Topological Design And Nonlinear Folding Behavior Of Conical Origami Structures

Origami structures have gradually attracted attention and gained popularity due to abundant deformation modes,high energy absorption,large folding aspect ratio,low weight,multi-stability and other advantages.However,there are still defects such as single crease design method,monotonous three-dimensional configuration,and instability during the folding process.In order to promote the engineering design and application of origami structures,it is urgent to enrich the crease design methods,expand the origami configuration space,and carry out research on the mechanical properties of new origami structures.Based on previous research,geometric analysis,deep neural network,and numerical simulation analysis methods are used here.Taking the deployable conical origami structure as the research object,crease design,folding motion analysis,and other mechanical properties analysis are discussed to make up for the current research gaps in the design and mechanical analysis of the conical origami structure.The main contents include:Based on data-driven,deep neural network models are constructed to achieve efficient and accurate design of multi-crease patterns of conical origami structures with specified geometric parameters.Deep neural networks have the ability to deal with nonlinear relationships between high-dimensional variables.So,deep neural network models are built to create the connection between the geometric parameters of the conical structures and crease pattern.The network models can accurately design the four-fold and six-fold patterns of the foldable conical structure.On the other hand,the conical structure can be taken as the basic component and create rich configuration such as cylinder,spindle,hourglass,and so on.Based on the periodic arrangement on crease patterns,Python algorithms for effectively solving the geometric topology and crease patterns of multi-crease conical origami structures are written.Using the geometric parameters and the expression parameters of the crease pattern,Python algorithms to automatically generate and draw the crease pattern of the foldable conical structure are written.In addition to drawing the crease pattern,the algorithm can also obtain the coordinates of each vertex and the errors of flat foldable condition for three vertices.Based on the control variable method,the evolution mechanism of geometric parameters in the folding motion of four-and six-fold conical origami structures is revealed.In ABAQUS,the quasi-static loading simulation was used to calculate the mechanical behavior of the foldable conical structures.The results show that with the increase of the number of breaks,the radius of the upper base circle or the thickness of the shell element,the external load,the total energy and strain energy of the structures become larger.Considering the cyclic symmetry properties of conical origami structures,a method for calculating generalized eigenvalues and natural frequencies of symmetric origami structures based on substructures is proposed.The generalized eigenvalues of cyclic symmetric origami structures are calculated based on substructures.First,the repeating units of the structure are identified and connectivity to adjacent repeating units is established.Then,calculate the stiffness and mass matrix of the repeating elements.Finally,determine the relationship between the generalized eigenvalues and the stiffness matrix,mass matrix of the repeating elements.An equivalent solution to the generalized eigenvalue problem for complex origami structures is realized.Based on the control variable method,the influence of geometric parameters on the stiffness,fatigue and energy dissipation characteristics of six-fold and four-fold conical origami structures is studied.Using the control variable method,the influence of geometric parameters on the frequency eigenvalues,fatigue life and energy absorption characteristics for the deployable conical structure is analyzed by dynamic theory,ABAQUS and FE-SAFE.The results show that with the increase of number of equal parts,the natural frequency value,stiffness and the fatigue life of the structure decreases.However,the energy absorption characteristic improves.When the radius of the upper bottom circle is 1/2 of the radius of the lower bottom circle,the maximum number of cycles that the six-fold foldable conical structure can withstand is at the maximum value.While,the maximum number of cycles that the fourfold conical structure can withstand is at a minimum.