Design And Properties Of Foldable Structures Based On Rigid Origami Principle

Origami is an ancient art.It not only can make art piece,but its origami principle has broad application prospects in many fields such as aerospace,automobile,and building.Rigid origami is an important subset of origami,which means its planes without strain during folding.The foldable structure based on rigid origami has important applications in solar of satellite,motion mechanism of robot,and energy box of vehicle because of the materials of structure with rigidity in actual.Recently,the origami metamaterials and tube with adjustable functions or characteristics have become a foreword in this field.However,many structural defects and limitations of engineering application are arisen in the existing origami structures.On the one hand,the existing origami metamaterial has been stacked between creases with low strength and high difficulty.As the unit of metamaterial,the origami tessellation does not have a negative out-of-plane Poisson's ratio,resulting in poor mechanical property of overall stack and singularity of structural design.On the other hand,the angle parametrization for the existing origami tube was adopted,which is cumbersome in representing geometric and physical characteristics,leading to difficult in modeling and manufacturing.In view of above defects and limitations,this paper systematically carried out the research on the design and characteristics of folded structure based on rigid origami.The main contents and results are as follows:(1)A crease pattern for constructing the origami tessellation with negative out-of-plane and in-plane Poisson's ratios and facets was designed.The folding behavior of pattern and Poisson's ratio and load of its corresponding structure were studied.The crease pattern was consisting of one vertex four crease configuration based on rigid origami,and a non-flat foldability and one degree of freedom are behaved.On this basis,modeling of origami tessellation was established,and the theoretical solution of Poisson's ratios and load were derived.(2)The intrinsic mechanism of the negative out-of-plane Poisson's ratio,the variation of load,the structural derivation,and the feasibility of polymeric vacuum forming were studied.It is found that some origami tessellations behave negative out-of-plane Poisson's ratio.A criterion for the positive and negative Poisson's ratio was proposed,which depends on the structural height ratio as the internal mechanism.It is found that the loads of some tessellations in spite of them with positive out-of-plane Poisson's ratio behave stability.The facet has no effect on the boundary between negative and positive of Poisson's ratio.The polymer origami tessellation was fabricated by vacuum forming technology,and corresponding stacked metamaterial was fabricated by the assembly of the high-strength and low-difficult facet-to-facet,indicating the superiority of the facet.(3)A generalized crease pattern of the origami tube with complex curved surface was designed.The motion behavior of the pattern folded into a tube,the mathematical model of the origami tube and the mechanism of the flat fold were studied.The crease pattern based on rigid origami was composed of a variety of isosceles trapezoids.It is found that the vertices on the same layer of the pattern were coplanar in the process of folding and the closed condition of the origami tube is obtained through the theory of spherical triangle geometry.Then,a unified parameterization for the origami tube was established.On this basis,a series of origami tube with various geometric patterns and axially folded forms were constructed.A criterion for the folding of origami tube was proposed after the mechanism of axial folding was analyzed.(4)The extrusion blow molding technology,layer spacing distribution and origami pattern on crush mode and energy absorption of polymeric origami tube were experimentally studied.A blowing mold with origami pattern was designed and manufactured according to the general mathematical model,and polyethylene origami tubes were manufactured.It is reliable and effective for the extrusion blow molding to produce the origami structure through analyzing the uniformity of the wall thickness.The axial compressive experiment showed that the crushing mode can be inferred based on the deformation state of the polymer tube which cannot be completely recovered.It is significant for the surface having crease pattern to reduce the initial peak load and initial stiffness.The crush mode and initial crush have great effect on the crease pattern and layer spacing distribution.In summary,the design and characteristics of origami tessellation and tube based on rigid origami were systematically studied through combining between theoretical analysis and experiment.The results can provide methodological guidance and technical support for the design and manufacture of origami structures with specific functions or characteristics.