CN116951036A - Three-dimensional mechanical superstructure with enhanced strength and rigidity - Google Patents
Three-dimensional mechanical superstructure with enhanced strength and rigidity Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
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- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
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- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
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- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
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Abstract
The technical field of structural mechanics discloses a three-dimensional mechanical superstructure with enhanced strength and rigidity, which comprises a plurality of unit cells arranged in an array, wherein each unit cell comprises a shared substrate, a first substrate, a second substrate, a first diagonal rod, a second diagonal rod and ligaments, the first substrate is connected with the shared substrate through a plurality of first diagonal rods, the second substrate is connected with the shared substrate through a plurality of second diagonal rods, the second diagonal rods and the first diagonal rods are in mirror symmetry relative to the shared substrate, the shared substrate has a torsion direction when the unit cells are pressed, the shared substrate is connected with the shared substrate of adjacent unit cells through the ligaments, the ligaments are tangent to the torsion direction of the shared substrate and are arranged back to the torsion direction of the shared substrate, one end of the ligaments is connected with the shared substrate, and the other end of the ligaments is connected with the shared substrate of the adjacent unit cells. The super structure can still maintain excellent mechanical properties under quite low relative density, and fully embody the excellent performance and wide application prospect of the structural design.
Description
Technical Field
The scheme belongs to the technical field of structural mechanics, and particularly relates to a three-dimensional mechanical superstructure with enhanced strength and rigidity.
Background
Because of the reasonable structure, artificially designed metamaterials show unprecedented mechanical and physical properties, and become a promising approach to customizing functions, such as negative poisson's ratio, negative shrinkage, reusability, programmability and adjustable stiffness. Metamaterials are generally composed of specific microscopic (or microscopic) structures: from a topological perspective, such materials are intermediate between purely natural materials with intrinsic physical properties and large structures with highly structural characteristics; on a microscopic scale, the physical behavior of a metamaterial is similar to that of a structure, but when the macroscopic effect of the metamaterial is observed, the physical properties of the metamaterial are closer to those of a homogeneous material.
The metamaterial has great engineering application value in the aspects of energy absorption, nonreciprocal unidirectional optical and acoustic devices, expandable wing design and the like. As a novel metamaterial, the compression-torsion coupling metamaterial can generate circumferential torsion deformation under the action of tensile or compressive load, and thus the compression-torsion coupling metamaterial is widely focused by students. Frenzel et al for the first time demonstrate this new 3D chiral mechanical metamaterial that undergoes transverse torsion upon axial compression, which can reach 2 per axial strain torsion. The Zheng, the Hu and the like provide a novel three-dimensional compression-torsion mechanical metamaterial design method based on a chiral mechanism of converting axial compression (or extension) into torsion by a diagonal rod; when the number of transverse units n=9, the torsion angle of the material under compression can still keep a larger value; and points out that weaker lateral constraints between cells are critical to achieving outstanding wringing performance. The structural design of the compression-torsion metamaterial is mature, the interests of students begin to turn to theoretical analysis and research at present, and the stiffness matrix of the three-dimensional chiral diagonal compression-torsion coupling metamaterial unit is deduced by applying a unit load method based on the Euler beam theory under the condition of considering the compression-torsion coupling effect aiming at diagonal compression-torsion coupling metamaterial, so that guidance is provided for the design and analysis of the compression-torsion coupling metamaterial, and a new way is opened up for theoretical analysis of the deformation coupling problem. The unique elastic response of the compression-torsion metamaterial in the direction orthogonal to the loading direction fills the expectations of students on the application scene of the compression-torsion metamaterial, but the relatively low specific stiffness and specific strength limit the engineering application of the compression-torsion metamaterial.
Through excellent structural design, the mechanical metamaterial can obtain excellent mechanical properties under the condition of ultralow density. Lightweight metamaterials with high strength and high rigidity have been the topic of interest to researchers and defense, automotive and aerospace industries, and some researchers have studied some measures to enhance the feasibility of structural strength and rigidity. Fu and Chen et al propose a new honeycomb design method for improving the in-plane mechanical properties of the honeycomb: the diamond structure is embedded into the concave angle hexagonal honeycomb, and the method of combining theoretical analysis and numerical simulation is adopted to calculate the in-plane mechanical properties of the novel honeycomb under uniaxial compression, including Young's modulus, poisson's ratio and critical buckling strength. The results show that the novel honeycomb structure has obviously improved in-plane Young's modulus and critical buckling strength while maintaining the auxetic performance.
Existing methods for improving the specific strength and specific stiffness of a structure generally optimize the material distribution of the structure in the loading direction or distribute the stress concentration of the structure, ignoring what is generally considered as a "connector" orthogonal to the loading direction for improving the strength and stiffness of the structure.
Disclosure of Invention
The scheme aims at overcoming at least one defect (deficiency) in the prior art, designs a three-dimensional mechanical superstructure with enhanced strength and rigidity, and aims at providing a novel structure reinforcement strategy by utilizing the compression-torsion coupling effect.
In order to solve the technical problems, the following technical scheme is adopted:
a three-dimensional mechanical superstructure comprises a plurality of unit cells arranged in an array, each unit cell comprising a common substrate, a first substrate, a second substrate, a first diagonal, a second diagonal, and ligaments, having a center line perpendicular to the common substrate. The first substrate is parallel to and opposite to one surface of the shared substrate, and is connected with the shared substrate through a plurality of first diagonal rods; the first inclined rods are arranged around the central line of the unit cell at equal angles, each first inclined rod forms an included angle with the normal line of the common substrate, one end of each first inclined rod is connected with one surface of the first substrate facing the common substrate, and the other end of each first inclined rod is connected with one surface of the common substrate facing the first substrate; the second substrate and the first substrate are in mirror symmetry relative to the common substrate, the second substrate is connected with the common substrate through a plurality of second inclined rods, and the second inclined rods and the first inclined rods are in mirror symmetry relative to the common substrate, so that the common substrate has a torsion direction when the unit cell is pressed. The common substrate is connected with the common substrate of the adjacent unit cells into a piece through a ligament, the ligament is tangential to the torsion direction of the common substrate and is arranged back to the torsion direction of the common substrate, one end of the ligament is connected with the common substrate, and the other end of the ligament is connected with the common substrate of the adjacent unit cells.
The mirror symmetry of the second substrate and the first substrate with respect to the common substrate means that the second substrate and the first substrate are identical in shape and size, the second substrate is parallel to and opposite to the other surface of the common substrate, and the distance between the second substrate and the common substrate is equal to the distance between the first substrate and the common substrate. The mirror symmetry of the second diagonal rods and the first diagonal rods relative to the common substrate means that the second diagonal rods are identical in shape, equal in size and consistent in quantity with the first diagonal rods, the second diagonal rods are distributed around the central line of the unit cell at equal angles, an included angle with the normal line of the common substrate is formed between each second diagonal rod and the second diagonal rod, the included angle is equal to the included angle between the first diagonal rod and the normal line of the common substrate, one end of each second diagonal rod is connected with one surface of the second substrate facing the common substrate, and the other end of each second diagonal rod is connected with one surface of the common substrate facing the second substrate.
In the above super structure, the first substrate, the first diagonal rod and the common substrate form a three-dimensional chiral diagonal rod pressing and twisting metamaterial cell, the second substrate, the second diagonal rod and the common substrate also form a three-dimensional chiral diagonal rod pressing and twisting metamaterial cell, the two three-dimensional chiral diagonal rod pressing and twisting metamaterial cells are in mirror symmetry, the symmetry plane is the common substrate, and the two three-dimensional chiral diagonal rod pressing and twisting metamaterial cell and the common substrate form a double-layer pressing and twisting super structure. In the stress mode, the ligament stress stretching ratio of the super structure is higher than the bending ratio, the diagonal rod stress compression ratio is higher than the bending ratio, and the ligament stress bending ratio of the multi-layer (more than three layers) compression-torsion super structure is higher than the stretching ratio, and the diagonal rod stress bending ratio is higher than the compression ratio. In short, the stress mode of the super structure takes ligament axial force stretching as a main factor, so that the overall rigidity and strength are higher than those of the multilayer compression-torsion super structure. Compared with the existing light high-strength structures, the super structure has much smaller relative density, and has great development potential and advantages in the aspects of shock absorption, energy absorption, high-strength structural design and the like.
The common substrate, the first substrate, and the second substrate may be configured as a circular ring, a regular polygonal ring, or other shaped ring, and may also be configured as a circular plate, a regular polygonal plate, or other shaped plate. The shapes of the common substrate, the first substrate and the second substrate do not have any influence on the super structure in terms of mechanical properties. In terms of structural density, configuring at least one of the common substrate, the first substrate, and the second substrate as a ring may reduce the overall density of the super-structure, wherein the first substrate and the second substrate are most preferably polygonal rings, and the number of sides of the polygonal rings is based on the number of diagonal rods (first diagonal rods/second diagonal rods), and the diagonal rods are preferably connected to the vertices of the polygonal rings. To facilitate the connection of the diagonal rod and the ligament, the common base is most preferably a circular ring.
Preferably, the first substrates of all unit cells are provided as one body and the second substrates of all unit cells are provided as one body, i.e. all unit cells share one first substrate and one second substrate. When analyzing the equivalent stress-strain curve of the superstructure, we found that when all the first substrates are joined together by the adhesive and the plate, and all the second substrates are joined together by the adhesive and the plate, the equivalent elastic modulus and strength limit of the superstructure are higher, which is beneficial for further enhancing the stiffness and strength of the superstructure.
Preferably, the first substrates of each unit cell are respectively arranged in isolation, and the second substrates of each unit cell are respectively arranged in isolation. The term "isolated arrangement" refers to that the first substrate/second substrate of each unit cell is not connected to the first substrate/second substrate of an adjacent unit cell in any way, and remains relatively independent. When analyzing the equivalent stress-strain curve of the superstructure, we have also found that when there is rotational freedom between the first substrate and the second substrate, a plateau section is present after the superstructure reaches the strength limit, which contributes to the energy absorption, which contributes to the improved damping capacity of the superstructure.
Each first substrate may be connected to the common substrate by three or more first diagonal bars, preferably by four or more first diagonal bars, more preferably by six or more first diagonal bars. Accordingly, each of the second substrates may be connected to the common substrate by three or more second diagonal bars, preferably by four or more second diagonal bars, and more preferably by six or more second diagonal bars.
The connection point of the first diagonal rod and the first substrate, the connection point of the first diagonal rod and the shared substrate, the connection point of the second diagonal rod and the second substrate, the connection point of the second diagonal rod and the shared substrate and the connection point of the ligament and the shared substrate are all distributed on the same right cylindrical surface taking the central line of the unit cell as an axis. Therefore, the connection points of the first diagonal rods and the first substrate are uniformly distributed on the intersecting line of the right circular cylindrical surface and the first substrate, the connection points of the first diagonal rods and the common substrate are uniformly distributed on the intersecting line of the right circular cylindrical surface and the common substrate, the connection points of the second diagonal rods and the second substrate are uniformly distributed on the intersecting line of the right circular cylindrical surface and the second substrate, the connection points of the second diagonal rods and the common substrate are uniformly distributed on the intersecting line of the right circular cylindrical surface and the common substrate, the connection points of the ligaments and the common substrate are the tangent points of the intersecting line of the ligaments and the right circular cylindrical surface and the common substrate.
The first diagonal and the second diagonal may be collectively referred to as diagonal, and they may be configured as hollow struts having a circular, regular polygonal or other annular cross-section, or as solid struts having a circular, regular polygonal or other shape cross-section. The configuration of the diagonal rods as hollow cylinders reduces the overall density of the superstructure, most preferably as hollow struts with circular cross-sections.
At different inclined angles theta 2 When numerical simulation is performed on the unit cell model of (a): θ 2 The smaller the superstructure the greater the equivalent modulus of elasticity and strength limit, and therefore the preferred angle θ between the diagonal rods and the common substrate normal 2 ∈(0,40]More preferably θ 2 ∈(0,30]More preferably θ 2 ∈(0,20]。
In different diagonal rod lengths L 2 When numerical simulation is performed on the unit cell model of (a): l (L) 2 The larger the superstructure the larger the equivalent elastic modulus and strength limit, and therefore the length (L 2 ) Radius from right cylinder ((D) 1 +d 1 ) The ratio of/2) is preferably 0.95 or more, more preferably 1.05 or more, and still more preferably 1.14 or more.
In the center distance 2.a between cells of different adjacent units 1 When numerical simulation is performed on the unit cell model of (a): a, a 1 The smaller the superstructure, the greater the equivalent elastic modulus and strength limit, and therefore the center-to-center distance (2 a 1 ) Radius from right cylinder ((D) 1 +d 1 ) The ratio of/2) is preferably 1.90 or less, more preferably 1.71 or less, and still more preferably 1.52 or less.
Wherein, the increase of the length of the diagonal rod or the decrease of the inclination angle of the diagonal rod can reduce the relative density of the super structure, and improve the strength and rigidity of the structure while reducing the relative density of the structure, which is significant for the light high-strength structure and the target of the material which are required by us.
The unit cells in the super structure can be arranged in a square array or in a triangular array. When the unit cells are arranged in a square array, the ligaments can be configured to be 2-4, and the specific number is determined by the position of the unit cells in the superstructure. When a unit cell is positioned at the corner of the superstructure, the unit cell is semi-surrounded by two adjacent unit cells, and the ligament can be configured as 2 ligaments; when a unit cell is at the edge of the superstructure, the unit cell is semi-surrounded by three adjacent unit cells, and the ligament can be configured to be 3; when a unit cell is inside the superstructure, the unit cell is fully surrounded by four adjacent unit cells, and the ligament may be configured to be 4.
When the unit cells are arranged in a triangular array, the ligaments can be configured to be 2-6, with the specific number being determined by the location of the unit cells in the superstructure. When a unit cell is positioned at the corner of the superstructure, the unit cell is semi-surrounded by two or three adjacent unit cells, and the ligament can be configured to be 2 or 3; when a unit cell is at the edge of the superstructure, the unit cell is semi-surrounded by four adjacent unit cells, and the ligament can be configured to be 4; when a unit cell is inside the superstructure, the unit cell is fully surrounded by six adjacent unit cells, and the ligament may be configured to be 6. The ligament may be configured as a band of rectangular cross-section having a thickness comparable to the thickness of the common substrate.
Compared with the prior art, the scheme has the following beneficial effects:
the super structure can still maintain excellent mechanical properties under quite low relative density, and fully embody the excellent performance and wide application prospect of the structural design. By fully utilizing the compression-torsion coupling effect, a novel method is provided for improving the strength and rigidity of the diagonal chiral structure.
Drawings
The drawings are for illustrative purposes only and are not to be construed as limiting the present solution; for better illustration of the present solution, some parts of the figures may be omitted, enlarged or reduced, and do not represent the dimensions of the actual product; it will be appreciated by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
Fig. 1 is a schematic diagram of a geometric model. Wherein (a) is a three-dimensional schematic of the superstructure, (b) is a unit cell, (c) is a representative cell, (d) is a top view of the superstructure, and (e) is a top view of the unit cell.
FIGS. 2 a-2 c are quasi-static compression experiments of three-dimensional superstructures. Wherein fig. 2a is a 3D printed sample, fig. 2b is a detail of a specimen sample and a plate, and fig. 2c is a compression experiment.
Figures 3 a-3 c are tests of the mechanical properties of 3D printed substrates. Wherein fig. 3a is the geometry of the tensile specimen, fig. 3b is the tensile specimen, and fig. 3c is the stress-strain curve of the substrate stretching.
Fig. 4a to 4b are schematic diagrams of models in numerical simulation. Wherein fig. 4a is a model of a numerical simulation versus an experiment, and fig. 4b is a model of a unit cell in a numerical simulation.
Fig. 5 a-5 b are comparisons of numerical simulations and experiments. Wherein fig. 5a is an equivalent stress-strain curve and fig. 5b is a picture of sample 2 after the end of the experiment.
Fig. 6a to 6c are the results of the parametric analysis. Wherein FIG. 6a is a different a 1 The results of the lower numerical simulation are shown in FIG. 6b, which shows a different L 2 The result of the lower numerical simulation is shown in FIG. 6c, which shows the difference θ 2 Results of the lower numerical simulation。
FIGS. 7 a-7 b are evaluations of mechanical properties of the superstructures. Wherein fig. 7a is the normalized intensity limit and fig. 7b is the normalized elastic modulus.
Reference numerals illustrate: the first base 110, the first diagonal 120, the second base 210, the second diagonal 220, the common base 310, and the ligament 330.
Detailed Description
In order to better understand the present solution, a further detailed description of the present solution will be provided below in conjunction with specific embodiments.
The unit cell of the super structure is obtained by mirror symmetry of two three-dimensional chiral diagonal press-twisting metamaterial cells, as shown in figure 1 (b), wherein the cross section of the diagonal is a circular ring with the outer diameter D and the inner diameter D, and the length of the diagonal is L 2 The included angle between the inclined rod and the axis of the circular ring is theta 2 All the endpoints of the diagonal rods are fixed on the plane of the circular rings, and the distance h=L between two adjacent layers of circular rings 2 *cosθ 2 The method comprises the steps of carrying out a first treatment on the surface of the The ring of the middle layer is connected with the chiral ligament, and the outer radius of the ring is D 1 An inner radius d 1 The thickness of the circular ring is 2.t, the ligament cross section is a rectangle with the width b and the thickness of 2.t, and the included angle between the connecting line of the centers of the ligament and the adjacent circular ring is theta 1 . From the symmetry of the structure, a schematic diagram of a representative cell can be obtained as shown in FIG. 1 (c), in which the thickness of the ligaments and the upper ring in the axial direction is half, the height H=h+3.t of the representative cell, the relative density of unit cells
The unit cells are periodically arranged to obtain a three-dimensional super structure as shown in the figure 1 (a), and the distance between the centers of adjacent circular rings of the same layer is 2.a 1 The ligament has the length ofTop views of the superstructure and unit cell are shown in fig. 1 (d) and (e). These ringsIt is entirely possible to replace it with rings or plates of other shape and aperture, and this replacement is such that it does not have any effect on the mechanical properties of the superstructure.
The super structure provided by the invention is used as a core layer of a sandwich structure in engineering application, when the core layer is loaded along the axial direction of the circular rings, the rotation degrees of freedom of the uppermost circular ring and the lowermost circular ring of the core layer are restrained, the circular rings of the second layer can rotate due to the existence of the local compression-torsion coupling effect, the existence of the ligaments is equivalent to the effect of obstructing the rotation of the circular rings of the second layer, the stress state of the diagonal rod is changed, and the strength and the rigidity of the structure are improved.
A local coordinate system O-x 'y' is established in the ligament and ring plane, where O is the location of the centroid of the ring, as shown in fig. 1 (e). The position of the ligament midpoint in the x '-y' plane is constant during deformation, so the periodic boundary conditions that the ligament midpoint should meet:
where u and v represent the displacement of points on the plane along the x 'and y' directions, respectively.
The 3D printing method of SLA is adopted, a photosensitive cured resin is used as a matrix material, and the super structure with enhanced strength and rigidity is prepared, as shown in fig. 2a, the model of the 3D printer is ZRapid SI600, and the manufacturer is ZRapid Technology. The overall dimension of the model is 160mm x 75mm, and the center-to-center distance between adjacent circular rings in the same layer is 2.a 1 51.2mm, ligament cross-section dimension b·t=3.2 mm×1.6mm, annular outer diameter D 1 =38.4mm, inner diameter d 1 28.8mm, thickness of the ring 2·t=3.2 mm; the inclined rod is a solid round rod with the diameter of 4mm, and the length of the inclined rod is L 2 The included angle between the inclined rod and the axis of the circular ring is theta 2 =30°. The uppermost and lowermost rings have hollow holes, and one side of each flat plate has corresponding protruding parts, as shown in figure 2b, which are shaped like artificial "buckles" and are formed byThe deformation of the super structure is conveniently and intuitively known and analyzed after the experiment. Typical substrate tensile specimens and their geometry are shown in FIG. 3a, three resulting tensile specimens are shown in FIG. 3b, and the stress-strain curves for substrate stretching are shown in FIG. 3 c. The displacement loading speed in the quasi-static experiment is 0.45mm/min.
The structure shown in fig. 2a was numerically simulated using large-scale general-purpose commercial finite element software LS-DYNA, the geometric dimensions of the model were consistent with those of the experimental samples, and a specific model schematic is shown in fig. 4 a. To simulate the more general conditions, we also performed numerical simulation on the unit cells shown in fig. 1b for the model with more lateral cell numbers, and a specific model diagram is shown in fig. 4 b. Simplifying engineering stress-strain curve obtained by stretching base material into ideal elastic plastic material model as the base material of super structure in numerical simulation, wherein the slope of linear stage is E s =1.2gpa, plastic yield strength Y s =30.5 MPa, poisson ratio μ s =0.35, density ρ s ＝1200kg/m 3 The breaking strain was 10%. Both models were grid-partitioned using Solid 185 units.
The upper and lower plates are set as rigid bodies, and the boundary conditions in the numerical simulation are as follows: the lower plate is completely fixed, and the upper plate is provided with a constant speed to compress the test piece; the circular rings of the upper plate, the first layer and the third layer have only axial degrees of freedom, and the degrees of freedom in other directions are all restrained; in addition, the unit cell needs to apply a corresponding periodic boundary condition, namely formula (2-1), to the node on the ligament midpoint cross section.
The equivalent stress-strain curve of the experimental sample is then analyzed. As shown in fig. 5a, the core layers of sample 1 and sample 2 are directly connected to the upper and lower panels by "snaps", and sample 3 is connected between the core layer and the panel with additional epoxy adhesive, and the comparison of equivalent parameters and numerical simulations of the structures obtained by the experimental samples are shown in table 1. The equivalent elastic modulus of sample 1 and sample 2 at the beginning of the experiment is still relatively low, since the "snap" fails to immediately constrain the rotational degrees of freedom of the uppermost and lowermost rings of the core at the beginning of compression, while at the same time being strongThe degree limit is also smaller than that of sample 3 and numerical simulations because the compression of the initial stages of the experiment results in a change in structural dimensions (e.g., θ 2 Smaller than the original model); when the core is glued to the panel, the curve obtained by the sample 3 and numerical simulation is substantially fitted, the error of the equivalent elastic modulus is only 7.7% and the error on the intensity limit is only 10.5%. In the deformation mode, the situation that the sample 1 and the sample 2 are broken one by one in the experiment, fig. 5b shows a graph of the result of the breaking of the ligament of the resin sample 2 after the experiment, and after the sample 1 and the sample 2 reach the strength limit, a platform section which is different from the curve trend of numerical simulation and is beneficial to energy absorption appears; whereas sample 3 is the substantial coincidence of the curves in numerical modeling, the ligaments break almost simultaneously.
Table 1 comparison of experimental and numerical simulation results
In order to obtain a superstructure with more excellent mechanical properties, we next discuss structural parameters such as the distance a between the ligament midpoint and the centroid of the torus 1 Length L of diagonal bar 2 And an inclination angle theta 2 The influence on the mechanical property of the unit cell is analyzed and discussed, and the result of numerical simulation of the unit cell is analyzed and discussed.
We respectively design seven groups of different a 1 Five different diagonal lengths L 2 And four different diagonal tilt angles theta 2 Performing numerical simulation on the unit cell model: a, a 1 15mm, 16mm, 17mm, 18mm, 20mm, 22mm and 24mm respectively; diagonal length L 2 16mm, 18mm, 20mm, 22mm and 24mm respectively; inclined angle theta of inclined rod 2 20 °, 30 °, 40 ° and 50 °, respectively. Numerical simulation pairs such as shown in fig. 6 a-6 c, the red data points represent the equivalent elastic modulus and the black data points represent the intensity limit. Along with the circle center distance 2.a of the adjacent circles on the same layer 1 The equivalent elastic modulus and strength limit of the superstructure are increasing; along with the length L of the diagonal rod 2 Is increased in strength and rigidity of unit cellTo an improvement; with theta 2 The equivalent elastic modulus and strength limit of the structure are increasing. It is important to note that as the length of the diagonal is increased or the angle of inclination of the diagonal is decreased, the relative density of the structure is decreased and the strength and stiffness of the structure are increased while the relative density of the structure is decreased, which is significant for the light weight high strength structure and material goals we are seeking.
Before evaluating the mechanical properties of the superstructure presented herein, two performance assessment indicators were defined: normalized strength limit NS (Normalized strength) and normalized equivalent elastic modulus NM (Normalized modulus), each defined as follows:
wherein sigma ys And E is s The yield strength and the elastic modulus, ρ, of the substrate, respectively r For the relative density of the structure,for the strength limit of the structure,/->Is the equivalent elastic modulus of the structure. After parameter optimization of the superstructure herein by finite elements, the following dimensional parameters are used: a, a 1 ＝18mm，b＝2mm，t＝1mm，L 2 ＝24mm，θ 2 ＝20°，D＝2.5mm，d＝0mm，D 1 ＝24mm，d 1 ＝18mm，a 3 =10.5 mm. The comparison between the mechanical properties and those of some light high strength structures at the present stage is shown in fig. 7 a-7 b. The model employed for the superstructures herein in FIGS. 7 a-7 b is superior to these lightweight high strength structures at the present stage, except that they are lower in normalized equivalent elastic modulus than the off-plane loaded regular hexagonal honeycomb of equal thickness; at the normalized intensity limit, although higher in value than we propose a superstructure, at NS (Normalized strength), corresponds toThe relative density is also much larger than that of the super structure, the superiority and wide application prospect of the reinforcement mechanism are fully reflected, the super structure has great development potential and advantages in the aspects of shock absorption, energy absorption, high-strength structural design and the like, and the super structure is even superior to an equal-thickness regular hexagonal honeycomb loaded outside the plane in the aspect of strength limit.
Aiming at a novel diagonal rod compression-torsion coupling mechanical metamaterial, a superstructure with enhanced rigidity and strength is innovatively provided by combining 2D four-ligament chiral honeycomb. The structure is prepared through a 3D printing technology, experimental analysis and verification are carried out, and the feasibility and effectiveness of the method are verified through experimental results; the influence of the geometric parameters of the super structure on the strength and the rigidity is researched based on the numerical simulation, and the result shows that the strength and the rigidity of the structure can be improved while the relative density of the structure is reduced by reducing the inclination angle of the inclined rod or increasing the length of the inclined rod; compared with some lattice porous with excellent mechanical properties at present, for example, body centered cubic lattice (BCC), face centered cubic lattice (FCC), octahedral truss structure (Octet) and out-of-plane loaded regular hexagonal honeycomb are used for evaluating the mechanical properties of the super structure proposed herein, and the result shows that the super structure can still maintain excellent mechanical properties under quite low relative density, thereby fully embodying the excellent performance and wide application prospect of the structural design. The work provides a new method for improving the strength and the rigidity of the chiral structure of the diagonal rod by fully utilizing the compression-torsion coupling effect.
It is apparent that the above examples of the present solution are merely examples for clearly illustrating the present solution and are not limiting of the embodiments of the present solution. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present solution should be included in the protection scope of the present solution claims.
Claims (10)
1. A three-dimensional mechanical superstructure comprising a plurality of unit cells arranged in an array, wherein each unit cell comprises a common substrate, a first substrate, a second substrate, a first diagonal, a second diagonal, and ligaments, having a centerline perpendicular to the common substrate;
the first substrate is parallel to and opposite to one surface of the shared substrate, and is connected with the shared substrate through a plurality of first diagonal rods; the first inclined rods are arranged around the central line of the unit cell at equal angles, each first inclined rod forms an included angle with the normal line of the common substrate, one end of each first inclined rod is connected with one surface of the first substrate facing the common substrate, and the other end of each first inclined rod is connected with one surface of the common substrate facing the first substrate; the second substrate and the first substrate are in mirror symmetry relative to the shared substrate, the shared substrate is connected through a plurality of second inclined rods, and the second inclined rods and the first inclined rods are in mirror symmetry relative to the shared substrate, so that the shared substrate has a torsion direction when the unit cell is pressed;
the common substrate is connected with the common substrate of the adjacent unit cells into a piece through a ligament, the ligament is tangential to the torsion direction of the common substrate and is arranged back to the torsion direction of the common substrate, one end of the ligament is connected with the common substrate, and the other end of the ligament is connected with the common substrate of the adjacent unit cells.
2. The three-dimensional mechanical superstructure according to claim 1, wherein the first substrates of all unit cells are provided as one body and the second substrates of all unit cells are provided as one body.
3. The three-dimensional mechanical superstructure according to claim 1, wherein the first substrates of each unit cell are disposed in isolation, and the second substrates of each unit cell are disposed in isolation.
4. The three-dimensional mechanical superstructure according to claim 1, wherein the first/second diagonal bars form an angle θ with the common substrate normal 2 ∈(0,40]。
5. According to claim 4The three-dimensional mechanical superstructure is characterized in that the included angle theta between the first inclined rod and the second inclined rod and the normal line of the shared substrate 2 ∈(0,30]。
6. The three-dimensional mechanical superstructure according to claim 1, wherein the first diagonal and the first base connection point, the first diagonal and the common base connection point, the second diagonal and the second base connection point, the second diagonal and the common base connection point, and the ligament and the common base connection point are all distributed on the same right cylindrical surface with the unit cell center line as the axis.
7. The three-dimensional mechanical superstructure according to claim 6, wherein the ratio of the length of the first/second diagonal rods to the radius of the right cylinder is above 0.95.
8. The three-dimensional mechanical superstructure according to claim 7, wherein the ratio of the length of the first/second diagonal rods to the radius of the right cylinder is above 1.05.
9. The three-dimensional mechanical superstructure according to claim 6, wherein the ratio of the center-to-center distance of two adjacent unit cells to the radius of a right circular cylinder is 1.90 or less.
10. The three-dimensional mechanical superstructure according to claim 6, wherein the ratio of the center-to-center distance of two adjacent unit cells to the radius of a right circular cylinder is 1.71 or less.
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