Form generation of rigid origami for approximation of a curved surface based on mechanical property of partially rigid frames

Hayakawa, Kentaro; Ohsaki, Makoto

doi:10.1016/j.ijsolstr.2020.12.007

Cited by 11 publications

(11 citation statements)

References 18 publications

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“…The positions of the vertices of a rigid origami where the additional nodes do not exist can be calculated by the positions of nodes on the edges. Details of the calculation of the positions of vertices can be found in Hayakawa and Ohsaki (2021).…”

Section: Configuration Of a Frame Modelmentioning

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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Section: Configuration Of a Frame Modelmentioning

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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“…In addition, finite deformation paths are generated by large deformation analysis of the frame model shown in Fig. 1(c), which consists of frame members and hinges and is suitable for analysis using general-purpose finite element analysis software [38,39]. By using the frame model, we can easily assign small rotation stiffness to the hinges, and this stiffness stabilizes the convergence process at each step in the large deformation analysis.…”

Section: Introductionmentioning

confidence: 99%

Analytical and Numerical Investigation of Second-Order Infinitesimal Mechanism in Rigid Origami

Hayakawa,

Ohba,

Ohsaki

2023

Preprint

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“…In light of this, engineers have used a variety of reduced order modeling techniques to investigate forward elastic equilibrium and stability problems, as well as to inversely design non-uniform mesostructures at a lesser computational expense. These techniques range from bar-and-hinge [37][38][39] and structural frame [40] models that capture the mechanics of folded sheets, to representations of structural element networks that are based on effective springs [41], equivalent lattices [42], Chebyshev nets [43], discrete elastic rods [43,44] and Kirchhoff rods [45].…”

Section: Introductionmentioning

confidence: 99%

Effective continuum models for the buckling of non-periodic architected sheets that display quasi-mechanism behaviors

McMahan,

Akerson,

Celli

et al. 2021

Preprint

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In this work, we construct an effective continuum model for architected sheets that are composed of bulky tiles connected by slender elastic joints. Due to their mesostructure, these sheets feature quasi-mechanisms -low-energy local kinematic modes that are strongly favored over other deformations. In sheets with non-uniform mesostructure, kinematic incompatibilities arise between neighboring regions, causing out-of-plane buckling. The effective continuum model is based on a geometric analysis of the sheets' unit cells and their energetically favorable modes of deformation. Its major feature is the construction of a strain energy that penalizes deviations from these preferred modes of deformation. The effect of non-periodicity is entirely described through the use of spatially varying geometric parameters in the model. Our simulations capture the out-of-plane buckling that occurs in non-periodic specimens and show good agreement with experiments. While we only consider one class of quasi-mechanisms, our modeling approach could be applied to a diverse set of shape-morphing systems that are of interest to the mechanics community.

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Form generation of rigid origami for approximation of a curved surface based on mechanical property of partially rigid frames

Cited by 11 publications

References 18 publications

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

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

Analytical and Numerical Investigation of Second-Order Infinitesimal Mechanism in Rigid Origami

Effective continuum models for the buckling of non-periodic architected sheets that display quasi-mechanism behaviors

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