprises two symmetrically parallel bottom edges, wherein the same sides of the two bottom edges are connected through a first inclined edge and a second inclined edge which are connected, the lengths of the first inclined edge and the second inclined edge are equal, and the first inclined edge and the second inclined edge of the same side are inclined inwards; the thicknesses of the first inclined edge, the second inclined edge and the bottom edge are t, and t is more than or equal to 0.6mm and less than or equal to 1.2mm; the widths of the first bevel edge, the second bevel edge and the bottom edge are b, and b is more than or equal to 2.2mm and less than or equal to 3mm; the included angle between each bevel edge and the adjacent bottom edge is d, and d is more than or equal to 55 degrees and less than or equal to 75 degrees; the length of the two bottom edges is a, and a is more than or equal to 12mm and less than or equal to 16mm; the vertical distance between the two bottom edges is h, and h is more than or equal to 8mm and less than or equal to 13mm. These 5 parameters determine the overall characteristics of the negative poisson's ratio cell structure, as well as its dimensional change. The negative poisson ratio unit cell structure is in a concave hexagonal honeycomb structure, and when the negative poisson ratio unit cell structure is subjected to uniaxial compression, the inclined side of the structure is bent and deformed so as to generate a negative poisson ratio effect.
The optimal solution of the invention is as follows: the thickness t of the first bevel edge, the second bevel edge and the bottom edge is 1.1575mm; the width b of the first bevel edge, the second bevel edge and the bottom edge is 2.2009mm; the included angle d between each bevel edge and the adjacent bottom edge is 74.684 degrees; the length a of the two bottom edges is 13.764mm; the vertical distance h between the two bottom edges was 12.877mm.
The two-dimensional negative poisson ratio structure inner core based on the negative poisson ratio unit cell structure comprises more than one negative poisson ratio unit cell structure, wherein the negative poisson ratio unit cell structures are arranged in an array manner along the extending direction of the width b, the negative poisson ratio unit cell structures are arranged in an array manner along the extending directions of two ends of the vertical distance h between two bottom edges, and the negative poisson ratio unit cell structures are arranged in an array manner along the extending directions of two ends of the length a of the two bottom edges; in the extending direction of the width b, the negative poisson ratio unit cell structures are stacked symmetrically; in the extending direction of the length a, the first inclined edge of the negative poisson ratio unit cell structure is overlapped with the second inclined edge of the adjacent negative poisson ratio unit cell structure; in the extending direction of the distance h, the bottom edges of the adjacent negative poisson ratio unit cell structures are mutually overlapped. The whole two-dimensional negative poisson ratio structure inner core 3 is designed into a square energy absorption structure consisting of 22 x 9 x 32=6336 negative poisson ratio unit cell structures.
As shown in fig. 1, the energy-absorbing box with the negative poisson ratio structure is internally provided with a two-dimensional inner core with the negative poisson ratio structure, and comprises an energy-absorbing box body 1, a front mounting plate 2 and a rear mounting plate 5, wherein one end of the energy-absorbing box body 1 is connected with the front mounting plate 2, and the other end of the energy-absorbing box body 1 is connected with the rear mounting plate 5. The front mounting plate 2 is used for being connected with a car bumper beam through four bolts, and the rear mounting plate 5 is used for being connected with a longitudinal beam of a car body through four bolts. The two-dimensional negative poisson ratio inner core shows special deformation performance different from that of common materials when being subjected to load, so that the energy absorption performance of the energy absorption box is better improved compared with that of the common materials in energy absorption.
The energy-absorbing box body 1 is of a hollow prismatic structure with a trapezoid cross section, the whole surface of the energy-absorbing box body 1 comprises an upper surface, a lower surface, a left side surface and a right side surface, the upper surface corresponds to the upper bottom of the trapezoid energy-absorbing box body 1, the lower surface corresponds to the lower bottom of the trapezoid energy-absorbing box body 1, and the left side surface and the right side surface correspond to the two side edges of the trapezoid energy-absorbing box body 1.
Two first induction grooves 41 are symmetrically arranged on the left side face and the right side face, and the first induction grooves 41 are positioned at the trisection points of the axial length of the energy-absorbing box body 1. The first guiding groove far away from the front mounting plate 2 is a first guiding groove, the first guiding groove far away from the rear mounting plate 5 is a second guiding groove, and the first guiding grooves 41 extend to the upper surface. The upper surface and the lower surface are symmetrically provided with three guiding grooves II 42, the first guiding groove II 42 on the upper surface is positioned in the middle of the upper surface projection of the front mounting plate 2 and the second guiding groove I, the second guiding groove II 42 on the upper surface is positioned in the middle of the upper surface projection of the first guiding groove I and the second guiding groove I, and the third guiding groove II 42 on the upper surface is positioned in the middle of the upper surface projection of the first guiding groove I and the rear mounting plate 5. The second guiding groove 42 and the first guiding groove 41 are concave, and the depth of the second guiding groove 42 is larger than that of the first guiding groove 41. In the direction from the front mounting plate 2 to the rear mounting plate 5, the depths of the three second induction grooves 42 are gradually reduced, and the depths of the two first induction grooves 41 are also gradually reduced, so that the deformation of the energy absorption box is more stable and sufficient in collision, and the energy absorption performance of the energy absorption box is improved.
As shown in fig. 4, in the multidisciplinary collaborative optimization method of the energy-absorbing box with the negative poisson ratio structure, a two-dimensional inner core with the negative poisson ratio structure based on a negative poisson ratio unit cell structure is arranged in the energy-absorbing box with the negative poisson ratio structure, the negative poisson ratio unit cell structure comprises two bottom edges which are symmetrically parallel, the same sides of the two bottom edges are connected through a first oblique edge and a second oblique edge which are connected, and the first oblique edge and the second oblique edge of the same side are inclined inwards; the thicknesses of the first inclined edge, the second inclined edge and the bottom edge are t, the widths of the first inclined edge, the second inclined edge and the bottom edge are b, the included angle d between each inclined edge and the adjacent bottom edge is a, the lengths of the two bottom edges are a, and the vertical distance between the two bottom edges is h; the two-dimensional negative poisson ratio structure inner core comprises more than one negative poisson ratio unit cell structure, the negative poisson ratio unit cell structures are arranged in an array along the extending direction of the width b, the negative poisson ratio unit cell structures are arranged in an array along the extending direction of the two ends of the vertical distance h between the two bottom edges, and the negative poisson ratio unit cell structures are arranged in an array along the extending direction of the two ends of the length a of the two bottom edges; in the extending direction of the width b, the negative poisson ratio unit cell structures are stacked symmetrically; in the extending direction of the length a, the first inclined edge of the negative poisson ratio unit cell structure is overlapped with the second inclined edge of the adjacent negative poisson ratio unit cell structure; in the extending direction of the distance h, the bottom edges of adjacent negative poisson ratio unit cell structures are mutually overlapped, and the method comprises the following steps:
step 1), firstly, selecting an orthogonal test design method in ISIGHT optimization software, and uniformly selecting N groups of design sample points in the variation range of each design variable, wherein the design variables are respectively the length a of the bottom edge of the negative poisson ratio unit cell structure, the included angle d between each inclined edge and the adjacent bottom edge, the vertical distance h between the two bottom edges, the thickness t of the negative poisson ratio unit cell structure and the width b of the negative poisson ratio unit cell structure.
The orthogonality table of the orthogonality test is L128 (45), namely, the 5-factor 4 level 128 tests, so that the N value is 128, and the variation ranges of all design variables are respectively as follows: a epsilon [12,16], b epsilon [2.2,3], h epsilon [8,13], d epsilon [55 DEG, 75 DEG ], t epsilon [0.6,1.2].
And 2) establishing a CAD model of the 128-group two-dimensional negative poisson ratio structure inner core in PROE software according to the 128 groups of design sample points.
The CAD model of the two-dimensional negative poisson's ratio structure core is shown in fig. 2: firstly, establishing a negative poisson ratio unit cell structure as shown in Step1 in fig. 2; performing array change in the X direction on the basis of the negative Poisson ratio unit cell structure to form a negative Poisson ratio multicellular structure shown as Step2 in FIG. 2; then performing array change in the Y direction on the negative Poisson ratio multicell structure as shown in Step3 in FIG. 2; finally, array change in the Z direction is carried out to form a two-dimensional negative Poisson ratio structure inner core, which is shown as Step4 in FIG. 2.
And 3) importing the CAD model of the two-dimensional negative poisson ratio structure inner core into HYPERMESH software, performing geometric cleaning and grid division on the CAD model, and setting the material and thickness of the two-dimensional negative poisson ratio structure inner core.
Step 4), a traditional energy-absorbing box shell model without an inner core of a two-dimensional negative poisson ratio structure and a rigid wall model for testing collision are led into HYPERMESH, the inner core of the two-dimensional negative poisson ratio structure is filled in the traditional energy-absorbing box shell, the collision speed between the rigid wall and the energy-absorbing box of the negative poisson ratio structure is set, 6 degrees of freedom of a node which is not contacted with the rigid wall when the energy-absorbing box of the negative poisson ratio structure collides are restrained, and meanwhile contact and output between the rigid wall and the energy-absorbing box of the negative poisson ratio structure are defined;
the collision speed between the rigid wall and the energy absorption box with the negative poisson ratio structure is 16km/h, and the defined output data of the energy absorption box with the negative poisson ratio structure comprises the following steps: mass m, peak impact force P, compression displacement S, total energy absorption W.
Step 5), importing the finite element simulation model of the energy-absorbing box with the N groups of negative poisson ratio structures into dynamics analysis software LS-DYNA to carry out solving calculation, and collecting data such as mass m, peak collision force P, compression displacement S, total energy absorption W and the like in the collision process of the energy-absorbing box in HYPERGRAPH and HYPERVIEW;
step 6), selecting a high-order response surface model in ISIGHT software, and constructing a response surface model of the mass m, a response surface model of the peak impact force P, a response surface model of the compression displacement S and a response surface model of the total energy absorption W by taking a bottom edge length a, an included angle d between a bevel edge and a bottom edge, a vertical distance h between two bottom edges, a thickness t of the negative poisson ratio unit structure and a width b of the negative poisson ratio unit structure corresponding to N groups of negative poisson ratio unit structures as inputs and taking a mass m, a peak impact force P, a compression displacement S and a total energy absorption W corresponding to N groups of negative poisson ratio unit structures as output parameters;
the order of the high-order response surface model is four-order, and the response surface model of the mass m, the response surface model of the peak collision force P, the response surface model of the compression displacement S and the response surface model of the total energy absorption W are respectively as follows:
1) Response surface model of mass m:
m＝211.3606+49.6045a+24.1501b+5.3261h+0.6283d+21.2653t-5.3558a 2 -12.2847b 2 -0.7646h 2 -0.0202d 2 -32.3845t 2 -0.0408ab-0.005471ah+0.004664ad-0.1212at-0.004321bh-0.005127bd+0.2367bt-0.001471hd+0.01352ht-0.01615dt+0.25515a 3 +2.8967b 3 +0.05h 3 +0.0002531d 3 +25.1231t 3 -0.004538a 4 -0.2558b 4 -0.001219h 4 -1.1354d 4 -7.2777t 4
2) Response surface model of peak impact force P:
P＝4668216.0363-524643.9041a-7708169.0354b+180530.2357h+116513.3631d+676777.0333t+53084.1734a 2 +4440679.005b 2 -27221.9961h 2 -2741.6867d 2 -1112772.4445t 2 -764.2867ab+92.2161ah+2.71103ad-3377.2085at-887.0286bh+0.6144bd+8016.8117bt-13.102hd-2325.5156ht-166.4317dt-2366.5567a 3 -1130853.1258b 3 +1820.4986h 3 +28.5245d 3 +888866.9604t 3 +39.4309a 4 +107640.8348b 4 -44.8933h 4 -0.1104d 4 -257318.5951t 4
3) Response surface model of compression displacement S:
S＝3164.2166-2619.5605a-3295.4876b-1502.5493h+753.841d+1092.6702t+269.7967a 2 +1835.7762b 2 +219.7779h 2 -17.4459d 2 -1698.359t 2 +1.6865ab+0.7515ah+0.0458ad-5.3776at-0.5554bh-0.3566bd+14.0272bt-0.06261hd-1.1016ht-0.1667dt-12.3464a 3 -452.8848b 3 -14.1708h 3 +0.1794d 3 +1199.2214t 3 +0.211a 4 +41.6366b 4 +0.3391h 4 -0.0006909d 4 -308.9682t 4
4) Response surface model of total energy absorption W:
W＝34302933.709+644211.1649a-50669721.7989b+2764796.5129h-344895.9615d+7488596.9982t-77930.7763a 2 +30603398.0454b 2 -417962.829h 2 +7361.5903d 2 -12384142.8218t 2 -5224.2092ab+1267.0536ah-161.2317ad+24530.8658at-1716.4935bh+1638.7714bd-117348.4422bt+30.2318hd+2382.9861ht-4541.5054dt+4175.07a 3 -8154173.7925b 3 +27621.0081h 3 -68.1648d 3 +9091335.913t 3 -83.9117a 4 +809729.5918b 4 -677.5896h 4 +0.2309d 4 -2449116.2989t 4
step 7), performing error check on the four fitted response surface models, namely respectively calculating the correlation coefficients R of the four fitted response surface models 2 And root mean square error sigma RMSE Comparing the correlation coefficient value with a preset correlation coefficient value and a preset root mean square error value;
correlation coefficient R 2 And the root mean square error calculation formula is as follows:
wherein N is the number of sample points, P is the polynomial term, i is the ith sample point, f i For the finite element analysis value of the i-th sample point,calculating a value for the response surface model of the ith sample point,/for>The mean value is analyzed for the finite elements of all sample points;
the preset correlation coefficient value is 0.93, and the preset root mean square error value is 0.1.
Step 8), if the correlation coefficient R of the four response surface models 2 All are greater than or equal to the preset correlation coefficient value and root mean square error sigma RMSE Are all smaller thanAnd (3) if the root mean square error value is equal to the preset root mean square error value, executing the step (9); otherwise, re-executing the steps 1) to 7) until the correlation coefficients R of the four response surface models 2 All are greater than or equal to the preset correlation coefficient value and root mean square error sigma RMSE All are smaller than or equal to preset root mean square error values;
step 9), constructing a multidisciplinary collaborative optimization calculation model of the negative poisson ratio structure energy absorption box taking the mass m as a main system, and taking the peak collision force P, the compression displacement S and the total energy absorption W as subsystems in the ISIGHT;
1) Mass m main system calculation model:
wherein: a is more than or equal to 12 and less than or equal to 16,2.2, b is more than or equal to 3, h is more than or equal to 8 and less than or equal to 13,55 degrees, d is more than or equal to 75 degrees, t is more than or equal to 0.6 and less than or equal to 1.2, and the relaxation factor epsilon=0.001
2) Peak collision force P subsystem calculation model:
3) Compression displacement S subsystem calculation model:
4) Total energy absorption W subsystem calculation model:
。
step 10), according to the established multidisciplinary collaborative optimization calculation model, a multidisciplinary genetic algorithm is adopted for a main system, a sequence quadratic programming algorithm is adopted for a subsystem, multidisciplinary collaborative optimization is carried out on the length a of the bottom edge of the negative poisson ratio unit cell structure, the included angle d between the inclined edge and the bottom edge, the height h between the two bottom edges, the thickness t of the negative poisson ratio unit cell structure and the width b of the negative poisson ratio unit cell structure, an optimized Pareto solution set is obtained, and finally a group of optimal solutions is selected from the Pareto solution set. Parameters of the multi-island genetic algorithm are set as follows: the sub population size is 10, the island number is 10, the genetic algebra is 10, the crossover rate is 1, and the mutation rate and the mobility are 0.01.
The foregoing is merely a preferred embodiment of the present invention and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which are intended to be comprehended within the scope of the present invention.
Claims (8)
1. An energy-absorbing box that inside is provided with two-dimensional negative poisson's ratio structure inner core, its characterized in that: the energy-absorbing box comprises an energy-absorbing box body (1), a front mounting plate (2) and a rear mounting plate (5), wherein one end of the energy-absorbing box body (1) is connected with the front mounting plate (2), and the other end of the energy-absorbing box body (1) is connected with the rear mounting plate (5); the front mounting plate (2) is used for being connected with a beam of an automobile bumper through bolts, and the rear mounting plate (5) is used for being connected with a longitudinal beam of an automobile body through bolts;
the two-dimensional negative poisson ratio structure inner core comprises more than one negative poisson ratio unit cell structure, the negative poisson ratio unit cell structures are arranged in an array along the extending direction of the width b, the negative poisson ratio unit cell structures are arranged in an array along the extending direction of the two ends of the vertical distance h between the two bottom edges, and the negative poisson ratio unit cell structures are arranged in an array along the extending direction of the two ends of the length a of the two bottom edges; in the extending direction of the width b, the negative poisson ratio unit cell structures are stacked symmetrically; in the extending direction of the length a, the first inclined edge of the negative poisson ratio unit cell structure is overlapped with the second inclined edge of the adjacent negative poisson ratio unit cell structure; in the extending direction of the distance h, the bottom edges of the adjacent negative poisson ratio unit cell structures are mutually overlapped;
the negative poisson ratio unit cell structure comprises two symmetrically parallel bottom edges, wherein the same sides of the two bottom edges are connected through a first inclined edge and a second inclined edge which are connected, the lengths of the first inclined edge and the second inclined edge are equal, and the first inclined edge and the second inclined edge of the same side are inclined inwards; the thicknesses of the first inclined edge, the second inclined edge and the bottom edge are t, and t is more than or equal to 0.6mm and less than or equal to 1.2mm; the widths of the first bevel edge, the second bevel edge and the bottom edge are b, and b is more than or equal to 2.2mm and less than or equal to 3mm; the included angle between each bevel edge and the adjacent bottom edge is d, and d is more than or equal to 55 degrees and less than or equal to 75 degrees; the length of the two bottom edges is a, and a is more than or equal to 12mm and less than or equal to 16mm; the vertical distance between the two bottom edges is h, and h is more than or equal to 8mm and less than or equal to 13mm;
the two-dimensional negative poisson ratio structure inner core is a square energy absorption structure consisting of 22 x 9 x 32=6336 negative poisson ratio unit cell structures.
2. The energy absorber of claim 1, wherein the energy absorber comprises an inner core having a two-dimensional negative poisson's ratio structure, and wherein: the energy-absorbing box body (1) is of a hollow prismatic structure with a trapezoid cross section, the whole surface of the energy-absorbing box body (1) comprises an upper surface, a lower surface, a left side surface and a right side surface, the upper surface corresponds to the upper bottom of the trapezoid energy-absorbing box body (1), the lower surface corresponds to the lower bottom of the trapezoid energy-absorbing box body (1), and the left side surface and the right side surface correspond to two side edges of the trapezoid energy-absorbing box body (1);
two first induction grooves (41) are symmetrically formed in the left side surface and the right side surface, the first induction grooves (41) are positioned at the trisection point of the axial length of the energy-absorbing box body (1), the first induction grooves far away from the front mounting plate (2) are the first induction grooves, the first induction grooves far away from the rear mounting plate (5) are the second induction grooves, and the first induction grooves (41) extend to the upper surface; three second induction grooves (42) are symmetrically formed in the upper surface and the lower surface, the first second induction groove (42) in the upper surface is positioned in the middle of the upper surface projection of the front mounting plate (2) and the second induction groove (42), the second induction groove (42) in the upper surface is positioned in the middle of the upper surface projection of the first induction groove and the second induction groove (42), and the third induction groove (42) in the upper surface is positioned in the middle of the upper surface projection of the first induction groove and the rear mounting plate (5); the second induction groove (42) and the first induction groove (41) are concave, and the depth of the second induction groove (42) is larger than that of the first induction groove (41); in the direction from the front mounting plate (2) to the rear mounting plate (5), the depths of the three second induction grooves (42) are gradually reduced, and the depths of the two first induction grooves (41) are also gradually reduced.
3. The energy absorber of claim 1, wherein the energy absorber comprises an inner core having a two-dimensional negative poisson's ratio structure, and wherein: the thickness t of the first bevel edge, the second bevel edge and the bottom edge is 1.1575mm; the width b of the first bevel edge, the second bevel edge and the bottom edge is 2.2009mm; the included angle d between each bevel edge and the adjacent bottom edge is 74.684 degrees; the length a of the two bottom edges is 13.764mm; the vertical distance h between the two bottom edges was 12.877mm.
4. The multidisciplinary collaborative optimization method of the energy-absorbing box is characterized in that a two-dimensional negative poisson ratio structure inner core is arranged in the energy-absorbing box, the two-dimensional negative poisson ratio structure inner core comprises more than one negative poisson ratio unit cell structure, the negative poisson ratio unit cell structure comprises two bottom edges which are symmetrically parallel, the same sides of the two bottom edges are connected through a first oblique edge and a second oblique edge which are connected, and the first oblique edge and the second oblique edge of the same side are inclined inwards; the thicknesses of the first inclined edge, the second inclined edge and the bottom edge are t, the widths of the first inclined edge, the second inclined edge and the bottom edge are b, the included angle d between each inclined edge and the adjacent bottom edge is a, the lengths of the two bottom edges are a, and the vertical distance between the two bottom edges is h; the two-dimensional negative poisson ratio structure inner core comprises more than one negative poisson ratio unit cell structure, the negative poisson ratio unit cell structures are arranged in an array along the extending direction of the width b, the negative poisson ratio unit cell structures are arranged in an array along the extending direction of the two ends of the vertical distance h between the two bottom edges, and the negative poisson ratio unit cell structures are arranged in an array along the extending direction of the two ends of the length a of the two bottom edges; in the extending direction of the width b, the negative poisson ratio unit cell structures are stacked symmetrically; in the extending direction of the length a, the first inclined edge of the negative poisson ratio unit cell structure is overlapped with the second inclined edge of the adjacent negative poisson ratio unit cell structure; in the extending direction of the distance h, the bottom edges of the adjacent negative poisson ratio unit cell structures are mutually overlapped,
the method is characterized in that: the method comprises the following steps:
step 1), firstly, selecting an orthogonal test design method in ISIGHT optimization software, and uniformly selecting N groups of design sample points in the variation range of each design variable, wherein the design variables are respectively the length a of the bottom edge of a negative Poisson ratio unit cell structure, the included angle d between each inclined edge and the adjacent bottom edge, the vertical distance h between the two bottom edges, the thickness t of the negative Poisson ratio unit cell structure and the width b of the negative Poisson ratio unit cell structure;
step 2), establishing CAD models of inner cores of the N groups of two-dimensional negative poisson ratio structures in PROE software according to the selected N groups of design sample points;
the specific forming process of the CAD model of the two-dimensional negative poisson ratio structure inner core comprises the following steps: firstly, carrying out array change in the X direction on the basis of a negative Poisson ratio unit cell structure to form a negative Poisson ratio multicellular structure; then, carrying out array change in the Y direction and the Z direction on the negative Poisson ratio multicell structure to form an inner core of the two-dimensional negative Poisson ratio structure;
step 3), importing a CAD model of the two-dimensional negative poisson ratio structure inner core into HYPERMESH software, performing geometric cleaning and grid division on the CAD model, and setting the material and thickness of the two-dimensional negative poisson ratio structure inner core;
step 4), a traditional energy-absorbing box shell model without an inner core with a two-dimensional negative poisson ratio structure and a rigid wall model for testing collision are led into HYPERMESH, the inner core with the two-dimensional negative poisson ratio structure is filled in the traditional energy-absorbing box shell, the collision speed between the rigid wall and the energy-absorbing box with the inner core with the two-dimensional negative poisson ratio structure is set, 6 degrees of freedom of a node which is not contacted with the rigid wall when the energy-absorbing box with the inner core with the two-dimensional negative poisson ratio structure collides are restrained, and meanwhile, contact and output between the rigid wall and the energy-absorbing box with the inner core with the two-dimensional negative poisson ratio structure are defined;
step 5), importing the finite element simulation model of the energy-absorbing boxes with the inner cores of the two-dimensional negative poisson ratio structures in the N groups into dynamics analysis software LS-DYNA to carry out solving calculation, and collecting data of mass m, peak collision force P, compression displacement S and total energy absorption W in the collision process of the energy-absorbing boxes in HYPERGRAPH and HYPERVIEW;
step 6), selecting a high-order response surface model in ISIGHT software, and constructing a response surface model of the mass m, a response surface model of the peak impact force P, a response surface model of the compression displacement S and a response surface model of the total energy absorption W by taking the length a of a bottom edge corresponding to the N groups of negative Poisson ratio unit cell structures, an included angle d between a bevel edge and the bottom edge, a vertical distance h between the two bottom edges, a thickness t of the negative Poisson ratio unit cell structures and a width b of the negative Poisson ratio unit cell structures as inputs, wherein the mass m, the peak impact force P, the compression displacement S and the total energy absorption W corresponding to the energy absorption boxes of the inner cores of the two-dimensional negative Poisson ratio unit cell structures are arranged in the N groups;
step 7), performing error check on the four fitted response surface models, namely respectively calculating the correlation coefficients R of the four fitted response surface models 2 And root mean square error sigma RMSE Comparing the correlation coefficient value with a preset correlation coefficient value and a preset root mean square error value; the preset correlation coefficient value is 0.93, and the preset root mean square error value is 0.1;
step 8), if the correlation coefficient R of the four response surface models 2 All are greater than or equal to the preset correlation coefficient value and root mean square error sigma RMSE And (3) executing the step (9) if the root mean square error value is smaller than or equal to the preset root mean square error value; otherwise, re-executing the steps 1) to 7) until the correlation coefficients R of the four response surface models 2 All are greater than or equal to the preset correlation coefficient value and root mean square error sigma RMSE All are smaller than or equal to preset root mean square error values;
step 9), constructing a multidisciplinary collaborative optimization calculation model with mass m as a main system, and peak collision force P, compression displacement S and total energy absorption W as energy absorption boxes with two-dimensional negative poisson ratio structure inner cores in the subsystem;
step 10), according to the established multidisciplinary collaborative optimization calculation model, a multidisciplinary genetic algorithm is adopted for a main system, a sequence quadratic programming algorithm is adopted for a subsystem, multidisciplinary collaborative optimization is carried out on the length a of the bottom edge of a negative poisson ratio unit cell structure, the included angle d between the inclined edge and the bottom edge, the height h between the two bottom edges, the thickness t of the negative poisson ratio unit cell structure and the width b of the negative poisson ratio unit cell structure, an optimized Pareto solution set is obtained, and finally a group of optimal solutions is selected from the Pareto solution set;
the parameters of the multi-island genetic algorithm are set as follows: the sub population size is 10, the island number is 10, the genetic algebra is 10, the crossover rate is 1, and the mutation rate and the mobility are 0.01.
5. The multidisciplinary collaborative optimization method of an energy absorber box according to claim 4, wherein: the N values in the N sets of design sample points described in step 1) are 128, and the orthogonal table for the orthogonal test described in step 1) is L128 (45), i.e., 128 tests at a 5-factor 4 level, and the ranges of variation of the design variables are respectively: a epsilon [12,16], b epsilon [2.2,3], h epsilon [8,13], d epsilon [55 DEG, 75 DEG ], t epsilon [0.6,1.2].
6. The multidisciplinary collaborative optimization method of an energy absorber box according to claim 4, wherein: the collision speed between the rigid wall and the energy absorption box with the inner core of the two-dimensional negative poisson ratio structure arranged in the step 4) is 16km/h.
7. The multidisciplinary collaborative optimization method of an energy absorber box according to claim 4, wherein: the order of the high-order response surface model in the step 6) is four, and the response surface model of the mass m, the response surface model of the peak collision force P, the response surface model of the compression displacement S and the response surface model of the total energy absorption W are respectively:
1) Response surface model of mass m:
m＝211.3606+49.6045a+24.1501b+5.3261h+0.6283d+21.2653t-5.3558a 2 -12.2847b 2 -0.7646h 2 -0.0202d 2 -32.3845t 2 -0.0408ab-0.005471ah+0.004664ad-0.1212at-0.004321bh-0.005127bd+0.2367bt-0.001471hd+0.01352ht-0.01615dt+0.25515a 3 +2.8967b 3 +0.05h 3 +0.0002531d 3 +25.1231t 3 -0.004538a 4 -0.2558b 4 -0.001219h 4 -1.1354d 4 -7.2777t 4
2) Response surface model of peak impact force P:
P＝4668216.0363-524643.9041a-7708169.0354b+180530.2357h+116513.3631d+676777.0333t+53084.1734a 2 +4440679.005b 2 -27221.9961h 2 -2741.6867d 2 -1112772.4445t 2 -764.2867ab+92.2161ah+2.71103ad-3377.2085at-887.0286bh+0.6144bd+8016.8117bt-13.102hd-2325.5156ht-166.4317dt-2366.5567a 3 -1130853.1258b 3 +1820.4986h 3 +28.5245d 3 +888866.9604t 3 +39.4309a 4 +107640.8348b 4 -44.8933h 4 -0.1104d 4 -257318.5951t 4
3) Response surface model of compression displacement S:
S＝3164.2166-2619.5605a-3295.4876b-1502.5493h+753.841d+1092.6702t+269.7967a 2 +1835.7762b 2 +219.7779h 2 -17.4459d 2 -1698.359t 2 +1.6865ab+0.7515ah+0.0458ad-5.3776at-0.5554bh-0.3566bd+14.0272bt-0.06261hd-1.1016ht-0.1667dt-12.3464a 3 -452.8848b 3 -14.1708h 3 +0.1794d 3 +1199.2214t 3 +0.211a 4 +41.6366b 4 +0.3391h 4 -0.0006909d 4 -308.9682t 4
4) Response surface model of total energy absorption W:
W＝34302933.709+644211.1649a-50669721.7989b+2764796.5129h-344895.9615d+7488596.9982t-77930.7763a 2 +30603398.0454b 2 -417962.829h 2 +7361.5903d 2 -12384142.8218t 2 -5224.2092ab+1267.0536ah-161.2317ad+24530.8658at-1716.4935bh+1638.7714bd-117348.4422bt+30.2318hd+2382.9861ht-4541.5054dt+4175.07a 3 -8154173.7925b 3 +27621.0081h 3 -68.1648d 3 +9091335.913t 3 -83.9117a 4 +809729.5918b 4 -677.5896h 4 +0.2309d 4 -2449116.2989t 4 。
8. the multidisciplinary collaborative optimization method of an energy absorber box according to claim 4, wherein: the construction in the step 9) uses the mass m as a main system, and peak collision force P, compression displacement S and total energy absorption W are respectively as follows:
1) Mass m main system calculation model:
wherein: a is more than or equal to 12 and less than or equal to 16,2.2, b is more than or equal to 3, h is more than or equal to 8 and less than or equal to 13, d is more than or equal to 55 and less than or equal to 75 degrees, t is more than or equal to 0.6 and less than or equal to 1.2, and the relaxation factor epsilon=0.001
2) Peak collision force P subsystem calculation model:
3) Compression displacement S subsystem calculation model:
4) Total energy absorption W subsystem calculation model:
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