CN112836250B - Dot matrix structural design for buckling driving large-angle torsion - Google Patents
Dot matrix structural design for buckling driving large-angle torsion Download PDFInfo
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Abstract
The invention provides a dot matrix structural design for buckling driving large-angle torsion, which comprises an X-shaped rod piece formed by two orthogonal connected inclined rods and a penetrating vertical rod which vertically penetrates through the inclined rods at two sides of an intersection point of the X-shaped rod piece respectively, wherein the height of the penetrating vertical rod is consistent with that of the X-shaped rod piece and forms an integral structure with the inclined rods, and two ends of the penetrating vertical rod penetrate through the inclined rods and are the same as the height of the X-shaped rod piece; the lattice structure consists of two lattice bars connected in quadrature and a panel for restraining the upper and lower ends of the lattice bars. The invention realizes the instantaneous large-angle torsion of the structure by utilizing the nonlinear buckling deformation of the rod piece, and the maximum instantaneous torsion angle of the unit axial deformation reaches 150 degrees/percent which is far higher than 2 degrees/percent in the compressive torsion chiral metamaterial; therefore, the instantaneous large-angle torsion induced by the nonlinear buckling deformation further expands the application range of the compression-torsion metamaterial.
Description
Technical Field
The invention relates to the field of lattice energy absorption structures, in particular to a lattice structure design for bending and driving large-angle torsion when external force is applied.
Background
The compression torsion mechanical metamaterial is a hot spot of the current mechanical metamaterial research, and is originally proposed in 2017 by Wegener team of Karl Lu Er institute of technology, the linear elastic deformation in a unit rod is converted into macroscopic torsion deformation through a three-dimensional chiral unit structure in the metamaterial, the constraint of Hooke's law in the traditional homogeneous material is broken, and higher design freedom degree is obtained.
The linear deformation of the rod in the chiral structure is converted into the torsional deformation of the structure to obtain a steadily increasing torsional angle, but the torsional angle driven by the linear elastic deformation of the rod is usually smaller, the maximum torsional angle obtained in the unit axial strain in the study is only 2 degrees/percent, and the design and preparation of the chiral structure are complex. Buckling deformation of a rod piece is used as a common nonlinear deformation characteristic and is often used for designing a multistable mechanical metamaterial, and researches for realizing instantaneous large-angle torsion by utilizing the nonlinear buckling deformation of a unit rod piece are recently reported, so that the application range of the compressive torsion metamaterial is further widened compared with the stable progressive small-angle torsion in a three-dimensional chiral metamaterial.
Disclosure of Invention
The invention aims to provide a lattice structure design for bending and driving large-angle torsion when external force is applied.
Specifically, the invention provides a lattice structure design for buckling driving large-angle torsion, which comprises the following steps:
the lattice rod piece comprises an X-shaped rod piece formed by two orthogonal connected inclined rods and a penetrating vertical rod which vertically penetrates through the inclined rods at two sides of the intersection point of the X-shaped rod piece respectively, the height of the penetrating vertical rod is consistent with that of the X-shaped rod piece and forms an integral structure with the inclined rods, and two ends of the penetrating vertical rod penetrate through the inclined rods and are identical with the height of the X-shaped rod piece;
the lattice structure consists of two lattice bars connected in quadrature and a panel for restraining the upper and lower ends of the lattice bars.
Compared with the three-dimensional chiral compression torsion metamaterial, the linear elastic load in the rod piece is converted into the torsion deformation of the macroscopic structure, the disclosed compression torsion point array structure realizes the instantaneous large-angle torsion of the structure by utilizing the nonlinear buckling deformation of the rod piece, and the maximum instantaneous torsion angle of unit axial deformation reaches 150 degrees/percent which is far higher than 2 degrees/percent in the compression torsion chiral metamaterial. The application range of the compression-torsion metamaterial is further expanded by the instantaneous large-angle torsion induced by nonlinear buckling deformation.
Drawings
FIG. 1 is a schematic diagram of a lattice structure according to an embodiment of the present invention; wherein (a) is a perspective view of the lattice structure and (b) is a front view of the lattice structure;
FIG. 2 is a diagram illustrating a distortion state of a lattice structure according to an embodiment of the present invention; wherein, (a) is a schematic diagram of a distortion state of the lattice structure, and (b) is a top view of (a);
FIG. 3 is a schematic view of a lattice bar structure according to an embodiment of the present invention;
FIG. 4 is a torque force diagram of a lattice structure;
FIG. 5 is a schematic illustration of a interlocking structure of a lattice structure;
FIG. 6 is a compressive torsional deformation of a lattice structure showing the deformation of the rod member at four torsional angles, wherein (a) is a top view and a front view of the lattice torsion under numerical simulation conditions, and (b) is a torsional deformation under experimental conditions;
FIG. 7 is a graph of load displacement and torsion angle displacement of the lattice structure of FIG. 6 during torsional deformation;
FIG. 8 is a schematic view of the arrangement of defects in a directional twisted lattice structure in accordance with one embodiment of the present invention;
fig. 9 is a graph of compressive stress and torsion angle versus compressive strain for both oriented and non-oriented twisted lattice structures.
Detailed Description
Specific structures and implementation procedures of the present solution are described in detail below through specific embodiments and drawings.
As shown in fig. 1 and 3, in one embodiment of the present invention, a lattice structure design for buckling driving a large angle torsion is disclosed, comprising: lattice bars and lattice structures.
The lattice rod piece comprises an X-shaped rod piece 1 formed by two orthogonal connection inclined rods 11 and a penetrating vertical rod 2 which vertically penetrates through the inclined rods on two sides of the intersection point of the cross rod 1, wherein the height of the penetrating vertical rod 2 is consistent with that of the X-shaped rod piece 1, and the penetrating vertical rod and the inclined rods 11 form an integral structure. When the X-shaped rod piece 1 is installed, the same end of the two inclined rods 11 contacts the ground to form a 45-degree inclined placing state, and the height of the penetrating vertical rod 2 is the same as that of the inclined X-shaped rod piece 1 and is perpendicular to the ground. In this embodiment, the cross sections of the inclined rod 11 and the penetrating vertical rod 2 are square, and the diameters of the inclined rod 11 and the penetrating vertical rod 2 are identical, that is, the shape and the size of the inclined rod 11 and the penetrating vertical rod 2 are identical.
The lattice structure is formed by orthogonally connecting two lattice bars 1 through intersecting points, and the two lattice bars 1 are vertically connected, so that the connected diagonal bars 11 are mutually spaced by 90 degrees in the circumferential range.
When in use, the lattice structures can be horizontally connected with each other through the end parts of the inclined rods 11; the connected lattice structure can be a frame which extends towards the periphery infinitely in the horizontal direction based on the single-point lattice structure.
The panel comprises an upper panel and a lower panel which are covered and fixed on the upper surface and the lower surface of the lattice structure; the concrete connection mode can be to fixedly connect the four end points of the inclined rod 11 and the two ends of the penetrating vertical rod 2. The panel may be any material used for devices having a lattice structure, such as a metal plate, a plastic plate, etc., and in this embodiment, a stainless steel plate is used.
In the lattice structure in this embodiment, the central node thereof rotates during the compression process, and the rotation axis forms a certain angle with the Z axis. In order to enable the plane of the panel of the lattice structure to rotate around the Z axis in the compression process, the rotating shaft of the central node is required to be overlapped with the Z axis. Therefore, in order to make the lattice structure rotate around the Z axis in the compression process, the penetrating vertical rod 12 is added on the X-shaped rod piece 1 along the Z axis direction, and the constraint capacity of the inclined rod 11 on the buckling deformation in the surface of the penetrating vertical rod 12 is higher than the capacity of the inclined rod 11 on the deformation out of the surface of the penetrating vertical rod 12. Therefore, the through vertical rods 12 of the lattice structure are all deformed in out-of-plane buckling during the compression process, and when buckling directions of the through vertical rods 12 of the lattice structure are consistent, the lattice structure has the minimum critical buckling load, and the panel has the torsional driving force provided by the through vertical rods 12.
As shown in fig. 2, the left side is the buckling deformation characteristic of the lattice structure under the out-of-plane (Z-axis) compression load, the right side gives out the out-of-plane compression numerical calculation result of the upper and lower panels under the constraint condition of the fixed end, and the buckling deformation is anticlockwise under the constraint action of the diagonal rod 11 and is consistent with the design.
Compared with the three-dimensional chiral compression torsion metamaterial, the compression torsion lattice structure provided by the embodiment converts linear elastic load in the rod piece into torsion deformation of a macroscopic structure, achieves instantaneous large-angle torsion of the structure by using nonlinear buckling deformation of the rod piece, and achieves the maximum instantaneous torsion angle per unit axial deformation of 150 degrees/percent which is far higher than 2 degrees/percent in the compression torsion chiral metamaterial; therefore, the instantaneous large-angle torsion induced by the nonlinear buckling deformation further expands the application range of the compression-torsion metamaterial.
In the foregoing description, the lattice structure is the object of description, but in practical application, the lattice structure forms of mutual connection are all present, and the whole stress form and reflection are consistent with the lattice structure.
In order to improve the firmness of the lattice structure, the connection points of the lattice bars and the panels can be fixed by welding.
When the through vertical rod 12 and the inclined rod 11 are intersected at the end part, the inclined rod 11 does not play any constraint role on the buckling direction of the through vertical rod 12; when the distance from the penetrating vertical rod 12 to the central connection point is too small, the torque generated after the buckling deformation of the penetrating vertical rod 12 is too small, and the continuous torsion of the lattice structure cannot be driven, so that in order to ensure the torsion of the lattice structure in the compression process, the connection position of the penetrating vertical rod 12 and the inclined rod 11 needs to satisfy the following constraint conditions:
the length of the penetrating vertical rod 12 between the two inclined rods 11 on the same side needs to be smaller than the height between the ends of the two inclined rods 11 on the same side, and at the same time, needs to be longer than the length of the penetrating vertical rod 12 exposed out of the inclined rods 11.
See FIG. 3, i.e., l 2 <l 1 <H。
As shown in fig. 4, the torque of the lattice structure is provided by a horizontal component during buckling of the through-going vertical rod 12, and the torque is as follows: m=4df T 。
For convenient connection, in two intersecting lattice bars, the intersection point of one lattice bar is provided with an inward concave clamping groove with an opening facing upwards, the intersection point of the other lattice bar is provided with an inward concave clamping groove with an opening facing downwards, and the two lattice bars are connected after being clamped with each other through the clamping groove. In actual operation, the opening directions are not distinguished, and only the connected lattice rod pieces are needed to be turned over and then inserted into the other lattice rod pieces.
In addition, be provided with the extension section that makes things convenient for the horizontal direction to connect at the tip of diagonal bar 11, the extension section is outside extension of level under the state of lattice member to make things convenient for adjacent lattice member interconnect, in addition, the extension section can also play the effect of increasing with the fixed strength between the panel.
In one embodiment of the present invention, for convenience in manufacturing the lattice bars, the lattice bars may be directly cut by stainless steel plates, that is, a row of structures formed by connecting the lattice bars to each other through the ends of the diagonal bars 11 is directly cut, and then spliced into a lattice structure having a certain area. The mode can reduce the manufacturing difficulty of the lattice rod piece, improve the installation efficiency and ensure the strength.
The lattice structure design effect is described below in connection with specific test examples.
The torsion observation in the compression process of the press torsion point array structure is realized, the rotation constraint of the panel is required to be released, and the rotation constraint of the panel is released once in numerical simulation. In the experiment, in order to ensure the free rotation of the lattice structure, a set of loading device is designed by means of a thrust bearing, so that the lattice structure is fixed on the loading device, and the relative rotation of the upper panel and the lower panel is realized by rotation, so that the middle lattice structure is in a distorted state.
As shown in fig. 5, the lattice bars in the lattice structure are printed by using the polymet 3D printing technology, and then the lattice bars are assembled into the lattice structure by using the interlocking assembly mode, so that the lattice bars are not broken due to large deformation in the loading process, wherein the height h=35 mm of the lattice structure, the diagonal bars and the penetrating vertical bars in all the lattice bars are square sections, the thickness is t=1.75 mm, the inclination angle ω=45°, and the distance d=5.5 mm between the penetrating vertical bars and the central node.
FIG. 6 shows the results of out-of-plane compression loading experiments and numerical simulations of the compression torsion lattice structure under one-sided boundary free rotation conditions. The numerical simulation is quasi-static loading, the unit is selected as tetrahedron unit, displacement loading is adopted in the experiment, and the loading speed is 1.5mm/min. FIG. 6 (a) is a plan view and an elevation view of the bar deformation in the torsion angle states of 0, 30, 60 and 90 for the compression torsion point array structure obtained by numerical simulation; fig. 6 (b) is an experimental result of deformation of the lattice bar in four torsion angle states. From the figures, it can be seen that the deformation torsion results obtained by the experiment and numerical simulation are consistent.
Fig. 7 shows a compressive stress-strain curve and a torsion angle-strain curve of a compressive torsion lattice structure, from which it can be seen that after the stress reaches a peak value of 1.13MPa, the stress rapidly develops a post-peak weakening phenomenon due to buckling deformation of the lattice rod, while the torsion angle of the lattice structure increases linearly and slowly before the stress reaches the peak value, when the load reaches the peak value, the torsion angle is only 4 °, and the torsion angle of the lattice structure increases rapidly with buckling deformation of the lattice rod, and on the premise that the strain increases by 0.14%, the torsion angle increases by 21 °, the torsion angle of the instantaneous unit axial strain reaches 150 °/%, which is far higher than 2 °/% in the compressive torsion metamaterial, and in this process, the stress value decreases to 71% of the peak stress. The torsion angle speed then starts to taper, and when the compression displacement reaches 0.145, the torsion angle has reached 100 °, at which point the stress value is only 32% of the peak stress.
In one embodiment of the invention, the two ends of the diagonal rod and the through vertical rod are respectively provided with a fixing section extending towards the vertical direction, namely extending towards the upper panel and the lower panel; and mounting holes corresponding to the positions of the fixing sections are respectively formed in the upper panel and the lower panel, and the lattice structure is welded and fixed after being inserted into the corresponding mounting holes in the panels through the fixing sections.
Furthermore, the mounting hole and all the inclined rods and the fixed sections penetrating through the vertical rods in the lattice structure are uniformly offset by a defect amount in the clockwise or anticlockwise direction, so that the lattice rod pieces in the lattice structure realize uniform directional torsion when the lattice structure is subjected to external pressure.
Because the torsion direction of the buckling lattice structure formed by the lattice bars is not deterministic, in order to realize the directional torsion of the buckling lattice structure, the buckling lattice structure can be provided with a response defect to induce the directional rotation of the lattice structure. For the interlocking assembled lattice structure, fig. 8 shows an arrangement of initial torsion defects, i.e. four holes in the inner part of a side panel are offset by a small amount in the counterclockwise direction (or clockwise direction), forming a defect of counterclockwise rotation. After the lattice rod piece is inserted into the panel, corresponding assembly defects are formed on the lattice rod piece, and the lattice structure is induced to rotate anticlockwise under the action of compression load. In this scheme, the offset is set to t/2.
Fig. 9 shows the compression deformation process of the counter-clockwise directional rotation press-torsion lattice structure, and as can be seen from the figure, fig. 9 is a comparison of the compressive stress-strain curve and the torsion angle-strain curve of the directional rotation and non-directional rotation lattice structure. It can be seen from the figure that the actual torsion direction of the lattice structure is consistent with the rotation direction of the defect setting, and the deformation modes of the rod pieces in the four torsion angle states are also basically consistent with the corresponding deformation modes in the non-directional torsion pressing lattice structure. The peak stress of the directional torsion lattice structure containing the defects is obviously lower than that of the non-directional torsion lattice structure, the directional torsion lattice structure does not have obvious post-peak weakening phenomenon after reaching peak load, and the rod piece is in a stable post-buckling state.
Unlike the torsion angle greatly increased instantaneously when the non-directional compressive torsion lattice structure is buckling unstable, the torsion angle of the directional compressive torsion lattice structure changes approximately linearly with compressive strain. Before buckling instability occurs to the non-directional torsion lattice structure, the torsion angle of the structure is obviously smaller than the torsion angle of the directional torsion lattice structure in the same strain state, after the rod piece is buckled and deformed, the torsion angle of the non-directional torsion lattice structure is gradually larger than the torsion angle of the directional torsion lattice structure, and after the compressive strain reaches 0.08, the torsion angle difference between the non-directional torsion lattice structure and the directional torsion lattice structure is basically unchanged.
By now it should be appreciated by those skilled in the art that while a number of exemplary embodiments of the invention have been shown and described herein in detail, many other variations or modifications of the invention consistent with the principles of the invention may be directly ascertained or inferred from the present disclosure without departing from the spirit and scope of the invention. Accordingly, the scope of the present invention should be understood and deemed to cover all such other variations or modifications.
Claims (5)
1. A buckling-driven high-angle torsional lattice structure design, comprising:
the lattice rod piece comprises an X-shaped rod piece formed by two orthogonal connected inclined rods and a penetrating vertical rod which vertically penetrates through the inclined rods at two sides of the intersection point of the X-shaped rod piece respectively, the height of the penetrating vertical rod is consistent with that of the X-shaped rod piece and forms an integral structure with the inclined rods, and two ends of the penetrating vertical rod penetrate through the inclined rods and are identical with the height of the X-shaped rod piece;
the lattice structure consists of two lattice rods which are connected in an orthogonal manner and a panel which constrains the upper end and the lower end of the lattice rods;
the connection position of the through vertical rod and the inclined rod needs to meet the following conditions:
the length of the penetrating vertical rod between the two inclined rods on the same side needs to be smaller than the height between the end parts of the two inclined rods on the same side, and meanwhile, the length of the penetrating vertical rod exposed out of the inclined rods needs to be larger than the length of the penetrating vertical rod;
the connecting position of the through vertical rod and the inclined rod is positioned in the middle of the inclined rod;
in the two intersecting lattice bars, an inner concave clamping groove with an opening facing upwards is arranged at the intersecting point of one lattice bar, an inner concave clamping groove with an opening facing downwards is arranged at the intersecting point of the other lattice bar, and the two lattice bars are connected after being mutually clamped through the clamping grooves;
the end part of the inclined rod is provided with an extension section which is convenient for the end parts of the adjacent inclined rods to be connected with each other, the two ends of the inclined rod and the penetrating vertical rod are respectively provided with a fixing section which extends towards the vertical direction, the panel is provided with a mounting hole corresponding to the fixing section, and the lattice structure is welded and fixed after being inserted into the corresponding mounting hole on the panel through the fixing section;
the positions of the mounting holes on the panel and the extension sections of all diagonal rods and penetrating vertical rods in the lattice structure are uniformly offset by a defect amount in the clockwise or anticlockwise direction, so that the lattice rod pieces in the lattice structure realize uniform directional torsion when the lattice structure is subjected to external pressure.
2. The lattice structure design of claim 1,
the cross sections of the inclined rods and the penetrating vertical rods are square.
3. The lattice structure design of claim 2,
the diameter of the inclined rod is consistent with that of the penetrating vertical rod.
4. The lattice structure design of claim 1,
the connection points of the two lattice bars are fixed through welding.
5. The lattice structure design of claim 1,
the lattice bars are formed by directly cutting stainless steel plates and then spliced into the lattice structure.
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