An Integrated Geometric-Graph-Theoretic Approach to Representing Origami Structures and Their Corresponding Truss Frameworks

National Natural Science Foundation of China (Grant No. 51850410513 and No. 51508089), and the Fundamental Research Funds for the Central Universities; Alexander von Humboldt-Foundation.

[1]  K. Koohestani,et al.  Exploitation of symmetry in graphs with applications to finite and boundary elements analysis , 2012 .

[2]  Jian Feng,et al.  Improved Symmetry Method for the Mobility of Regular Structures Using Graph Products , 2016 .

[3]  Gert Sabidussi,et al.  Graph multiplication , 1959 .

[4]  U. Feige,et al.  Spectral Graph Theory , 2015 .

[5]  P. Sareh,et al.  Design of isomorphic symmetric descendants of the Miura-ori , 2015 .

[6]  Hugo A. Akitaya,et al.  Rigid Foldability is NP-Hard , 2018, J. Comput. Geom..

[7]  G. Hunt,et al.  Twist buckling and the foldable cylinder: an exercise in origami , 2005 .

[8]  K. Kuribayashi,et al.  Self-deployable origami stent grafts as a biomedical application of Ni-rich TiNi shape memory alloy foil , 2006 .

[9]  Jian Feng,et al.  Lower-order symmetric mechanism modes and bifurcation behavior of deployable bar structures with cyclic symmetry , 2017 .

[10]  Jian Feng,et al.  A computational method for automated detection of engineering structures with cyclic symmetries , 2017 .

[11]  Jian Feng,et al.  Efficient Symmetry Method for Calculating Integral Prestress Modes of Statically Indeterminate Cable-Strut Structures , 2015 .

[12]  B. Chen,et al.  Origami multistability: from single vertices to metasheets. , 2014, Physical review letters.

[13]  Tomohiro Tachi Geometric Considerations for the Design of Rigid Origami Structures , 2010 .

[14]  Simon D. Guest,et al.  A Framework for the Symmetric Generalisation of the Miura-ori , 2015 .

[15]  A. Kaveh,et al.  Improved group-theoretical method for eigenvalue problems of special symmetric structures, using graph theory , 2010, Adv. Eng. Softw..

[16]  Ali Kaveh,et al.  A UNIFIED METHOD FOR EIGENDECOMPOSITION OF GRAPH PRODUCTS , 2005 .

[17]  Erik D. Demaine,et al.  Geometric folding algorithms - linkages, origami, polyhedra , 2007 .

[18]  Z. You Folding structures out of flat materials , 2014, Science.

[19]  Jian Feng,et al.  Kinematic of symmetric deployable scissor-hinge structures with integral mechanism mode , 2017 .

[20]  Ali Kaveh,et al.  Graph products for configuration processing of space structures , 2008 .

[21]  Thomas C. Hull,et al.  Origami structures with a critical transition to bistability arising from hidden degrees of freedom. , 2015, Nature materials.

[22]  Glaucio H. Paulino,et al.  Bar and hinge models for scalable analysis of origami , 2017 .

[23]  Ali Kaveh,et al.  Optimal Analysis of Structures by Concepts of Symmetry and Regularity , 2013 .

[24]  Ali Kaveh,et al.  A general theorem for adjacency matrices of graph products and application in graph partitioning for parallel computing , 2009 .

[25]  Jinkyu Yang,et al.  Reentrant Origami-Based Metamaterials with Negative Poisson's Ratio and Bistability. , 2015, Physical review letters.

[26]  Jian Feng,et al.  FOLDING OF A TYPE OF DEPLOYABLE ORIGAMI STRUCTURES , 2012 .

[27]  P. Sareh,et al.  Design of non-isomorphic symmetric descendants of the Miura-ori , 2015 .

[28]  Rui Peng,et al.  Symmetric waterbomb origami , 2016, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[29]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[30]  Rui Peng,et al.  Origami of thick panels , 2015, Science.

[31]  Thomas C. Hull,et al.  Using origami design principles to fold reprogrammable mechanical metamaterials , 2014, Science.

[32]  Jian Feng,et al.  Numerical approach for detecting bifurcation points of the compatibility paths of symmetric deployable structures , 2016 .

[33]  M. Adda-Bedia,et al.  Elastic theory of origami-based metamaterials. , 2016, Physical review. E.

[34]  Z. You,et al.  Miura-Base Rigid Origami: Parameterizations of First-Level Derivative and Piecewise Geometries , 2013 .

[35]  Tomohiro Tachi Generalization of rigid foldable quadrilateral mesh origami , 2009 .

[36]  Csaba D. Tóth,et al.  Graphs That Admit Polyline Drawings with Few Crossing Angles , 2012, SIAM J. Discret. Math..

[37]  Simon D. Guest,et al.  Designing Symmetric Derivatives of the Miura-ori , 2014, AAG.

[38]  Levi H. Dudte,et al.  Geometric mechanics of periodic pleated origami. , 2012, Physical review letters.

[39]  Zhou Ya,et al.  Folding Behavior of a Foldable Prismatic Mast With Kresling Origami Pattern , 2016 .

[40]  Zhong You,et al.  Energy absorption of axially compressed thin-walled square tubes with patterns , 2007 .

[41]  Jian Feng,et al.  Generalized Eigenvalue Analysis of Symmetric Prestressed Structures Using Group Theory , 2012, J. Comput. Civ. Eng..