Novel Crease Patterns And Nonlinear Folding Analysis Of Low-order Symmetric Origami Structures

Origami structures with specific peak valley crease patterns can exhibit extraordinary characteristics such as negative Poisson’s ratio,high folding rate,multistability,and adjustable stiffness.This kind of new structure has been gradually favored in many fields such as aerospace,biomedicine,metamaterials,intelligent structures and robots.Among them,crease design and folding process analysis are the focus and difficulty of modern origami structure research.On the basis of previous studies,this paper comprehensively uses geometric analysis,graph theory,optimization algorithm,matrix theory and dynamic analysis methods,takes loworder symmetrical four-fold origami and six-fold origami as the research objects,and carries out systematic research on the design and unfolding process of origami creases,so as to make up for the current research vacancy of low-order symmetrical origami structure.The main research contents are as follows:According to the topology of traditional origami and the concept of symmetry breaking in group theory,the symmetry of origami units is reduced actively,and the four-fold and six-fold origami units with low-order symmetry are developed.According to the plane folding constraints of origami vertex,the constraint equations are established to determine the plane folding point of origami element.By solving the constraint equations of origami vertex,the distribution of creases in origami cell is obtained.Based on the graph theory method,the geometric parameters of origami crease are introduced,and the graph theory representation method of origami crease pattern is given.Based on the mixed integer linear programming(MILP)model,an automatic peak valley crease distribution method for origami structure is proposed.On this basis,considering the plane folding constraints of origami vertices,the multi-objective optimization problem is transformed into a single objective optimization problem,and the particle swarm optimization algorithm is introduced to construct the optimization model of crease distribution in origami structure.The calculation results show that the method can solve the inner crease distribution of origami with any number of elements stably,and has good calculation accuracy and convergence performance.Based on the theoretical formula of folding angle of four-fold origami,an algorithm for solving the folding configuration of low-order symmetrical four-fold origami is proposed,and the motion characteristics of this kind of origami are analyzed.The proposed algorithm combines the space rotation transformation of vector to solve the vertex coordinates of origami unit in turn,and then obtains the motion configuration of origami structure,which can be extended to the motion configuration of multi crease origami structure.Based on the generalized inverse theory of matrix and the displacement compatibility matrix of the equivalent bar system structure of origami,the initial displacement of the origami vertex is introduced,and the non singular and non planar origami initial configuration is obtained by iteratively modifying the displacement of the origami vertex,which solves the defect that the traditional method can not track the whole process of the origami motion due to the singularity of the origami motion.Based on the obtained spatial configuration and nonlinear prediction correction algorithm,the whole motion process of low-order symmetrical four-fold origami structure is solved iteratively.This method can solve all origami vertex coordinates in parallel,and solve the limitation of low efficiency of solving origami configuration unit by unit by using the theoretical formula of folding angle.Based on the dynamic analysis,according to the given target configuration,the binding force in the motion process of low-order symmetric six-fold origami is calculated.According to the connection relationship of origami vertex,crease and panel,the node equivalent force is integrated.According to Newton’s second law of motion,the acceleration and displacement of Origami vertex are calculated,and the whole motion process of six-fold origami is solved iteratively,The complete motion path of the folded plane origami to the target configuration is obtained.This method solves the motion analysis problem of six-fold origami structure,and provides an important reference for generalized multi fold origami structure design and folding performance research.