Assigning mountain-valley fold lines of flat-foldable origami patterns based on graph theory and mixed-integer linear programming

Chen, Yao; Fan, Linzi; Bai, Yongtao; Feng, Jian; Sareh, Pooya

doi:10.1016/j.compstruc.2020.106328

Cited by 54 publications

(9 citation statements)

References 37 publications

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“…With the development of computer science, computational geometry, and graph theory, origami design and analysis techniques have developed rapidly over the past few decades. [1][2][3][4][5][6][7][8][9][10][11] Importantly, in recent years, origami techniques have been applied to a broad range of design problems in various fields of science and engineering. [12][13][14][15][16][17] In particular, researchers have discovered a range of desirable properties such as negative Poisson's ratio, [18][19][20] programmable morphology, [21][22][23][24][25][26][27] and energy absorption capacity [28][29][30][31][32][33][34][35] in some origami structures and have demonstrated them using various analytical, numerical, and experimental methods.…”

Section: Introductionmentioning

confidence: 99%

Computational Parametric Analysis of Cellular Solids with the Miura‐Ori Metamaterial Geometry under Quasistatic Compressive Loads

Chen

Shi

et al. 2023

Adv Eng Mater

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Origami‐based metamaterials have widespread application prospects in various industries including aerospace, automotive, flexible electronics, and civil engineering structures. Among the wide range of origami patterns, the fourfold tessellation known as Miura‐ori is of particular attraction to engineers and designers. More specifically, researchers have proposed different 3D structures and metamaterials based on the geometric characteristics of this classic origami pattern. Herein, a computational modeling approach for the design and evaluation of 3D cellular solids with the Miura‐ori metamaterial geometry which can be of zero or nonzero thicknesses is presented. To this end, first, a range of design alternatives generated based on a numerical parametric model is designed. Next, their mechanical properties and failure behavior under quasistatic axial compressive loads along three perpendicular directions are analyzed. Then, the effects of various geometric parameters on their energy absorption behavior under compression in the most appropriate direction are investigated. The findings of this study provide a basis for future experimental investigations and the potential application of such cellular solids for energy‐absorbing purposes.

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Section: Introductionmentioning

confidence: 99%

Computational Parametric Analysis of Cellular Solids with the Miura‐Ori Metamaterial Geometry under Quasistatic Compressive Loads

Chen

Shi

et al. 2023

Adv Eng Mater

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“…Chen et al 17 developed a comprehensive kinematic synthesis for rigid origami of thick panels that differs from the existing kinematic model but is capable of reproducing motions identical to that of zero-thickness origami. In addition, by considering folding methods, Tang et al 18 proposed a new scheme for folding rotating discrete surfaces based on the waterbomb origami model, Hu et al 19 proposed a circular axisymmetric origami structure design scheme based on the generalized Miura origami unit, Wang et al 20 proposed an in-plane design method based on the approximate surface of the generalized Miura origami unit, and Chen et al 21 assigned mountain-valley fold lines of flat-foldable origami patterns based on graph theory and mixed-integer linear programing and tackled the challenging problem of automated design of scalene-faceted flat-foldable origami tessellations using an efficient metaheuristic algorithm. 22 These origami structure design schemes construct a target folding surface through a basic origami unit through different design processes, providing ideas for the design and practical application of new origami structures.…”

Section: Introductionmentioning

confidence: 99%

Synthesis analysis of the morphologies of convex polygonal tubular origami structures based on Yoshimura origami patterns

Wei

Zhao

Fan

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this paper, the basic elements of Yoshimura origami patterns are extracted, a discrete splicing construction method to control the circumference of a tubular origami structure based on basic elements is created by summarizing morphological laws, and a construction function and a solution process for the Yoshimura origami pattern tubular structure based on a combination of the basic elements are proposed. A concrete form of the convex polygonal origami structure based on the Yoshimura origami pattern with different numbers of edges is designed by synthesizing the construction function and geometric constraints. This theoretical synthesis approach provides new ideas for the innovative design of origami robots, mechanical metamaterials, and energy-absorbing cushioned structures.

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“…There are many studies on the kinematics and the mechanical properties of rigid origami. Various techniques such as optimization and graph theory of mathematics and structural engineering are utilized; e.g., simulation of the folding process based on the projection to the constraint space (Tachi, 2009), origami design based on the Bayesian topology optimization (Shende et al, 2021), rigidity analysis based on the theory of combinatorial rigidity (Katoh and Tanigawa, 2011), and assigning mountain or valley fold to each crease line based on graph theory and mixed-integer linear programming (Chen et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

Equilibrium path and stability analysis of rigid origami using energy minimization of frame model

Hayakawa

Ohsaki

2022

Front. Built Environ.

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This paper presents a method of equilibrium path analysis and stability analysis of an equilibrium state for a rigid origami, which consists of rigid flat faces connected by straight crease lines (folding lines) and can be folded and unfolded without deformation of its faces. This property is well suited to the application to deployable structures and morphing building envelopes consisting of stiff panels. In this study, a frame model which consists of hinges and rigid frame members is used to model the kinematics of a rigid origami. Faces and crease lines of a rigid origami are represented by frame members and hinges, respectively. External loads are applied to the nodes of a frame model, and the displacements of some nodes are fixed. Small rotational stiffness proportional to the length of a crease line is assumed in each hinge to uniquely determine the equilibrium state, which is obtained by solving the optimization problem for minimizing the total potential energy under the conditions so that the displacements of the nodes and the members are compatible. The optimization problem is solved by the augmented Lagrangian method, and the positive definiteness of the Hessian of the augmented Lagrangian is investigated to determine the stability of the equilibrium state. Equilibrium path analyses are carried out and bifurcations of the equilibrium paths are investigated for examples with waterbomb patterns.

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Assigning mountain-valley fold lines of flat-foldable origami patterns based on graph theory and mixed-integer linear programming

Cited by 54 publications

References 37 publications

Computational Parametric Analysis of Cellular Solids with the Miura‐Ori Metamaterial Geometry under Quasistatic Compressive Loads

Computational Parametric Analysis of Cellular Solids with the Miura‐Ori Metamaterial Geometry under Quasistatic Compressive Loads

Synthesis analysis of the morphologies of convex polygonal tubular origami structures based on Yoshimura origami patterns

Equilibrium path and stability analysis of rigid origami using energy minimization of frame model

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