CN115618665B - Bionic spider web lattice structure design and energy absorption method thereof - Google Patents

Bionic spider web lattice structure design and energy absorption method thereof Download PDF

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CN115618665B
CN115618665B CN202210810924.2A CN202210810924A CN115618665B CN 115618665 B CN115618665 B CN 115618665B CN 202210810924 A CN202210810924 A CN 202210810924A CN 115618665 B CN115618665 B CN 115618665B
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解宝成
王嘉伟
徐家旺
杨国涛
刘晓宇
冀旭晖
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Harbin University of Science and Technology
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Abstract

The invention discloses a bionic spider web lattice structure design and an energy absorption method thereof, and relates to the technical field of bionics; the method comprises the following steps: step one, analyzing influence of spider web structure parameters on an energy absorption effect; step two, designing a bionic spider web lattice structure; step three, researching the dot matrix energy absorption effect under quasi-static load; the spider web simulation model is constructed by analyzing the spider web mechanical model; taking total energy absorption, peak stress and specific energy absorption as energy absorption effect evaluation criteria; simulating a dynamic response process of insect impact on the spider web by using a finite element method, and obtaining an influence rule of structural parameters of the spider web structure on the energy absorption effect of the spider web based on a response curved surface method; simulation verification is carried out on the energy absorption effects of the three obtained bionic spider webs under low-speed impact load and quasi-static compression load; the energy absorption effect of the three bionic spider-web lattices under quasi-static load is summarized through analyzing the relationship between the compression force and the compression displacement of the three bionic spider-web lattice structure sandwich plates.

Description

Bionic spider web lattice structure design and energy absorption method thereof
Technical Field
The invention belongs to the technical field of bionics, and particularly relates to a bionic spider web lattice structure design and an energy absorption method thereof.
Background
Bionics is a discipline for researching various excellent characteristics of biological systems, such as structure, characteristics, functions, working principles and the like, and providing design ideas and methods for imitative design of products with specific biological advantages. Scholars at home and abroad are carrying out a great deal of creative research aiming at different natural biological phenomena. The bionic design adopts scientific bionic thinking, and avoids the mechanical wrong bionic problem. The dot matrix structure with biological characteristics is manufactured by mainly adopting a simulation and experimental mutual verification method and deeply summarizing and summarizing the relation between the biological structure and the biological characteristics by means of a 3D printing and finite element simulation technology. Therefore, the bionics provides a new thought for designing a new lattice structure; and related information is not provided for the design of the bionic spider web lattice structure and the energy absorption of the bionic spider web lattice structure.
Disclosure of Invention
To solve the problems of the background technology; the invention aims to provide a bionic spider web lattice structure design and an energy absorption method thereof.
The invention relates to a bionic spider web lattice structure design and an energy absorption method thereof, which comprises the following steps:
Step one, analyzing influence of spider web structural parameters on energy absorption effect:
(1.1), spider web structure composition analysis:
(1.1.1), spider silk deformation energy absorption analysis:
firstly, researching a mechanical model of spider silk under impact load; to simplify the model, insects can be equivalent to a mass m particle, impact the midpoint of spider silk at an initial speed and vibrate with the spider web;
the geometric analysis of the picture can be seen as follows:
Figure GDA0004229064880000011
wherein y is the position quantity of the particles in the vertical direction; θ is the angle between the spider silk and the horizontal line; the increase in spider silk length is:
Figure GDA0004229064880000021
the strain of the material is as follows:
Figure GDA0004229064880000022
according to the analysis of the radial line mechanics of the circular net spider, the relation expression of the radial line stress-strain is as follows: loading
Figure GDA0004229064880000023
Unloading:
Figure GDA0004229064880000024
wherein sigma is material stress; epsilon is the material strain; epsilon y Is the material yield strain; whereas the stress-strain relationship of a contour can be expressed in terms of a polynomial power function:
σ＝a(ε+bε n ) 0＜ε＜2.7 (0-23)
from the above, it is known that the stress and strain of spider silk are always in a linear relationship, whether loaded or unloaded, and therefore the stress σ of spider silk can be uniformly expressed as:
σ＝Eε+S (0-24)
wherein E, S is a constant determined by different loading conditions. Substituting the expression into
Figure GDA0004229064880000025
In the middle of
B＝S-E。 (0-26)
After neglecting the weight of the spider silk, the kinetic equation of the spider silk can be obtained:
Figure GDA0004229064880000031
If the angle θ is taken as an independent variable, a differential equation can be obtained:
Figure GDA0004229064880000032
solving the differential equation, and performing variable substitution:
Figure GDA0004229064880000033
p 2 ＝T (0-30)
then there are:
Figure GDA0004229064880000034
the equation can thus be changed to a first order linear differential equation with θ as an argument:
Figure GDA0004229064880000035
solving to obtain
Figure GDA0004229064880000036
Thus, the theoretical solution of the dynamic response of spider silk after impact depends on the initial conditions, the dynamic response of spider silk being an up-and-down oscillation;
(1.1.2), spider web structure analysis:
exploring the ratio of the area of the spider web which can block insects to the total length of the used gland silk; drawing a spider web model using a vortex line instead of a logarithmic spiral line;
(1.1.3), radial line number and spiral coil number study:
exploring the relation between the number of spider web lines and the number of spiral turns; the number of spider web diameter lines and the number of spiral turns are directly affected by the maximum area of the spider web and the maximum impact force of the insects. As the spider web area and insect impact force increases, the increase in the number of radial lines helps to increase the strength of the spider web, while the increase in the number of helical turns helps to better disperse the impact energy into the radial lines. In addition, as the bearing capacity of the radial lines increases, the number of radial lines required decreases correspondingly, and vice versa for the spiral. Thus, when the spider web area and insect impact force are fixed, the bearing capacity of the radial wire and the adhesion of the spiral directly influence the factors of the number of radial wires and the number of turns of the spiral. Therefore, in the simulation model, the influence relationship of the ratio of different diameter lines to the number of turns of the spiral line on the absorption of impact energy by the spider web can be obtained by changing the cross-sectional areas of the spider web diameter lines and the spiral line.
(1.1.4), study of the effect of insect impact on spider web tension:
the spider web model can thus be regarded as a wood board of smaller thickness, and the impact of insects on the spider web can be regarded as a force of a certain magnitude acting on the wood board;
(1.1.5), spider web and wall connection structure study:
in simulation experiments where the spider web intercepts insect impact, each radial line of the spider web may be directly immobilized and constrained.
(1.2), spider web energy absorption effect evaluation indexes and simulation experiment design:
(1.2.1), a spider web interception flying insect dynamic response simulation design:
simulating the dynamic response of the flying insects intercepted by the spider web by utilizing an ANSYLS-DYNA solving module; modeling by using a spiral wire net, and setting five main structural factors affecting the energy absorbing effect of the spider net, namely, the length of a radial wire, the diameter of a radial wire section, the number of turns of a spiral wire, the pitch of the spiral wire and the diameter of the section of the spiral wire; the total energy absorption capacity, peak stress and specific energy absorption capacity of the spider web are taken as evaluation standards of energy absorption effects.
(1.2.2), simulation test data analysis based on the response surface method:
designing an experiment by adopting a response surface method; performing experimental analysis by adopting a response surface method to obtain the influence rule of spider web structural parameters on the energy absorption effect; and (3) performing simulation experiment design of an influence rule of spider web structural parameters on absorbed energy by utilizing a BBD design method.
Step two, designing a bionic spider web lattice structure:
(2.1), a bionic spider web lattice structure design method:
firstly, aiming at the rule analysis of the spider web structural parameters on the energy absorption effect, the influence of the radial line and the spiral line in the spider web on the energy absorption effect can be obtained. The spider web structure with the best energy absorption effect can be obtained through optimizing parameters of the spider web diameter line and the spiral line. The lattice structure is thus designed to have a spider web-like radial and helical winding pattern and with the longitudinal material as the radial, the transverse material as the helical,
(2.2), three bionic spider web lattice structure optimization designs:
three bionic spider web lattice structures are designed and respectively named as: a common bionic spider web lattice structure, a spiral bionic spider web lattice structure and a composite bionic spider web lattice structure. The optimization process is divided into two steps: firstly, obtaining lattice original unit cells through preliminary optimization, and finally, obtaining three different bionic spider web lattice structures through secondary optimization.
(2.2.1), lattice primitive unit cell design:
five coordinate size fitting spline curves of three control points are set to parametrize and control the radial line structure of the basic bionic spider web lattice.
(2.2.2), design of common bionic spider web lattice unit cell:
The characteristics of the spider web lines and the spiral lines are jointly introduced into a bionic spider web lattice and named as a common bionic spider web lattice structure;
(2.2.3), spiral bionic spider web lattice unit cell design:
spider web threads are designed in the same rotational form as a spiral line. The radial lines and the spiral lines form a lattice according to opposite rotation directions, wherein the rotation angles of the radial lines and the rotation angles of the spiral lines are set to be the same in order to ensure the symmetry of a lattice structure.
(2.2.4), design of composite bionic spider web lattice unit cell:
the common bionic spider web lattice and the spiral bionic spider web lattice radial line structure are combined together, so that the composite bionic spider web lattice is named as a composite bionic spider web lattice. Wherein, starting from the optimization of radial line structure, the radial line characteristic of ordinary bionic spider web is kept at the middle part of the composite bionic spider web lattice radial line, and the two ends of the composite bionic spider web lattice radial line keep the warp line characteristic of spiral bionic spider web lattice. For this purpose, spline curves are used and three control points are set to model a composite biomimetic spider web lattice structure.
(2.2.5), three bionic spider web lattice structure optimization designs:
taking the total energy absorption, the peak load and the specific energy absorption as objective functions, and defining the expression of the optimization problem as follows:
Figure GDA0004229064880000051
Wherein EA (X) is total energy absorption of the bionic spider web lattice, stress (X) is peak Stress of the bionic spider web lattice, SEA (X) is specific energy absorption of the bionic spider web lattice, and X is a value range of structural parameters.
(2.3), comparing the energy absorption effects of the bionic spider web lattice under dynamic and static loads:
(2.3.1), comparison of energy absorption effects of bionic spider web lattice under low-speed impact load:
from the aspect of specific energy absorption, the composite bionic spider web lattice is the optimal bionic spider web lattice design.
(2.3.2), comparing the energy absorption effects of the bionic spider web lattice under quasi-static load:
under quasi-static load, the composite bionic spider web lattice energy absorption effect is optimal.
Step three, researching lattice energy absorption effect under quasi-static load:
(3.1) quasi-static compression test of bionic spider web lattice sandwich board
Three bionic spider web lattice sandwich panels were fabricated and 3 quasi-static compression experiments were performed respectively. The mechanical behavior and deformation failure modes of the three bionic spider web lattice structures under static load can be obtained through a quasi-static compression experiment. In addition, the compression displacement and the compression force data are output according to a quasi-static compression experiment to be fitted and integrated, and the relation between the total energy absorption amount and the specific energy absorption amount of the three bionic spider web lattice structures under static load can be obtained, so that the optimal bionic spider web lattice structure is selected.
(3.1.1), preparation of a bionic spider web lattice sandwich board:
setting supporting parameters by adopting an e-stage; according to the setting to the support parameter, add the support to three kind of bionical spider web lattice battenboard, after accomplishing to bearing structure setting, in order to guarantee three kind of bionical spider web lattice battenboard's manufacturing accuracy furthest, set up the section thickness to 0.1mm, print.
(3.1.2), quasi-static compression protocol:
and testing the mechanical behaviors and the energy absorption effects of the three bionic spider web lattice structures under a quasi-static compression experiment by adopting an INSTRON3382 universal tester. In the experiment, the compression displacement is set to be 10mm according to the compression displacement loading. To ensure quasi-static compression slow loading conditions, the loading rate was set to 0.1mm/min. The sampling time interval is 0.2s, i.e. 5 points of data are acquired per second. Because the strength of the experimental material is smaller, 3 quasi-static compression experiments are respectively carried out on the 3 bionic spider web lattice structure sandwich plates and the experimental data are averaged in order to reduce errors caused by the material and machine factors.
(3.1.3), three biomimetic spider web lattice deformation format analyses:
in order to explore three bionic spider web lattice structure deformation forms under quasi-static load, three bionic lattices are photographed respectively before compression, at a platform stage and after compression.
Compared with the prior art, the invention has the beneficial effects that:
1. through the analysis of the spider web mechanical model, a spider web simulation model taking the spider web radial line length, the radial line section diameter, the spiral line number of turns, the spiral line spacing and the spiral line section diameter as structural parameters is constructed. And taking the total energy absorption amount, the peak stress and the specific energy absorption amount as energy absorption effect evaluation criteria. The finite element method is utilized to simulate the dynamic response process of the insects impacting the spider web and the influence rule of the structural parameters of the spider web structure on the spider web energy absorption effect is obtained based on the response curved surface method.
2. Based on the influence law of different structural parameters of the spider web on the energy absorption effect, three bionic spider web lattice structures with different structures are obtained through bionic design. And taking the total energy absorption amount, the peak stress and the specific energy absorption amount as energy absorption effect evaluation standards, obtaining the influence rule of structural parameters of three bionic spider web lattice structures on the energy absorption effect by using a response surface method, and carrying out structural optimization design. Simulation verification is carried out on the energy absorption effects of the three obtained bionic spider webs under low-speed impact load and quasi-static compression load.
3. Three bionic spider web lattice structure sandwich boards are prepared by utilizing a 3D printing technology, and a universal testing machine is used for carrying out quasi-static compression experiments. And analyzing deformation forms of the three bionic spider web lattices under quasi-static load. The energy absorption effect of the three bionic spider-web lattices under quasi-static load is summarized through analyzing the relationship between the compression force and the compression displacement of the three bionic spider-web lattice structure sandwich plates.
Drawings
For ease of illustration, the invention is described in detail by the following detailed description and the accompanying drawings.
FIG. 1 is a schematic view of a spider silk impact model of the present invention; FIG. 2 is a schematic illustration of a spider web-like structure model in accordance with the present invention; FIG. 3 is a schematic diagram of a model construction in accordance with the present invention; FIG. 4 is a schematic diagram of boundary condition definition in the present invention; FIG. 5 is a schematic representation of spider web dynamic response in the present invention; FIG. 6 is a response surface schematic of the EA of the present invention; FIG. 7 is a response surface diagram of Stress in the present invention; FIG. 8 is a schematic representation of the response surface of an SEA in the present invention; FIG. 9 is a schematic diagram of a method of designing a simulated spider web lattice in accordance with the present invention; FIG. 10 is a schematic diagram of the original unit cell of the lattice according to the present invention; FIG. 11 is a schematic view of an EA response surface in the present invention; FIG. 12 is a schematic view of Stress response surface in the present invention; FIG. 13 is a schematic view of a SEA response curve in accordance with the present invention; FIG. 14 is a schematic view of an EA response surface in the present invention; FIG. 15 is a schematic view of Stress response surface in the present invention; FIG. 16 is a schematic view of a SEA response curve in accordance with the present invention; FIG. 17 is a schematic view of an EA response surface in the present invention; FIG. 18 is a schematic view of Stress response surface in the present invention; FIG. 19 is a schematic view of a SEA response curve in accordance with the present invention; FIG. 20 is a schematic diagram of a composite bionic spider web lattice in accordance with the present invention; FIG. 21 is a schematic view of an EA response surface in the present invention; FIG. 22 is a schematic view of Stress response surface in the present invention; FIG. 23 is a schematic view of a SEA response curve in accordance with the present invention; FIG. 24 is a graph showing the total energy absorbed by the lattice at low impact in the present invention; FIG. 25 is a graph showing the peak stress of the lattice at low impact in the present invention; FIG. 26 is a graph showing lattice ratio energy absorption at low impact in the present invention; FIG. 27 is a schematic view of a lattice porosity development model in accordance with the present invention; FIG. 28 is a graph showing compression force versus compression displacement in accordance with the present invention.
Detailed Description
The specific implementation mode adopts the following technical scheme:
1. spider web structural parameters influence research on energy absorption effect:
1.1 spider web structure composition analysis:
taking a circular net spider as an example, two gland silk structural characteristics of a net inner diameter line (large pot-shaped gland silk) and a spiral line (flagellum-shaped gland silk) are taken as main study objects. Wherein, the radial line is taken as the main structural line of the spider web and is radial outwards from the center of the spider web. The spiral line is a capturing line of the spider web and is circumferentially distributed from the center to the outside.
1.1.1, spider silk deformation energy absorption analysis:
the spider web energy absorbing effect depends on the mechanical properties of the spider silk. Therefore, a mechanical model of spider silks under impact load was first studied. Assume that the cross-sectional area of a spider silk is the length. When it is subjected to an insect of mass m, impacting the spider silk midpoint location at a rate, the viscosity of the spider silk causes the insect to stick to the web and vibrate with the spider web as the ends of the spider silk are immobilized. The spider silk deforms to consume the kinetic energy of the insect impact. As shown in fig. 1. Thus, to simplify the model, an insect can be equivalent to a mass m particles that impact the midpoint of a spider silk at an initial velocity and oscillate with the spider web.
1.1.2 spider web structural analysis:
when the netting is in the form of concentric circular net, it is assumed that the spider weaves a concentric circular spider net composed of k concentric circles in space, the innermost radius of circle is r, and the difference between the radii of two adjacent concentric circles is also r for the sake of simplifying calculation.
1.1.3, study of radial line number and spiral coil number:
the number of spider web diameter lines and the number of spiral turns are directly affected by the maximum area of the spider web and the maximum impact force of the insects. As the spider web area and insect impact force increases, the increase in the number of radial lines helps to increase the strength of the spider web, while the increase in the number of helical turns helps to better disperse the impact energy into the radial lines. In addition, as the bearing capacity of the radial lines increases, the number of radial lines required decreases correspondingly, and vice versa for the spiral. Thus, when the spider web area and insect impact force are fixed, the bearing capacity of the radial wire and the adhesion of the spiral directly influence the factors of the number of radial wires and the number of turns of the spiral. Therefore, in the simulation model, the influence relationship of the ratio of different diameter lines to the number of turns of the spiral line on the absorption of impact energy by the spider web can be obtained by changing the cross-sectional areas of the spider web diameter lines and the spiral line.
1.1.4 study of the action of insect impact on spider web tension:
according to the above, the spider-web helix is distributed in a logarithmic helix structure. The spider web model can thus be regarded as a wood board of smaller thickness, and the impact of insects on the spider web can be regarded as a force of a certain magnitude acting on the wood board. Further investigation may result in the same magnitude of positive and principal stresses, so that the forces experienced by the board may eventually be equivalent to positive stresses. Similarly, the stress of an insect striking the spider web may be equivalent to a positive stress. Therefore, when F increases to a certain limit, the wood board center position becomes the first damaged portion for the wood board model. Whereas for spider web models, the spider web center is subjected to the greatest strain. Because of this, dense gland threads distributed in the center of the spider web are effective against impact energy from insects. Therefore, research on the energy absorbing effect of the spider web may be focused on the spider web central structure. The influence rule of the spider web internal structural parameters on the spider web energy absorption effect can be explored through experiments of designing particle impact spider web central positions.
1.1.5 spider web and wall connection structure study:
since the connection of the spider web and the wall is a cohesive state, it can be equivalently a peeling model connected by an adhesive. And the bonding state of the radial line and the spiral line with the wall body. Therefore, a simple elastic anchoring theoretical model is firstly constructed, and the critical delamination force is obtained as follows:
F d ＝2YA c sinε d (0-35)
Wherein Y is elastic modulus, A c Epsilon for the cross-sectional area of each pin d The calculation formula of the critical strain quantity representing the detachment is as follows:
Figure GDA0004229064880000091
wherein alpha represents the included angle between the anchor line pin and the horizontal direction. Mu is a dimensionless parameter. Defining a variable gamma to represent the adhesion energy of the anchor line per unit length, wherein the calculation formula is as follows:
Figure GDA0004229064880000101
thus, the magnitude of the adhesion can be controlled by varying the value of α, ε as α increases d Gradually decreasing. Then there must be an angle alpha max The adhesive force is maximized, and the derivation can be obtained:
Figure GDA0004229064880000102
from this, it can be derived that:
Figure GDA0004229064880000103
when alpha is max When approaching 90 °, εx approaches infinity. It is clear that the angle between the pins and the horizontal plane plays a key role in adhesion and directly affects adhesion energy. Therefore, the direct cause of the difference in the behavior of the connection forces of the spider web wire and the spiral wire to the wall is the difference in the bonding angle of the anchor wire to the wall. And the bonding energy between the radial line and the wall surface can approach infinity by analyzing from the theoretical angle alone. Therefore, in the simulation experiment of the spider web intercepting insect impact, each radial line of the spider web can be directly fixed and restrained.
1.2, spider web energy absorption effect evaluation indexes and simulation experiment design:
1.2.1, spider web energy absorption effect evaluation index:
the total energy absorption EA refers to the amount of energy that the spider web converts the kinetic energy of flying insects into its own energy after blocking the impact of the flying insects. The larger the value, the better the energy absorbing effect.
EA＝∫ 0 d f(x)dx(0-40)
Where d is the displacement of the structural impact and f (x) is the stress-strain relationship.
Peak stress refers to the maximum value of the equivalent stress experienced by the spider web during a collision, with a greater value representing a greater susceptibility of the spider web to damage during impact.
The specific energy absorption SEA refers to the ratio of the total energy absorption to the mass. The larger the value thereof represents the greater the energy absorbed by the spider web per mass of material, i.e. the greater the efficiency of energy absorption.
Figure GDA0004229064880000104
Where M is mass.
1.2.2.2 dynamic response simulation design of spider web interception flying insects:
based on the finite element method, the ANSYLS-DYNA solving module is utilized to simulate the dynamic response of the spider web to intercept flying insects. Five main structural factors influencing the energy absorbing effect of the spider web, namely the radial line length, the radial line section diameter, the spiral line number of turns, the spiral line spacing and the spiral line section diameter, are set by spiral line net modeling. The total energy absorption capacity, peak stress and specific energy absorption capacity of the spider web are taken as evaluation standards of energy absorption effects.
Because the computing module has higher sensitivity to the grid, the size of the grid is set to be 0.02mm in consideration of the computer capability, and the grid is divided by adopting a hexahedral grid in a sweeping method based on the spiral line structure curved surface characteristics of the spider web simulation model, as shown in fig. 3.
According to the adhesive force analysis of the spider web and the wall surface, the adhesive energy of the spider web diameter line and the wall surface can reach infinity in theory, and the spider web spiral line has smaller adhesive energy, so the end constraint of the spider web diameter line can be set as fixed constraint, and the end of the spiral line is negligible. The spider-web gland silk is replaced by nylon material, the insect model is simplified into rigid body, and the central part of the spider-web is impacted by 16mJ energy. The whole process that the spider web is elastically deformed to absorb the impact energy of insects and then release the energy to bounce the balls is simulated. The simulation results are shown in fig. 4.
To demonstrate the process of insect impact on the spider web dynamics, stress patterns of the spider web were taken from the time the impact was initially received to the time the impact energy was fully absorbed, as shown in fig. 5. As can be seen from the figures, after the spider web is subjected to insect impact, impact energy is transferred from the spider web center to the spider web diameter line ends, i.e., the bond of the spider web to the wall. The spiral line is subjected to smaller stress, and the dynamic response form of the spiral line is that the spiral line oscillates along with the net under the condition that insects do not directly strike the spiral line. The radial line structure is subjected to larger stress, and the maximum stress occurs at the end of the radial line, and the dynamic response mode is stretching and absorbing energy.
1.2.3 analysis of simulation test data based on response surface method:
the response surface method has two design modes, namely a first-order response surface model and a second-order response surface model. When the horizontal value of the current test factor is far away from the optimal position of the curved surface, a first-order model is adopted to approach the optimal solution so as to accelerate the approach speed. Wherein: beta i Is x i Linear effect of (2)
Figure GDA0004229064880000111
When the horizontal value of the current test factor is close to the optimal position of the curved surface, a second-order model is adopted to approach an optimal solution so as to improve the precision, and the model is shown as a formula (0-43);
Figure GDA0004229064880000121
wherein: beta i Is x i Linear effects of (2); beta ii Is x i Second order effects of (2); beta ij Is x i And x j Is a function of the interaction effect of (a).
The BBD experimental design method can effectively avoid the level which cannot be realized by certain factors, for example, the number of spiral turns in the experiment is preferably an integer number. Other experimental designs may result in non-integer loops that are difficult to achieve.
Therefore, the experiment utilizes the BBD design method to carry out simulation experiment design of the influence rule of the spider web structural parameters on the absorption energy. An experiment was set with 5 variables of spider web radial line length (a), radial line cross-section diameter (B), spiral wire turns (C), spiral wire spacing (D), and spiral wire cross-section diameter (E) as factors. In this experiment, when the factor arrangement approaches the optimum point, a model with flexibility is used to approximate the response, so a second order model is used to express the relationship between the response and the individual factors. Multiple regression fits are made to the functional relationship of each response to the relevant factors according to the ideas and experimental data of the BBD experimental design method as follows.
EA＝14.05-0.525A+0.035B+0.127C+0.286D-0.071E-0.03A*B-0.115AC-0.1245AD+0.022AE-0.135BC-0.051BD-0.08BE+0.075CD+0.037CE-0.14DE+0.19A 2 +0.052B 2 +0.268C 2 +0.13D 2 +0.06E 2 (0-44)
Stress＝36.18-2.97A+0.883B-4.13C-4.08D-0.315E-0.77AB-4.61AC-6.06AD+0.453AE-1.42BC-2.08BD+0.11BE-6.89CD-1.97DE-3.91A 2 -0.43B 2 -2.71C 2 +1.33D 2 -0.37E 2 (0-45)
SEA＝38.56-3.87A-3.08B-11.2C-2.65D-4.87E-0.07AB+1.37AC+0.16AD+0.82AE+1.49BC+0.34BD+0.57BE+0.17CD+0.32CE+0.002DE+0.76A 2 +0.22B 2 +2.5C 2 +0.62D2+0.44E 2 (0-46)
In order to verify the significance level of the model and each factor, the credibility of the influence rule of the spider web structure parameters on the energy absorption effect is ensured to be obtained, and the significance test is carried out on the experiment. The basic principle of the significance test is to discriminate against the probability that the invalid hypothesis is established. When the probability of the null hypothesis being established reaches 5%, the null hypothesis is established. When the invalid assumption of the model is established, the rule of influence of the spider web structural parameter on the energy absorption effect is invalid, and the obtained conclusion is also not established. In addition, through checking the significance level of each factor, the relativity of each structural parameter of the spider web on the influence of the energy absorption effect can be obtained, so that the significance level of each of three responses and the multiple regression fit equation among the factors is checked respectively.
1.2.4, a spider web structural parameter impact rule summary on energy absorption effect:
the influence rule of three variables of the spider web radial line length, the spiral line number of turns and the spiral line spacing on the total energy absorption is firstly arranged as shown in figure 6. As can be seen from the figure, the total energy absorption of the spider web tends to decrease as the length of the spider web wire increases. The main reason for this is that as the radial length increases, the amount of strain generated after an impact is reduced. As the number of turns of the spider web spiral line and the pitch of the spiral line increase, the total energy absorption of the spider web tends to increase. The reason is that when the impact point is at the center of the spider web, the farther the spider web spiral is from the center, the greater the amount of strain generated. The increase of the number of turns of the spiral wire and the pitch of the spiral wire directly increases the distance between the spiral wire and the center part of the spider web, namely increases the strain quantity of the spiral wire in the impact process, so that the total energy absorption quantity of the spider web is increased.
The law of influence of three variables of spider web diameter line length and spiral coil number, spiral coil number and spiral coil interval on peak stress is then collated as in fig. 7. From the above figures, the spider web peak stress tends to decrease as the spider web wire length increases. Therefore, it is assumed that the spider web is extremely short and has both ends fixed, and the strain amount exhibited by the spider web when receiving an impact force is extremely small, and the stress value to which the web is subjected is extremely large because the impact energy is unchanged. When the radial length is increased, the strain quantity is increased and the peak stress is reduced under the same impact energy. Thus, it is possible to explain the phenomenon that the radial length is increased and the peak stress of the spider web is reduced. The influence relationship of the spider net spiral coil number and the spiral coil distance on the spider net peak stress is complex. From the above figures, when the number of spider spiral turns and the pitch of the spiral turns are increased, the spider peak stress tends to decrease rapidly and is minimized when the number of spiral turns and the pitch of the spiral turns are maximized. In addition, when one of the number of turns of the spiral wire and the pitch of the spiral wire takes a minimum value, the peak stress of the spider web takes a maximum value. The reason is that when the number of turns of the spiral line is too small, the increase of the interval of the spiral line can lead to insufficient overall strength of the spider-web spiral line, and impact energy from the radial line cannot be shared. Conversely, a reduction in the pitch of the helix directly results in a spider-web helix overall structure that is too small to share impact energy from the radial line. Similarly, when the pitch of the spiral lines is too small, no matter the number of the spiral lines is increased or decreased, the peak stress of the spider web is too large. Thus, to reduce the peak stress of the spider web during impact, the number of turns of the helix and the pitch of the helix must be increased simultaneously.
Finally, the influence rules of the three variables of the spider web diameter line length, the spiral coil number and the spiral coil interval are compared with the energy absorption amount are collated as shown in figure 8. From the above figures, it is seen that as the spider web wire length increases, the spider web specific energy absorption decreases. Likewise, as the number of turns of the helix increases, the specific energy absorption of the spider web also decreases. When the diameter line length and the spiral line number of turns take minimum values, the spider web ratio energy absorption takes maximum values. From the analysis of the energy absorption of the spider web, it is known that as the length of the spider web is reduced, the energy absorption of the spider web is increased. In addition, the reduction in spider web wire length also directly reduces the overall quality of the spider web. Since the specific energy absorption of the spider web is obtained by the ratio of the total energy absorption of the spider web to the total mass of the spider web. The spider web wire length thus plays a decisive role in the spider web specific energy absorption. Furthermore, as can be seen from the foregoing, the spiral has less impact on the total energy absorption of the spider web, and both the number of turns of the spiral and the increase in pitch of the spiral lead to an increase in the total mass of the spider web. Thus, as the number of turns of the helix and the pitch of the helix increases, the spider web specific energy absorption decreases. When the number of turns of the spiral line and the interval between the spiral lines are taken as minimum values, the energy absorption rate of the spider web is taken as maximum values.
2. Bionic spider web lattice structure design:
2.1, a bionic spider web lattice structure design method:
in order to design a bionic lattice structure with the energy absorption characteristic of a spider web, firstly, the influence of a radial line and a spiral line in the spider web on the energy absorption effect can be obtained by aiming at the rule analysis of the spider web structural parameters on the energy absorption effect. The spider web structure with the best energy absorption effect can be obtained through optimizing parameters of the spider web diameter line and the spiral line. Thus, the lattice structure is designed to have a spider web-like radial line and spiral wound form with the longitudinal material as the radial line and the transverse material as the spiral line, as shown in fig. 9. When facing the longitudinal impact, the bionic spider web lattice radial line and the spiral line respectively exert the functional characteristics of the spider web radial line and the spiral line. Finally, the bionic spider web lattice with the optimal energy absorption effect can be obtained by optimizing the structural parameters of the bionic spider web lattice.
2.2, three bionic spider web lattice structure optimization designs:
based on the influence law of the spider web structural parameters on the energy absorption effect, namely the influence relationship between five factors of spider web radial line length (A), radial line section diameter (B), spiral line number of turns (C), spiral line interval (D) and spiral line section diameter (E) on three responses of spider web total energy absorption amount (EA), peak Stress (Stress) and specific energy absorption amount (SEA), three bionic spider web lattice structures are designed and respectively named as: a common bionic spider web lattice structure, a spiral bionic spider web lattice structure and a composite bionic spider web lattice structure. The optimization process is divided into two steps: firstly, obtaining lattice original unit cells through preliminary optimization, and finally, obtaining three different bionic spider web lattice structures through secondary optimization.
2.2.1, lattice primitive unit cell design:
according to the influence law of the spider web structural parameters on the spider web energy absorption effect, the influence significance of the spider web radial line structure on the energy absorption effect is higher, namely the influence degree of the bionic spider web lattice radial line structure parameter optimization on the energy absorption effect is larger. Therefore, the design of the basic bionic spider web structure should be optimized for lattice structure longitudinal materials. Five coordinate size fitting spline curves of three control points are set to parametrize and control the radial line structure of the basic bionic spider web lattice. Respectively named as minor diameter (A) 1 ) Total height (B) 1 ) Middle height (C) 1 ) Large diameter (D) 1 ) Diameter (E) 1 ). As shown in fig. 10.
FirstThe curve of the response of the lattice structure parameters to the total energy absorption of the lattice is fitted as shown in figure 11. From the figure, it can be seen that following A 1 And B 1 The total energy absorption amount tends to decrease. Conversely, with D 1 And the total energy absorption tends to increase. Wherein B is 1 And D 1 The influence on the total energy absorption is more obvious. As can be easily imagined, when B 1 Reduced and D 1 When the spider web lattice radial line structure is increased, the bending degree of the bionic spider web lattice radial line structure is increased, which is equivalent to applying certain pretightening force to the spider web radial line structure, and the phenomenon that the spider web generates 'loose feeling' is effectively avoided. Therefore, in order to improve the total energy absorption of the bionic spider web lattice unit cell, the bending degree of the radial line structure can be further increased.
Then, a response curve is fitted to the peak stress as in fig. 12. From the graph, it can be seen that following B 1 And the total energy absorption tends to decrease. Conversely, with D 1 Is increased, the peak stress tends to increase. Wherein A is 1 Less influence on peak stress, B 1 And D 1 The effect on peak stress is more pronounced. As can be easily imagined, when B 1 Reduced and D 1 When the bionic spider web lattice radial line structure is increased, the bending degree of the bionic spider web lattice radial line structure is increased, and the stress born by the radial line is also increased. Similarly, when B 1 Increase and D 1 When the bending degree of the bionic spider web lattice single-cell radial line structure is reduced, larger strain can be generated when the bionic spider web lattice single-cell radial line structure bears impact, and excessive stress is avoided. Therefore, in order to reduce peak stress of the bionic spider web lattice unit cell, the bending degree of the bionic spider web lattice unit cell radial line should be reduced.
Finally, the response curves are fitted against the energy absorption as shown in FIG. 13. From the figure, it can be seen that A 1 And D 1 Is less influenced by the specific energy absorption amount, B 1 The change in (c) has a greater influence on its specific energy absorption. With B 1 The specific energy absorption is reduced and the specific energy absorption is increased. The main reason for this can be found by analysis of both the total energy absorption and the total mass. When B1 is reduced, the bending degree of the bionic spider web lattice radial line structure is increased, the total energy absorption amount of the lattice is increased, and the total mass of the lattice is reduced. Since the specific energy is the ratio of the total energy to the total mass, the reduction of B1 can maximally increase the specific energy, i.e The bending degree of the bionic spider web lattice radial line structure should be increased.
2.2.2, design of common bionic spider web lattice unit cell:
based on the influence law of the spider web pore-forming structure on the energy absorption effect, the bionic spider web lattice original unit cell design effectively introduces the spider web pore-forming structure characteristics into the bionic lattice design. However, the lattice energy absorption effect designed based on the influence rule of the radial line structure on the energy absorption effect cannot meet the requirement. Therefore, spider web and spiral line features are co-introduced into a biomimetic spider web lattice and named as a common biomimetic spider web lattice structure. Simulation tests are carried out on the energy absorption effect of the composite material under the impact energy of 1.8J.
First, the curve of the lattice structure parameter response to the total energy absorption of the lattice is fitted, as shown in fig. 14. From the figure, it can be seen that when the spiral is rotated by an angle (A 2 ) Increase and spiral section diameter (B) 2 ) When the total energy absorption amount (EA) of the common bionic spider web lattice is reduced, the total energy absorption amount (EA) is in an increasing trend. While the radial line cross-sectional diameter (C 2 ) Sum diameter line number (D) 2 ) When the total energy absorption amount (EA) of the common bionic spider web lattice is reduced, the total energy absorption amount (EA) is in an increasing trend. Wherein the rotation angle of the spiral line (A 2 ) Is increased by the diameter B of the spiral section 2 The reduction of the size of the artificial cobweb lattice is helpful for the deformation of the common bionic cobweb lattice under the impact action and the absorption of energy. Therefore, in order to improve the total Energy Absorption (EA) of the common bionic spider web lattice structure, the rotation number of the spiral line is increased and the section diameter of the spiral line is reduced.
Then, as can be seen from the graph of fig. 15, the response curve is fitted to the peak stress, and the response curve is obtained with the rotation angle (a of the spiral line 2 ) Sum diameter line number (D) 2 ) The peak stress of the common bionic spider web lattice is increased and then reduced. While the diameter of the spiral section (B) 2 ) And radial line section diameter (C) 2 ) The effect on peak stress is insignificant. It can be easily seen that when the rotation angle of the spiral (A 2 ) When non-integer turns occur, stresses increase due to structural asymmetry. Similarly, when the number of radial lines is an odd number, the stress increase phenomenon also occurs. Therefore, to reduce peak stress, the occurrence of helix angle of rotation (A 2 ) Not being an integerAnd the case where the number of radial lines is an odd number.
Finally, a response surface is fitted to the Specific Energy Absorption (SEA) as shown in fig. 16. From the figure, it can be seen that the rotation angle (A 2 ) Diameter of spiral section (B) 2 ) Diameter of radial line section (C) 2 ) Sum diameter line number (D) 2 ) The energy absorption capacity of the ordinary bionic spider web lattice is increased. Wherein the helix rotates by an angle (A 2 ) And radial line section diameter (C) 2 ) The influence of the contrast energy absorption is more obvious. Due to the angle of rotation of the helix (A 2 ) And radial line section diameter (C) 2 ) When the total mass of the common bionic spider lattice is increased, the total mass is increased more remarkably than the total energy absorption amount, so that the total mass of the common bionic spider lattice is reduced compared with the energy absorption amount. Therefore, in order to improve the Specific Energy Absorption (SEA) of the common bionic spider web lattice, the rotation angle (A) of the spiral line should be reduced 2 ) Diameter of radial line section (C) 2 )。
2.2.3, design of spiral bionic spider web lattice unit cell:
the influence rule of the spider web radial line structural parameters on the energy absorption effect is obtained, and the spiral line structural parameters have a remarkable effect on reducing the spider web peak stress. Therefore, in order to obtain a bionic spider lattice structure with smaller peak stress in the impact process, a bionic spider lattice structure which is completely composed of spiral lines is designed. The spider web threads are thus designed in the same rotational form of a spiral line. The radial lines and the spiral lines form a lattice according to opposite rotation directions, wherein the rotation angles of the radial lines and the rotation angles of the spiral lines are set to be the same in order to ensure the symmetry of a lattice structure. So the spiral bionic spider web lattice is named as the spiral bionic spider web lattice. And carrying out an energy absorption effect simulation test under the impact energy of 1.8J.
First, a response surface of lattice structure parameters to total Energy Absorption (EA) of the lattice is fitted, as shown in fig. 17. As can be seen, as the helix rotates by an angle (a 3 ) Diameter of spiral section (B) 3 ) And radial line section diameter (C) 3 ) The total energy absorption of the spiral bionic spider web lattice is increased, wherein the diameter (B) of the section of the spiral line 3 ) The effect on the total Energy Absorption (EA) is more pronounced. Thus, to enhance helical spider The total energy absorption of the cobweb lattice structure should be increased by the rotation angle (A of the spiral line 3 ) Diameter of spiral section (B) 3 ) And radial line section diameter (C) 3 )。
Then, the lattice structure parameters are fitted to the lattice peak Stress (Stress) response surface as shown in fig. 18. As can be seen, as the helix rotates by an angle (a 3 ) The peak Stress (Stress) of the spiral bionic spider web lattice shows a tendency of descending and increasing, when the spiral line rotates by an angle A 3 So that the peak Stress (Stress) is lowest when the spiral is a non-integer number of turns. Diameter of spiral section (B) 3 ) And radial line section diameter (C) 3 ) Less impact on peak stress. And as the diameter of the section of the spiral line increases, the peak Stress (Stress) of the spiral bionic spider web lattice is in a decreasing trend. Wherein the number of turns of the spiral has a significant effect on peak Stress (Stress). Therefore, to reduce peak Stress (Stress) of the spiral bionic spider web lattice, the rotation angle of the spiral line should be reduced (A 3 )。
Finally, the lattice structure parameters are fitted to the lattice Specific Energy Absorption (SEA) response surface, as shown in fig. 19. From the above figures, it can be seen that the rotation angle (A 3 ) The increase of the spiral bionic spider web lattice ratio energy absorption (SEA) is in a decreasing trend. And as the diameter of the section of the spiral line increases, the Specific Energy Absorption (SEA) of the spiral bionic spider web lattice tends to decrease first and then increase. Wherein the helix rotates by an angle (A 3 ) The impact of the contrast energy absorption (SEA) is more pronounced. Diameter of spiral section (B) 3 ) And radial line section diameter (C) 3 ) The effect is not significant. Therefore, in order to improve the Specific Energy Absorption (SEA) of the spiral bionic spider web lattice, the rotation angle (A) of the spiral line should be reduced 3 )。
2.2.4, design of composite bionic spider web lattice unit cell:
according to the research on the energy absorption effect of the common bionic spider web lattice structure and the spiral bionic spider web lattice structure, when the lattice radial line structure presents spider web warp structural characteristics, the lattice presents higher total energy absorption amount in impact, and when the lattice radial line presents spider web spiral structural characteristics, the lattice receives smaller peak stress in impact. Thus, to obtain a biomimetic spider-web lattice structure with the dual advantages of higher total energy absorption and lower peak stress. The common bionic spider web lattice and the spiral bionic spider web lattice radial line structure are combined together, so that the composite bionic spider web lattice is named as a composite bionic spider web lattice. Wherein, starting from the optimization of radial line structure, the radial line characteristic of ordinary bionic spider web is kept at the middle part of the composite bionic spider web lattice radial line, and the two ends of the composite bionic spider web lattice radial line keep the warp line characteristic of spiral bionic spider web lattice. For this purpose, spline curves are used and three control points are set to model a composite biomimetic spider web lattice structure. An impact load of 1.8J was also set for the simulation test, as shown in FIG. 20.
First, the curve of the lattice structure parameter response to the total energy absorption of the lattice is fitted, as shown in fig. 21. It can be seen that when the spline size (B 4 ) When the composite bionic spider web lattice total Energy Absorption (EA) is increased, the total Energy Absorption (EA) is increased, and the total Energy Absorption (EA) is increased along with the diameter (E 4 ) When the composite bionic spider web lattice is increased, the total energy absorption capacity of the composite bionic spider web lattice is reduced. Wherein the diameter of the radial cross section (E 4 ) And spline size (C 4 ) The change in (c) has no significant effect on the total energy absorption. Therefore, to increase the total Energy Absorption (EA) of the composite bionic spider web lattice, the spline size should be further increased (B 4 ) Even if the radial line has a more pronounced helical characteristic.
Then, the lattice structure parameters are fitted to the lattice peak Stress (Stress) response surface as shown in fig. 22. It can be seen that when the spline size (B 4 ) When increasing, the peak Stress (Stress) of the composite bionic spider web lattice increases and decreases firstly, and the peak Stress (Stress) is increased and then decreased along with the spline size (C 4 ) And radial line cross-sectional diameter (E 4 ) When the Stress is increased, the peak Stress (Stress) of the composite bionic spider web lattice shows a trend of increasing firstly and then reducing. Wherein, the three variables have significant influence on peak stress of the composite bionic spider web lattice. Thus, to reduce peak Stress (Stress) of composite biomimetic spider web lattice, when spline size (B 4 ) And radial line cross-sectional diameter (E 4 ) Obtain minimum value and spline size (C 4 ) When the maximum value is obtained, the peak stress of the composite bionic spider web lattice is obtained to be the minimum value.
Finally, fitting the lattice structure parameters to the latticeSpecific Energy Absorption (SEA) response curves, as shown in fig. 23. As can be seen from the figure, when the diameter of the radial line cross section increases (E 4 ) When the total energy absorption of the composite bionic spider web lattice is reduced, the variable spline size (B 4 ) And spline size (C 4 ) The effect on the composite bionic spider web lattice ratio energy absorption (SEA) is not obvious. The main reason for this is when the spline size (B 4 ) When the composite bionic spider web lattice total energy absorption (FA) is increased, the lattice total mass is also increased. Spline size (C) 4 ) The total Energy Absorption (EA) of the composite bionic spider web lattice is less affected and the total mass of the lattice is less affected. Due to the influence of the accuracy of the second order response surface fitting model, spline size (B 4 ) And spline size (C 4 ) The interactive effect of the contrast energy absorption (SEA) is insignificant. Therefore, in order to improve the total energy absorption of the composite bionic spider web lattice, the diameter of the cross section of the diameter line of the composite bionic spider web lattice should be reduced (E 4 )。
2.2.5, three bionic spider web lattice structure optimization designs:
through the research of the interactive influence of three bionic spider web lattice structure parameters on the energy absorption effect of the three bionic spider web lattice structure parameters, the influence rule of the three bionic spider web lattice structure parameters on the energy absorption effect of the three bionic spider web lattice structure parameters can be obtained. In order to further improve the energy absorption effect of the three bionic spider web lattice structures, structural parameters of the three bionic spider web lattice structures are optimized based on a response surface method. Based on the influence rule of structural parameters of three bionic spider web lattice structures on the energy absorption effect, the total energy absorption amount, peak load and specific energy absorption amount are taken as objective functions, and the expression of the optimization problem is defined as
Figure GDA0004229064880000191
Wherein EA (X) is total energy absorption of the bionic spider web lattice, stress (X) is peak Stress of the bionic spider web lattice, SEA (X) is specific energy absorption of the bionic spider web lattice, and X is a value range of structural parameters.
2.3, comparing the energy absorption effects of the bionic spider web lattice under dynamic and static loads:
2.3.1, comparing the energy absorption effects of the bionic spider web lattice under low-speed impact load:
based on the three bionic spider web lattice structure optimizations, constructing three bionic spider web lattice models of the optimization sum; in order to verify the energy absorption effect of three bionic spider web lattices after optimization, simulation tests are carried out on the energy absorption effect of the three bionic spider web lattices under low-speed impact, 15 groups of three bionic lattices are arranged by taking aluminum alloy as a material and impacted by different impact energies, and three data of total energy absorption, peak stress and specific energy absorption are recorded.
The data of the total energy absorption of three bionic spider-web lattice unit cells fitted under different impact energy are shown in figure 24, and under the action of different impact energy, the three bionic spider-web lattice unit cells all show good energy absorption effect. The total energy absorption of the spiral bionic spider web lattice is relatively high, and the total energy absorption of the common bionic spider web lattice and the composite bionic spider web lattice is low. Thus, from the perspective of total energy absorption, all three biomimetic spider webs effectively combine the spider web energy absorption characteristics.
Peak stress data of three bionic spider web lattice unit cells fitted at different impact energies are shown in figure 25. Under the action of different impact energies, the peak stress difference of the three bionic spider web lattice is large. Wherein the peak stress of the common bionic spider web lattice is relatively high, and the peak stress of the spiral bionic spider web lattice and the composite bionic spider web lattice is low. Therefore, both the spiral bionic spider web lattice and the composite bionic spider web lattice effectively combine the characteristics of spiral lines in the spider web to reduce peak stress. From the point of view of peak stress, the composite bionic spider web lattice is the best bionic spider web lattice design.
The data of the specific energy absorption of three bionic spider web lattice unit cells fitted at different impact energies are shown in figure 26. Under the action of different impact energy, the three bionic spider web lattices have smaller difference in specific energy absorption. Wherein the composite bionic spider web lattice has relatively higher energy absorption capacity, and the peak stress of the common bionic spider web lattice and the spiral bionic spider web lattice is lower. Wherein, after the composite bionic spider web lattice radial line is optimized, the quality is smaller than other two lattices. Therefore, from the aspect of specific energy absorption, the composite bionic spider web lattice is the optimal bionic spider web lattice design.
2.3.2, comparing the energy absorption effects of the bionic spider web lattice under quasi-static load:
from the above, all three bionic spider web lattices show good energy absorption effect under low-speed impact load. In order to further explore the energy absorption effect of three bionic spider web lattices under quasi-static load, aluminum alloy is used as a material, compression displacement is set to be 10mm, and deformation forms of the three lattices are compared and analyzed.
The total energy absorption capacity of the composite bionic spider web lattice is 34% higher than that of the common bionic spider web lattice and 46% higher than that of the spiral bionic lattice. The peak stress of the spiral bionic spider web lattice is 42% lower than that of the common bionic spider web lattice and 33% lower than that of the composite bionic spider web lattice. The energy absorption capacity of the composite bionic spider web lattice is about 47% higher than that of the common bionic spider web lattice and 51% higher than that of the spiral bionic spider web lattice. Therefore, under quasi-static load, the composite bionic spider web lattice energy absorption effect is optimal.
3. Dot matrix energy absorption effect research under quasi-static load:
3.1, quasi-static compression test of bionic spider web lattice sandwich board:
to further verify the difference of the energy absorption effect of the three bionic spider web lattice structures under static load. Three bionic spider web lattice sandwich panels were fabricated and 3 quasi-static compression experiments were performed respectively. The mechanical behavior and deformation failure modes of the three bionic spider web lattice structures under static load can be obtained through a quasi-static compression experiment. In addition, the compression displacement and the compression force data are output according to a quasi-static compression experiment to be fitted and integrated, and the relation between the total energy absorption amount and the specific energy absorption amount of the three bionic spider web lattice structures under static load can be obtained, so that the optimal bionic spider web lattice structure is selected.
3.1.1, preparing a bionic spider web lattice sandwich board:
because three kinds of bionical spider web lattice structures are complicated relatively, in order to avoid 3D to print the in-process, unreasonable bearing structure leads to printing failure or lattice structure's defect, also avoid in the aftertreatment simultaneously, bearing structure is difficult to get rid of and influences experimental result, combines printer experimental conditions, adopts e-stage to set up supporting parameter.
According to the setting to the support parameter, add the support to three kind of bionical spider web lattice battenboard, after accomplishing to bearing structure setting, in order to guarantee three kind of bionical spider web lattice battenboard's manufacturing accuracy furthest, set up the section thickness to 0.1mm, print.
The experiment was prepared by using a photosensitive resin material instead of a metal material to perform a bionic spider-web lattice sandwich panel structure due to the limitations of experimental conditions. The 3D printer model used was Lite600HD and the photosensitive resin material used was UTR9000.
Because of the influence of printer precision, in order to avoid the damage of bionical spider web lattice structure in printing and influence experimental result, set up three bionical spider web lattice structure's width and high size 25mm 16mm.
When the printing material is replaced by the resin by the aluminum alloy, the difference of the experimental results of the three bionic spider web lattice is not obvious enough, namely the experimental results obtained by carrying out the quasi-static compression experiment on the bionic spider web lattice unit cell are less different. Therefore, in order to more intuitively compare the difference of the energy absorption effect of three bionic spider web lattice structures under static load and adapt to a subsequent testing machine, a sandwich panel consisting of 19 lattice unit cells is prepared.
3.1.2, quasi-static compression protocol:
the experiment adopts an INSTRON3382 universal tester to test the mechanical behavior and the energy absorption effect of three bionic spider web lattice structures under a quasi-static compression experiment. In the experiment, the compression displacement is set to be 10mm according to the compression displacement loading. To ensure quasi-static compression slow loading conditions, the loading rate was set to 0.1mm/min. The sampling time interval is 0.2s, i.e. 5 points of data are acquired per second. Because the strength of the experimental material is smaller, 3 quasi-static compression experiments are respectively carried out on the 3 bionic spider web lattice structure sandwich plates and the experimental data are averaged in order to reduce errors caused by the material and machine factors.
3.2.3, analysis of deformation forms of three bionic spider web lattices:
Firstly, shooting a deformation picture of a common bionic spider web lattice under quasi-static load. According to the results of the quasi-static compression simulation test of the common bionic spider web lattice, the common bionic spider web lattice is known to slip and deform when entering a platform stage. The deformation form is represented by radial fracture, and the lattice unit cell is slipped and broken into two parts under the action of compression force. And the lattice slippage is more serious with the increase of the compression displacement. The main reason is that the rotation direction of the spiral line is single, so that the radial line is broken under the shearing stress from the spiral line, and then the lattice unit cell is broken into two parts and transversely slides. Thus, the pores of the lattice are not compacted and still do not enter the compaction stage when the compression displacement reaches 10 mm.
Then, shooting a deformation picture of the spiral bionic spider web lattice under a quasi-static load. The combination results of the quasi-static compression simulation test on the spiral bionic spider web lattice can show that when the spiral bionic spider web lattice enters the stage of the platform, the radial line and the spiral line structure are uniformly bent and then broken. Wherein, the lattice turns outwards in the radial line and the spiral line at the stage of the platform to form a 'turtle shell' shape. As the compression displacement increases, the lattice diameter and helix no longer evert and the bottom void begins to compact. When the compression displacement reaches 9.28mm, the lattice enters the compaction stage.
Finally, shooting a deformation picture of the composite bionic spider web lattice under quasi-static load. The combination pair compound bionic spider web lattice quasi-static compression simulation test results show that when the compound bionic spider web lattice enters a platform stage, the radial line and the spiral line structure are uniformly bent. Compared with the common bionic spider web lattice, the compression force does not cause the composite bionic spider web lattice to fracture and slide. The reason for this is that the composite bionic spider web wire structure is optimized to a curve of opposite spin direction to the spiral wire. Therefore, the damage of the shearing stress to the radial line structure caused by the unidirectional rotation of the spiral line is effectively avoided. Wherein, the lattice turns outwards in the radial line and the spiral line at the stage of the platform to form a 'turtle shell' shape. With the increase of the compression displacement, the lattice radial line and the spiral line are continuously turned outwards, the deformation degree of the tortoise shell shape of the lattice is deepened, and when the compression displacement is 10mm, the pores of the lattice are not compacted all the time.
3.2.4, analysis of energy absorption effects of three bionic spider web lattices:
under quasi-static loading, the lattice structure deforms and absorbs the compression energy. The difference of the dot matrix energy absorption effect can be verified on the side face through analysis of the dot matrix deformation form. On the basis of the deformation forms of the three bionic spider lattice structures, in order to further compare the energy absorption effects of the three bionic spider lattice sandwich panels, a compression force-compression displacement data fitting curve is shown in fig. 28.
The trigger force of the common bionic spider-web lattice sandwich board structure is 450.53N, and the average value of the platform force is 367.42N. When the compression displacement reaches 10mm, the compaction stage is still not entered. The trigger force of the spiral bionic spider-web lattice sandwich board structure is 484.29N, and the average value of the platform force is 521.07N. When the compression displacement reaches 9.28mm, the lattice enters the compaction stage. However, the force average value of the spiral bionic spider web lattice platform is larger than the theoretical predicted value, and the main reason is that the force average value is influenced by 3D printing precision, and partial lattice unit cells have internal defects to lead to entering a compaction stage in advance under the condition of the same compression displacement. This causes the platform force average to exceed the trigger force. In addition, compared with the common bionic spider web lattice, the spiral bionic spider web lattice has higher platform force. Therefore, the energy absorption effect of the common bionic spider web lattice is relatively good. The triggering force of the composite bionic spider web lattice sandwich board structure is 716.31N, and the average value of the platform force is 709.65N. When the compression displacement reaches 10mm, the compaction stage is still not entered. The composite bionic spider web lattice is in a horizontal stage, the average value of the triggering force and the platform force is smaller, and the platform force is always larger than the other two bionic spider web lattices along with the deep compression displacement. Therefore, the composite bionic spider web lattice structure has more remarkable energy absorption effect.

Claims (1)

1. A bionic spider web lattice structure design and an energy absorption method thereof are characterized in that: the method comprises the following steps:
step one, analyzing influence of spider web structural parameters on energy absorption effect:
(1.1), spider web structure composition analysis:
(1.1.1), spider silk deformation energy absorption analysis:
firstly, researching a mechanical model of spider silk under impact load; to simplify the model, insects can be equivalent to a mass m particle, impact the midpoint of spider silk at an initial speed and vibrate with the spider web;
the geometric analysis of the picture can be seen as follows:
Figure FDA0004229064860000011
wherein y is the position quantity of the particles in the vertical direction; θ is the angle between the spider silk and the horizontal line; the increase in spider silk length is:
Figure FDA0004229064860000012
the strain of the material is as follows:
Figure FDA0004229064860000013
according to the analysis of the radial line mechanics of the circular net spider, the relation expression of the radial line stress-strain is as follows: loading
Figure FDA0004229064860000014
Unloading:
Figure FDA0004229064860000015
wherein sigma is material stress; epsilon is the material strain; epsilon y Yield to the materialStrain; whereas the stress-strain relationship of a contour can be expressed in terms of a polynomial power function:
σ＝a(ε+bε n ) 0＜ε＜2.7 (0-6)
from the above, it is known that the stress and strain of spider silk are always in a linear relationship, whether loaded or unloaded, and therefore the stress σ of spider silk can be uniformly expressed as:
σ＝Eε+S (0-7)
wherein E, S is a constant determined by different loading conditions; substituting the expression into
Figure FDA0004229064860000021
In the middle of
B＝S-E (0-9)
After neglecting the weight of the spider silk, the kinetic equation of the spider silk can be obtained:
Figure FDA0004229064860000022
where the angle θ is used as an independent variable, a differential equation can be obtained:
Figure FDA0004229064860000023
solving the differential equation, and performing variable substitution:
Figure FDA0004229064860000024
p 2 ＝T (0-13)
then there are:
Figure FDA0004229064860000025
the equation can thus be changed to a first order linear differential equation with θ as an argument:
Figure FDA0004229064860000026
solving to obtain
Figure FDA0004229064860000027
Thus, the theoretical solution of the dynamic response of spider silk after impact depends on the initial conditions, the dynamic response of spider silk being an up-and-down oscillation;
(1.1.2), spider web structure analysis:
exploring the ratio of the area of the spider web which can block insects to the total length of the used gland silk; drawing a spider web model using a vortex line instead of a logarithmic spiral line;
(1.1.3), radial line number and spiral coil number study:
exploring the relation between the number of spider web lines and the number of spiral turns; the number of the spider web diameter lines and the number of the spiral line turns are directly influenced by the maximum area of the spider web and the maximum impact force of insects; when the area of the spider web and the impact force of insects are increased, the increase of the number of the radial lines is helpful for increasing the strength of the spider web, and the increase of the number of spiral turns is helpful for better dispersing the impact energy into the radial lines; in addition, when the bearing capacity of the radial lines is improved, the number of the radial lines required is correspondingly reduced, and the spiral line is vice versa; therefore, when the spider web area and the insect impact force are fixed, the bearing capacity of the radial lines and the adhesion force of the spiral lines directly influence factors of the number of the radial lines and the number of turns of the spiral lines; therefore, in the simulation model, the influence relationship of the ratio of different diameter lines to the number of turns of the spiral line on the absorption of impact energy by the spider web can be obtained by changing the cross-sectional areas of the spider web diameter lines and the spiral line;
(1.1.4), study of the effect of insect impact on spider web tension:
the spider web model can thus be regarded as a wood board of smaller thickness, and the impact of insects on the spider web can be regarded as a force of a certain magnitude acting on the wood board;
(1.1.5), spider web and wall connection structure study:
in simulation experiments of the spider web intercepting insect impact, each radial line of the spider web can be directly fixed and restrained;
(1.2), spider web energy absorption effect evaluation indexes and simulation experiment design:
(1.2.1), a spider web interception flying insect dynamic response simulation design:
simulating the dynamic response of the flying insects intercepted by the spider web by utilizing an ANSYLS-DYNA solving module; modeling by using a spiral wire net, and setting five main structural factors affecting the energy absorbing effect of the spider net, namely, the length of a radial wire, the diameter of a radial wire section, the number of turns of a spiral wire, the pitch of the spiral wire and the diameter of the section of the spiral wire; taking the total energy absorption amount, peak stress and specific energy absorption amount of the spider web as evaluation criteria of energy absorption effect;
(1.2.2), simulation test data analysis based on the response surface method:
designing an experiment by adopting a response surface method; performing experimental analysis by adopting a response surface method to obtain the influence rule of spider web structural parameters on the energy absorption effect; performing simulation experiment design of an influence rule of spider web structural parameters on absorbed energy by utilizing a BBD design method;
Step two, designing a bionic spider web lattice structure:
(2.1), a bionic spider web lattice structure design method:
firstly, aiming at the rule analysis of the spider web structural parameters on the energy absorption effect, the influence of the radial line and the spiral line in the spider web on the energy absorption effect can be obtained; the spider web structure with the best energy absorption effect can be obtained by optimizing parameters of the spider web diameter line and the spiral line; thus, the lattice structure is designed to have a form similar to the winding of spider web radial lines and spiral lines, and the longitudinal material is taken as the radial lines, and the transverse material is taken as the spiral lines;
(2.2), three bionic spider web lattice structure optimization designs:
three bionic spider web lattice structures are designed and respectively named as: a common bionic spider web lattice structure, a spiral bionic spider web lattice structure and a composite bionic spider web lattice structure; the optimization process is divided into two steps: firstly, obtaining lattice original unit cells through preliminary optimization, and finally, obtaining three different bionic spider web lattice structures through secondary optimization;
(2.2.1), lattice primitive unit cell design:
five coordinate size fitting spline curves of three control points are set to parametrize and control the radial line structure of the basic bionic spider web lattice;
(2.2.2), design of common bionic spider web lattice unit cell:
The characteristics of the spider web lines and the spiral lines are jointly introduced into a bionic spider web lattice and named as a common bionic spider web lattice structure;
(2.2.3), spiral bionic spider web lattice unit cell design:
designing spider web threads into a rotating form with the same spiral line; the radial lines and the spiral lines form a lattice according to opposite rotation directions, wherein the rotation angles of the radial lines and the rotation angles of the spiral lines are set to be the same in order to ensure the symmetry of a lattice structure;
(2.2.4), design of composite bionic spider web lattice unit cell:
the common bionic spider web lattice and the spiral bionic spider web lattice radial line structure are combined together, so that the common bionic spider web lattice and the spiral bionic spider web lattice radial line structure are named as a composite bionic spider web lattice; starting from optimization of the radial line structure, the radial line characteristics of the common bionic spider web are maintained in the middle of the composite bionic spider web lattice radial line, and the spiral bionic spider web lattice warp characteristics are maintained at the two ends of the composite bionic spider web lattice radial line; for this purpose, a spline curve is used and three control points are set to model a composite bionic spider web lattice structure;
(2.2.5), three bionic spider web lattice structure optimization designs:
taking the total energy absorption, the peak load and the specific energy absorption as objective functions, and defining the expression of the optimization problem as follows:
Figure FDA0004229064860000051
Wherein EA (X) is total energy absorption of the bionic spider web lattice, stress (X) is peak Stress of the bionic spider web lattice, SEA (X) is specific energy absorption of the bionic spider web lattice, and X is a value range of structural parameters;
(2.3), comparing the energy absorption effects of the bionic spider web lattice under dynamic and static loads:
(2.3.1), comparison of energy absorption effects of bionic spider web lattice under low-speed impact load:
from the aspect of specific energy absorption, the composite bionic spider web lattice is the optimal bionic spider web lattice design;
(2.3.2), comparing the energy absorption effects of the bionic spider web lattice under quasi-static load:
under quasi-static load, the composite bionic spider web lattice energy absorption effect is optimal;
step three, researching lattice energy absorption effect under quasi-static load:
(3.1), quasi-static compression test of bionic spider web lattice sandwich plate:
manufacturing three bionic spider web lattice sandwich boards and respectively carrying out 3 times of quasi-static compression experiments; the mechanical behavior and deformation failure modes of three bionic spider web lattice structures under static load can be obtained through a quasi-static compression experiment; in addition, according to the quasi-static compression experiment, the compression displacement and the compression force data are output to be fitted and integrated, and the relation between the total energy absorption amount and the specific energy absorption amount of the three bionic spider web lattice structures under static load can be obtained, so that the optimal bionic spider web lattice structure is selected;
(3.1.1), preparation of a bionic spider web lattice sandwich board:
setting supporting parameters by adopting an e-stage; according to the setting of the supporting parameters, adding support to the three bionic spider-web lattice sandwich boards, and after the setting of the supporting structure is completed, setting the slice thickness to be 0.1mm for printing in order to ensure the manufacturing precision of the three bionic spider-web lattice sandwich boards to the maximum extent;
(3.1.2), quasi-static compression protocol:
testing the mechanical behaviors and the energy absorption effects of three bionic spider web lattice structures under a quasi-static compression experiment by adopting an INSTRON3382 universal tester; in the experiment, the compression displacement is set to be 10mm according to the compression displacement loading; to ensure quasi-static compression slow loading conditions, the loading rate was set to 0.1mm/min; the sampling time interval is 0.2s, namely 5 points of data are collected every second; because the strength of the experimental material is smaller, 3 quasi-static compression experiments are respectively carried out on the 3 bionic spider web lattice structure sandwich panels and the experimental data are averaged in order to reduce errors caused by the material and machine factors;
(3.1.3), three biomimetic spider web lattice deformation format analyses:
in order to explore three bionic spider web lattice structure deformation forms under quasi-static load, three bionic lattices are photographed respectively before compression, at a platform stage and after compression.
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