CN105350646A - Two-dimensional tensegrity structure unit based on hexagon geometry - Google Patents

Abstract

The invention discloses a tensegrity integral structure configuration based on hexagonal geometry, which includes 6 hinged nodes, 6 stay cables and 3 compression bar components. The 6 hinge nodes are respectively located on the 6 vertices of the two-dimensional hexagonal geometry, and the 3 struts are respectively arranged on the three internal diagonal lines of the hexagon, and the two ends are connected with the three sets of opposite vertices of the hexagon. The root cables are interlaced to form a hexagonal star. There is pretension in the cables and preload in the compression rods, and the structural unit is a self-balancing cable-strut system with good structural rigidity, and has a good application prospect in the prestressed cable-strut structure system.

Description

A 2D tensegrity structural element based on hexagonal geometry

technical field

The invention is a method applied to architectural structure design and modern space structure design, in particular to a two-dimensional tensioned integral structural unit based on hexagonal geometry.

Background technique

The tensegrity structure is a prestressed self-balancing system composed of compression rods and tension cables. The structural stiffness is provided by the balanced prestress between the tension unit and the compression unit. Before the prestress is applied, the structure There is almost no stiffness, but due to the existence of self-stress, in a specific geometric state, the structure acquires stiffness and becomes a structure that can bear loads, which is its essential feature different from traditional structures. It is precisely because of this essential feature that the internal force and shape of the tensegrity structure are highly correlated, showing strong geometric nonlinearity and shape adjustability. The tensegrity structure can adjust or control the shape of the structure by changing the internal force of the components, which makes the tensegrity structure particularly suitable as an adaptive structure and a deployable structure. The former makes the structural shape meet certain functions by actively changing the internal force of the components. The latter makes it a structure with a certain shape and stiffness or degenerates into a compact state without stiffness by applying or completely releasing the prestress. The tensegrity structure has the advantages of light weight, large span, beautiful shape, and full use of materials, etc., and has broad application prospects in engineering.

Although some tensegrity structures based on hexagonal geometry have appeared at present, due to the difference in the geometric configuration and initial prestress of the structure, the stiffness of different structures is also different, and there are still great gaps in the application in practical engineering. difference. Therefore, it is of great significance to develop and design a two-dimensional tensegrity structural unit based on hexagonal geometry.

Contents of the invention

Technical problem: The present invention provides a two-dimensional tensile integral structural unit based on hexagonal geometry that can be expanded and derived, and can be efficiently applied to prestressed cable-strut structural systems.

Technical solution: The two-dimensional tensioned overall structure based on hexagonal geometry of the present invention includes 6 hinged nodes, 6 stay cables and 3 compression rod members, the six hinged nodes A, B, C, D, E and F are respectively located on six vertices arranged counterclockwise in a two-dimensional hexagonal geometry; Rods, the compression rods connecting nodes B and E, the compression rods connecting nodes C and F; the six cables are located inside the hexagon and interlaced to form a hexagonal star, including connecting nodes A and C The cable connecting node A to node E, the cable connecting node B to node D, the cable connecting node B to node F, the cable connecting node C to node E, the cable connecting node D to node F the lasso.

Further, in the two-dimensional tensioned integral structural unit based on the hexagonal geometry of the present invention, the lengths of the three compression rod members are the same, all of which are 21; the lengths of the six stay cables are the same, all of which are

Further, in the two-dimensional tensegrity structural unit based on the hexagonal geometry of the present invention, in the working state, the said tensegrity structural unit maintains a stable self-balancing state, and the preloads of the three compression rod components are the same, both F _b , the pretension of the six cables is the same, all of which are F _c , and satisfy

Beneficial effect: compared with the prior art, the present invention has the following advantages:

In the components of the traditional two-dimensional truss structure, there is no prestress, the material utilization efficiency is low, and the overall weight is relatively large. However, in the cable-strut structure unit of the present invention, there is pretension in all the cables, and there is preload in all compression bars. The pre-tension force of the cable and the pre-pressure of the compression rod are balanced with each other. When the external load acts, the structure resists the external load by actively adjusting the internal force of the member, and the cable is always in tension and the compression rod is always in compression. , the configuration is reasonable, the structure is lighter, and the material utilization rate is higher. In addition, in the existing tensegrity structure system based on hexagonal geometry, the cables are located outside the hexagon, which is inconvenient in the process of deriving and building multiple similar units to form a large-scale overall structure, and the overall structure The rigidity is low, and the ability to resist deformation is weak, while the six cables in the present invention are not only continuous but also arranged inside the hexagon, each forming a more stable triangle, and interlaced to form a hexagonal star, which is not only novel and beautiful in shape, It can also ensure that the structure has good structural rigidity and mechanical performance under working conditions, and it is easy to build a large cable-strut structure. The tensegrity structural unit of the present invention is completely different from the existing prestressed cable bars based on hexagonal geometry (three independent compression bars are located inside, and the continuous six stay cables of the outer ring are located on each side of the hexagon. ), the outer cables of the proposed structural unit are interlaced to form a hexagonal star. Beautiful appearance, better structural performance, and can stably bear external loads.

Description of drawings

Figure 1 is a schematic diagram of six vertices of a two-dimensional hexagonal geometry.

Fig. 2 is a schematic diagram of the configuration of the tensegrity structural unit of the present invention.

In Fig. 1 and Fig. 2, the thin solid lines represent the cable components, and the thick solid lines represent the pressure bar components. A, B, C, D, E, and F in all the figures represent the hinge nodes located at the vertices of the hexagon, and the compression bars 101, 102, and 103 all belong to the same type of compression bars, and the drag cables 201, 202, 203, 204, 205 and 206 all belong to the same type of stay cables.

detailed description

The present invention will be further described below in conjunction with embodiment and accompanying drawing.

1. Component connection relationship and classification.

As shown in Figures 1 and 2, the two-dimensional tensioned integral structural unit based on hexagonal geometry of the present invention includes 6 hinged nodes, 6 stay cables and 3 compression rod members, the six hinged nodes A, B, C, D, E, and F are respectively located on six vertices sorted counterclockwise of a two-dimensional hexagonal geometry. In Fig. 2, the thick line represents the compression rod member, a total of 3 compression rods, and the three compression rod members are respectively arranged on the three diagonals of the hexagon, including the compression rod 101 connecting nodes A and D, connecting nodes B and The compression bar 102 of E connects the compression bars 103 of nodes C and F. In Fig. 2, the thin lines represent the cables, and the six cables are all located inside the hexagon and interlaced to form a six-pointed star, including the cables 201 connecting nodes A and C, connecting nodes A and E The cable 202 connects node B to node D, the cable 204 connects node B to node F, the cable 205 connects node C to node E, and the cable 206 connects node D to node F.

2. The geometric length of the member.

As shown in Figure 1 and Figure 2, use l to represent the side length of the hexagon, all the compression rod members have the same geometric length, which is 2l, and all the cable members have the same geometric length as

3. The pre-tension (compression) stress of the component.

In order to ensure that the structure is in a self-balancing state when there is no external load, the pretension (compression) force of various components must satisfy the following relationship:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; =</span>\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}$

Among them, F _b and F _c are the axial force in the compression rod member and the cable member, respectively.

4. The blanking length of the component.

The blanking length of the component refers to the length when the component is processed, and the component is in a stress-free state at this time. The blanking length of various components is:

${\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; l</span>}$

${\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}}\mathrm{<span\; class="notranslate">\; l</span>}$

in, are the blanking lengths of the compression rod and cable member, respectively, E _b , A _b are the elastic modulus and cross-sectional area of the compression rod member, E _c , A _c are the elastic modulus and cross-sectional area of the cable member, respectively.

5. Assembly of the structure.

The components processed according to the material length are assembled together through six given hinge nodes and according to the geometric connection relationship between the aforementioned components, and the final structure will be a two-dimensional tensioned overall structure based on hexagonal geometry unit, and all the cable members are in tension, all the compression rod members are in compression, and the whole structure is in a stable self-balancing state.

The foregoing embodiments are only preferred implementations of the present invention. It should be pointed out that those skilled in the art can make several improvements and equivalent replacements without departing from the principle of the present invention. Technical solutions requiring improvement and equivalent replacement all fall within the protection scope of the present invention.

Claims (3)

1. A two-dimensional tensioning integral structure based on hexagonal geometry is characterized by comprising 6 hinge nodes, 6 pull cables and 3 pressure rod members, wherein the six hinge nodes A, B, C, D, E and F are respectively positioned on 6 vertexes of the two-dimensional hexagonal geometry in a counterclockwise sequence; the three pressure lever components are respectively arranged on three diagonal lines of the hexagon and comprise pressure levers (101) for connecting nodes A and D, pressure levers (102) for connecting nodes B and E and pressure levers (103) for connecting nodes C and F; the 6 inhaul cables are all located inside the hexagon and are mutually staggered to form a hexagon star shape, and the inhaul cable comprises an inhaul cable (201) connecting a node A and a node C, an inhaul cable (202) connecting the node A and the node E, an inhaul cable (203) connecting the node B and the node D, an inhaul cable (204) connecting the node B and the node F, an inhaul cable (205) connecting the node C and the node E, and an inhaul cable (206) connecting the node D and the node F.

2. A two-dimensional tensegrity structural unit based on hexagonal geometry, according to claim 1, characterized in that said three strut members are of the same length, all 2 l; the six inhaul cables are the same in length and are all

3. A two-dimensional tensegrity structural unit according to claim 2, wherein in operation, said tensegrity structural unit maintains a stable self-balancing state, and the pre-stresses of the three strut members are the same and all F_bThe pretension forces of the six inhaul cables are the same and are all F_cAnd satisfy