Paper folding type protection structure based on generalized four folds and design method

Abstract

The invention discloses a paper folding type protection structure based on generalized four folds and a design method. The problems that a traditional design method is single in mode, low in digitization degree and the like can be solved. The structure comprises a plurality of four-fold paper folding units, the units are arranged in an array mode in the horizontal direction and the vertical direction, the whole structure of the units is connected in a head-to-tail mode in a certain folding state, and a closed paper folding type structure is formed. The paper folding type protection structure has the single degree of freedom, the paper folding units have the good energy dissipation buffering effect when folded, and the good engineering application prospect is achieved.

Description

Technical Field

[0001] The invention relates to a foldable structure, in particular to an origami-type protective structure based on generalized four folds and a design method. Background Art

[0002] Origami is a traditional art from ancient China. In recent years, with the continuous development of origami engineering and advanced computational analysis methods, origami-inspired structures have attracted a lot of attention due to their reconfigurability, adjustable stiffness, high energy absorption and programmable properties. At present, origami structures have been successfully applied to robots, energy absorption devices, deployable structures and metamaterials.

[0003] Origami protective structures utilize the principles of origami. Through carefully designed folding patterns, the geometric shape of the origami structure can be adjusted through folding parameters to adapt to different protection needs and application scenarios, achieving efficient use of materials. On the one hand, origami structures have excellent impact resistance and energy absorption characteristics. When impacted, this structure can effectively absorb and disperse the impact force by changing the deformation mode of the module unit, reducing the impact on the protected object. On the other hand, lightweight is also a significant advantage of origami protective structures. Origami structures are usually made of lighter materials, such as aluminum alloys or composite materials, which makes them more convenient in modular production, transportation, installation, etc. In addition, in some cases, origami protective structures can also exhibit unique mechanical properties, such as the negative Poisson's ratio effect, that is, the structure can shrink laterally when subjected to vertical loads, thereby improving energy absorption efficiency. In contrast, traditional protective structures, such as reinforced concrete walls or metal protective structures, although they can withstand great impacts and loads, have limitations in weight, cost and installation flexibility.

[0004] Traditional protective structures have disadvantages such as heavy weight, insufficient energy consumption, high impact acceleration, and inability to customize the structural form through reverse design. With the increasing demand for applications in civil structures, mechanical engineering, aerospace and other fields, these protective structures can no longer meet the increasingly stringent application requirements. On the other hand, origami-type protective structures have shown great application potential and advantages in modern protective engineering with their adjustable shape, lightweight, and high energy absorption. The continuous development and improvement of origami-type protective structures will better meet the needs of impact protection in different application scenarios. The structure not only achieves the design concept of lightweight and high strength, but also demonstrates excellent customizability, injecting new vitality into the development of protective engineering. The existing origami-type protective structures have room for improvement in terms of the degree of plastic deformation, the degree of structural morphology regulation, and energy absorption performance. Summary of the invention

[0005] Technical problem: The present invention applies the foldable principle to the design of a protective structure, providing an origami-type protective structure with a large degree of plastic deformation, adjustable structural morphology, and good energy absorption performance.

[0006] Technical solution: An origami-type protective structure based on generalized four folds, which includes a plurality of four-fold origami units, wherein the units are arranged in an array in the horizontal and vertical directions, and the overall structure of the units is connected head to tail in a certain folded state to form a closed origami-type structure.

[0007] Furthermore, each four-fold origami unit includes external vertices N1, N2, N3, N4, N5, N6, N7, N8 and an internal flat folding point N9, and its corresponding four folds are N2N9, N4N9, N6N9, N8N9, including a valley fold and three peak folds. The position distribution of the external vertices and internal flat folding points of the four-fold unit is determined by parameters k1 and k2.

[0008] N1N2N9N8 is panel 1, N2N3N4N9 is panel 2, N9N4N5N6 is panel 3, N8N9N6N7 is panel 4, the folding angle between panels 1 and 2 is γ1, the folding angle between panels 2 and 3 is γ2, the folding angle between panels 3 and 4 is γ3, and the folding angle between panel 4 and 1 is γ4;

[0009] The number of arrays of four-fold origami units in the x and y directions are respectively x and array y , the translation vectors along the x-axis and y-axis are τ1, τ2 respectively; the rotation angles around the x-axis and y-axis are θ1, θ2 respectively;

[0010] The parameters of the four-fold origami unit satisfy the constrained optimization model:

[0011] minimize F(k1,k2,γ2,array x ,array y )

[0012]

[0013] Among them, F(k1,k2,γ2,array x ,array y )=|array x τ1+array y τ2|+|array x θ1+array y θ2-2π|.

[0014] Furthermore, fold N2N9 is parallel to boundaries N1N8 and N3N4, fold N6N9 is parallel to boundaries N7N8 and N5N4, fold N8N9 is parallel to boundaries N1N2 and N6N7, and fold N4N9 is parallel to boundaries N2N3 and N6N5.

[0015] Furthermore, it is characterized in that γ2=π, and the structure is a flat ring structure.

[0016] Furthermore, it is characterized in that γ2≠π, and the structure is a closed tubular structure.

[0017] Furthermore, N3 and N7 are closed points, and the structure is a spiral structure.

[0018] The present invention also provides a design method of an origami-type protective structure based on generalized four folds, comprising the steps of:

[0019] Step 1: Take any four-fold basic unit, and define the vertex numbers of the octagon as N1 to N9 in counterclockwise order, N1N2N9N8 is panel 1, N2N3N4N9 is panel 2, N9N4N5N6 is panel 3, N8N9N6N7 is panel 4, the folding angle between panels 1 and 2 is γ1, the folding angle between panels 2 and 3 is γ2, the folding angle between panels 3 and 4 is γ3, and the folding angle between panel 4 and 1 is γ4;

[0020] Step 2: define the folding angle γ2 between panels 2 and 3 as an independent variable, and calculate the coordinates of each boundary vertex in the folding process according to the folding angle relationship of four-fold origami;

[0021] Step 3: Based on the closing conditions of the head and tail units, a constrained optimization model is established and solved to ensure that the overall structure is closed at the head and tail without self-intersection.

[0022] Furthermore, in step 3: according to the design requirements, several independent variables of the constrained optimization model are set to fixed values, and the reverse design of the structure is performed.

[0023] The origami-type protective structure based on generalized four folds of the present invention is characterized in that the structure comprises a plurality of generalized four-fold origami units. Each four-fold origami unit consists of external vertices N1, N2, N3, N4, N5, N6, N7, N8 and an internal flattenable point N9, and its corresponding four folds are N2N9, N4N9, N6N9, N8N9, including a valley fold and three peak folds. The position distribution of the external vertices and flattenable points of the four-fold unit is determined by parameters k1 and k2, The four-fold basic unit is composed of four quadrilaterals, and the overall four-fold unit morphology can be adjusted by k1 and k2. The generalized Miura, that is, the fold N2N9 is parallel to the boundaries N1N8 and N3N4, the fold N6N9 is parallel to the boundaries N7N8 and N5N4, the fold N8N9 is parallel to the boundaries N1N2 and N6N7, and the fold N4N9 is parallel to the boundaries N2N3 and N6N5, is also a special case of the generalized four folds.

[0024] According to the origami-type protective structure based on generalized four-fold marks as described in claim 1, it is characterized in that, by arbitrarily taking a four-fold basic unit, the vertices of the octagon are defined in counterclockwise order as N1 to N9, N1N2N9N8 is panel 1, N2N3N4N9 is panel 2, N9N4N5N6 is panel 3, N8N9N6N7 is panel 4, the folding angle between panels 1 and 2 is γ1, the folding angle between panels 2 and 3 is γ2, the folding angle between panels 3 and 4 is γ3, and the folding angle between panel 4 and 1 is γ4.

[0025] The head and tail of a single unit are defined as S and F respectively. If you want to close a single unit, you must satisfy both the coincidence of the two points and The sum of the rotation angles (θ1, θ2) of the two vectors around the x and y axes is 360°.

[0026]

[0027] Furthermore, when the four-fold origami unit is arrayed in the x and y directions, the closure condition can be written as

[0028]

[0029] Among them, array x and array y Represents the number of arrays in the x and y directions respectively. τ1,τ2 represent the translation vectors along the x and y axes respectively, and θ1,θ2 represent the rotation angles around the x and y axes respectively.

[0030] Based on the above content, a constraint optimization model can be established based on a specific four-fold unit to calculate the unit morphological parameters (k1, k2), array parameters (array x 、array y ) and the folding angle parameter (γ2), considering the array y It will not affect the closure of the structure. To simplify the calculation process, it is set to a constant value, and the fitness function can be written as:

[0031] F(array x ,γ2,k1,k2)=|array x τ1+array yτ2|+|array x θ1+array y θ2-2π|

[0032] In summary, the constrained optimization model can be written as:

[0033] minimize F(k1,k2,γ2,array x ,array y )

[0034]

[0035] Furthermore, for any four-fold basic unit, when the unit node coordinates are given, the constrained optimization model can be solved to quickly determine whether the unit can form a closed structure, and the number of arrays of units in the x and y directions when the structure is closed can be given. x 、array y , unit morphology parameters k1, k2, and folding degree parameter γ2.

[0036] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0037] (1) Simplified origami protective structure unit morphology: The generalized four-fold crease is a crease pattern with the characteristics of single degree of freedom, rigid folding, simple structure, and large folding-expansion ratio. During the folding and unfolding process, each panel is a zero-strain surface with high overall stiffness and good stability, and it is easy to accurately calculate the structural morphology to meet different application requirements;

[0038] And it can dynamically adjust the number of arrays in the vertical direction to achieve dynamic adjustment of the structural height; this design method realizes the transformation from octagonal planar units to closed three-dimensional structures by rationally arranging the units, realizes the reverse design of the structure, and solves the problem that the traditional design method cannot customize the structural geometry as needed.

[0039] (2) The design method is highly applicable: The design method of the present invention is not only applicable to special units such as generalized Miura, but also has good applicability to all octagonal generalized four-fold units. During the design process, only the geometric relationship between the unit boundary vectors needs to be adjusted to reconstruct the constrained optimization model and digitally solve the origami-type protective structure composed of different generalized four-fold units;

[0040] (3) Reverse customization of various forms: The design method of the present invention can dynamically adjust the closure constraint conditions based on application requirements, coordinate the unit structure morphological parameters, array parameters, and folding degree parameters, and reverse customize various tubular, annular, and spiral origami-shaped protective structures to meet the morphological requirements of various real scenarios for specific impact protection structures;

[0041] (4) Modular structure and high lightness: The design method of the present invention uses four generalized folds as the basic unit, which has a small number of folds, a simple structure, and a low weight. The basic unit can be pre-designed for on-site assembly. This method is not only convenient for manufacturing and transportation, but also effectively reduces the difficulty of subsequent maintenance and replacement of the structure;

[0042] (5) High structural energy absorption efficiency: The origami-type protective structure based on generalized four folds proposed in the present invention has a single degree of freedom, a single movement mode, and very good stability during the folding process. Each unit has good energy absorption and buffering performance when compressed and folded, and has good engineering application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 The present invention provides two unit forms in the origami-type protective structure: generalized four-fold and generalized Miura.

[0044] Figure 2 This is a plan view of the generalized four-fold unit provided by the present invention in a fully unfolded state.

[0045] Figure 3 Schematic diagram of the folding process from a fully unfolded state to a closed state of three different generalized four-fold origami-type structures provided by the present invention.

[0046] Figure 4 , Figure 5 , Figure 6 The present invention provides three different crease patterns and final closed structural forms based on the generalized four-crease origami-type protective structure. DETAILED DESCRIPTION

[0047] The present invention will be further described below with reference to specific embodiments and accompanying drawings:

[0048] Figure 1 The present invention provides two unit forms in the origami-type protective structure: generalized four-fold and generalized Miura.

[0049] The basic unit based on the generalized four-fold origami type protection structure provided by the present invention is composed of Figure 1 The generalized four-fold or generalized Miura composition shown. Figure 2 For example, each four-fold origami unit consists of external vertices N1, N2, N3, N4, N5, N6, N7, N8 and an internal flattenable point N9. The corresponding four folds are N2N9, N4N9, N6N9, N8N9, including a valley fold and three peak folds. The position distribution of the external vertices and flattenable points of the four-fold unit is determined by the parameters k1 and k2. The four-fold basic unit is composed of four quadrilaterals, and the overall four-fold unit morphology can be adjusted by k1 and k2. The generalized Miura, that is, the fold N2N9 is parallel to the boundaries N1N8 and N3N4, the fold N6N9 is parallel to the boundaries N7N8 and N5N4, the fold N8N9 is parallel to the boundaries N1N2 and N6N7, and the fold N4N9 is parallel to the boundaries N2N3 and N6N5, is also a special case of the generalized four folds.

[0050] The design method of the present invention realizes the transformation from octagonal plane units to closed three-dimensional structures by reasonably arranging the units, realizes the reverse design of the structure, and solves the problem that the geometric form of the structure cannot be customized on demand in the traditional design method. When the structure is subjected to external loads in the vertical direction, the foldable characteristics of the four-fold origami unit are utilized to uniformly absorb energy through the folding deformation of each generalized four-fold unit of the structure, so as to achieve the protective effect of energy dissipation and energy absorption buffering.

[0051] In the present invention, in order to achieve structural closure in a certain folding process, it is necessary to accurately analyze the node coordinates in the folding process of the structure. For this, the vertex numbers of the octagon are defined in counterclockwise order as N1 to N9, N1N2N9N8 is panel 1, N2N3N4N9 is panel 2, N9N4N5N6 is panel 3, N8N9N6N7 is panel 4, the folding angle between panels 1 and 2 is γ1, the folding angle between panels 2 and 3 is γ2, the folding angle between panels 3 and 4 is γ3, and the folding angle between panels 4 and 1 is γ4. The head and tail of a single unit are defined as S and F respectively. In order to close a single unit, the two points must coincide and The sum of the rotation angles (θ1, θ2) of the two vectors around the x and y axes is 360°.

[0052] For generalized four-fold units with different characteristic sizes, the shape (k1, k2) and array number (array x 、array y ), folded state (γ2), a series of different structural morphologies can be obtained. For example, when the folded state γ2 = π, the structure becomes a flat ring structure; when γ2 ≠ π, a closed tubular structure can be obtained; when the position of the closing point is changed, a spiral structure can be formed.

[0053] Furthermore, to ensure Figure 3 The S and F points are closed. When the four-fold origami unit is arrayed in the x and y directions, the closing condition can be written as

[0054]

[0055] Among them, array x and array yRepresents the number of arrays in the x and y directions respectively. τ1, τ2 represent the translation vectors along the x and y axes respectively, and θ1, θ2 represent the rotation angles around the x and y axes respectively. To calculate τ1, τ2 and θ1, θ2, use the unit side length vector a1 = N1-N3, a2 = N7-N5, b1 = N5-N3, b2 = N7-N1 to define a new right-handed coordinate system:

[0056]

[0057] The rotation axis around which all units rotate when folding and rolling into a closed structure can be defined as:

[0058]

[0059] in, It represents the angle between n and axis e1, and the expression is

[0060]

[0061] Then θ1,θ2 can be written as,

[0062]

[0063] in, represents the projection transformation matrix that projects the vector onto the plane with normal vector n. At the same time, the translation vectors τ1, τ2 can be written as,

[0064] τ1=n·b1,τ2=n·a1

[0065] Based on the above content, a constraint optimization model can be established based on a specific four-fold unit to calculate the unit morphological parameters (k1, k2), array parameters (array x 、array y ) and the folding angle parameter (γ2), considering the array y It will not affect the closure of the structure. To simplify the calculation process, it is set to a constant value, and the fitness function is:

[0066] F(k1,k2,γ2,array x ,array y )=|array x τ1+array y τ2|+|array x θ1+array y θ2-2π|

[0067] In summary, the constrained optimization model can be written as:

[0068] minimize F(k1,k2,γ2,array x ,array y )

[0069]

[0070] Figure 3 The simulation of the folding process of three origami-type protective structures from full expansion to closure is given under the conditions of the same basic unit, different array numbers and folding degrees. During the folding process, the folding degree of each generalized four-fold basic unit is consistent, and the structure is closed without generating self-intersection of the panel.

[0071] Figure 4 Another origami-type protective structure based on generalized four folds is given in its fully unfolded and closed states. Figure 3 The difference is that for Figure 3 The tubular structure in the structure is further constrained, and the unit morphology of the generalized four folds is adjusted to form Figure 4 The spiral structure in.

[0072] Figure 5 exist Figure 4 On this basis, the generalized four-fold unit shape was further adjusted. Figure 4 The spiral structure in the vortex is further compressed to form another flatter spiral structure.

[0073] Figure 6 A ring structure based on generalized four folds is proposed. By simultaneously modifying the number of arrays, the morphology of the basic units of the generalized four folds and the degree of folding, a ring structure that is approximately flat is formed.

[0074] In summary, since the origami-type protective structure based on the generalized four folds proposed in the present invention has a variety of structural forms, a single degree of freedom, a large folding ratio, and an easy-to-track folding form, it can dissipate energy through the folding deformation of the origami unit during the process of bearing vertical loads, and is widely used in impact protection.

[0075] The present invention is not limited to the above-described embodiments. The above description of the specific embodiments is intended to describe and illustrate the technical solution of the present invention. The above-mentioned specific embodiments are merely illustrative and not restrictive. Without departing from the purpose of the present invention and the scope of protection of the claims, ordinary technicians in this field can also make many forms of specific changes under the guidance of the present invention, which all fall within the scope of protection of the present invention.

Claims

1. An origami-type protective structure based on generalized four folds, characterized in that: The structure comprises a plurality of four-fold origami units, wherein the plurality of the units are arranged in an array in the horizontal and vertical directions, and the overall structure of the plurality of the units is connected head to tail in a certain folding state to form a closed origami structure.

2. The origami-type protective structure based on generalized four folds according to claim 1, characterized in that: Each four-fold origami unit includes external vertices N1, N2, N3, N4, N5, N6, N7, N8 and an internal flattenable point N9. The corresponding four folds are N2N9, N4N9, N6N9, N8N9, including a valley fold and three peak folds. The position distribution of the external vertices and internal flattenable points of the four-fold unit is determined by parameters k1 and k2. N1N2N9N8 is panel 1, N2N3N4N9 is panel 2, N9N4N5N6 is panel 3, N8N9N6N7 is panel 4, the folding angle between panels 1 and 2 is γ1, the folding angle between panels 2 and 3 is γ2, the folding angle between panels 3 and 4 is γ3, and the folding angle between panel 4 and 1 is γ4; The number of arrays of four-fold origami units in the x and y directions are respectively x and array y , the translation vectors along the x-axis and y-axis are τ1, τ2 respectively; the rotation angles around the x-axis and y-axis are θ1, θ2 respectively; The parameters of the four-fold origami unit satisfy the constrained optimization model: where, F(k1, k2, γ2, array x , array y ) = |array x τ1 + array y τ2| + |array x θ1 + array y θ2 - 2π|.

3. The origami-type protective structure based on generalized four folds according to claim 2, characterized in that: Fold N2N9 is parallel to boundaries N1N8 and N3N4, fold N6N9 is parallel to boundaries N7N8 and N5N4, fold N8N9 is parallel to boundaries N1N2 and N6N7, and fold N4N9 is parallel to boundaries N2N3 and N6N5.

4. The origami-type protective structure based on generalized four folds according to claim 2, characterized in that: γ2=π, and the structure is a flat ring structure.

5. The origami-type protective structure based on generalized four folds according to claim 2, characterized in that: γ2≠π, the structure is a closed tubular structure.

6. The origami-type protective structure based on generalized four folds according to claim 2, characterized in that: N3 and N7 are closed points, and the structure is a spiral structure.

7. A design method for an origami-type protective structure based on generalized four folds as claimed in claim 2, characterized in that: Includes steps: Step 1: Take any four-fold basic unit, and define the vertex numbers of the octagon as N1 to N9 in counterclockwise order, N1N2N9N8 is panel 1, N2N3N4N9 is panel 2, N9N4N5N6 is panel 3, N8N9N6N7 is panel 4, the folding angle between panels 1 and 2 is γ1, the folding angle between panels 2 and 3 is γ2, the folding angle between panels 3 and 4 is γ3, and the folding angle between panel 4 and 1 is γ4; Step 2: define the folding angle γ2 between panels 2 and 3 as an independent variable, and calculate the coordinates of each boundary vertex in the folding process according to the folding angle relationship of four-fold origami; Step 3: Based on the closing conditions of the head and tail units, a constrained optimization model is established and solved to ensure that the overall structure is closed at the head and tail without self-intersection.

8. The design method of the origami-type protective structure based on generalized four folds according to claim 7 is characterized in that: In step 3: according to the design requirements, several independent variables of the constrained optimization model are set to constant values, and the reverse design of the structure is performed.

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