This research focuses on integrated origami and tensegrity structures in equilibrium and form-finding analysis. Using an analytical approach, the software enables modeling and evaluating both origami and tensegrity paradigms as a cohesive system. Parameters such as nodal coordinates and hinge angles among origami panels characterize tensegrity and origami structures. This software is released as open-source to assist researchers interested in this multidisciplinary field.
This user guide provides details on all aspects of the software to improve its usability. Questions and suggestions for enhancement are highly encouraged. The software specializes in performance modeling, structural design, and nonlinear static simulations of origami and tensegrity systems. The primary contributions of this software are in the following areas:
- Enable modeling of any origami and tensegrity structures via nodal coordinates, node connectivity, and hinge angles between panels.
- Provide the capability to specify constraints on nodal coordinates, such as limiting movements in the X-, Y-, or Z-axes for particular nodes.
- Allow for the grouping of structural members within the software.
- Execute prestress and mechanism mode evaluations through singular value decomposition of the equilibrium matrix.
- Conduct stiffness and stability analyses.
- Resolve equilibrium equations considering any applied external forces and the nonlinearity of geometry and material properties.
- Facilitate simulations of forced motions by inputting nodal sequences or adjusting the rest lengths of specific structure members.
The name OriTsgEFA is suggested to be pronounced as "Ori Tenseg EFA." The software provides a platform for static analysis of origami and tensegrity structures, encompassing:
- Load analysis that accounts for either elastic or plastic deformations in bars and strings.
- Both infinitesimal and large deformation analyses for a better understanding of structural stress and actuation strategies.
- The ability to adapt to various boundary conditions, such as fixing or applying static loads at any nodes in any direction (e.g., gravitational force, specified forces, or moments).
- Stiffness analysis features that include calculations of eigenvalues and their modes.
A foundational understanding of undergraduate-level linear algebra, material or continuum mechanics, finite element methods, and basic MATLAB knowledge is advised for effective software utilization. The software is developed for:
- 64-bit Windows
- MATLAB
Note: While the software is compatible with MATLAB versions later than 2009a on platforms like Win7/Win10/Mac OS/Linux/Win XP/Win Vista, using the most up-to-date release of MATLAB is strongly recommended. Further information regarding MATLAB versions can be accessed here.
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Origami and Tensegrity Equilibrium and Form-finding Analysis (OriTsgEFA) folder contains the following parts:
To utilize the OriTsgEFA software, initially execute the setup.m script. Open MATLAB and run setup.m, which performs the following actions:
- Incorporate all requisite library functions into the MATLAB path,
- Include the Software Verification and Examples folders,
- Add the User Guide,
- Add the Videos directory,
- Add the JOSS paper.
Note: It is imperative to run setup.m each time MATLAB is initiated before executing other files.
This directory houses the academic paper associated with the software, complete with source files and reference materials. The paper offers an introductory background, a project summary, its applications, citations, and more.
Stored in this folder are the following:
All the functions are essential for origami-tensegrity statics analysis. To perform said analysis, follow the guidelines outlined in User_Guide.pdf.
This folder incorporates:
-
Five Statics Examples
Herein, examples are presented to validate and showcase the statics capabilities of this software. -
auto all static test. mFile
A.mfile is provided to execute all five statics examples sequentially.
This directory contains User_Guide.pdf, which elaborates on software usage, application variety, and developer onboarding.
This folder showcases intriguing animations related to origami-tensegrity systems.
We are eager to assist with any inquiries you may have. Clearly articulate your questions and email Muhao Chen: muhaochen@uky.edu Shuo Ma: mashuo@zjut.edu.cn. Your correspondence is appreciated.
The authors extend their heartfelt gratitude to Mr. Xueshi Wang and Dr. Hongying Zhang for their invaluable assistance. Indeed, many thanks!
Your feedback and contributions are valuable. For seamless communication, adhere to consistent terminology.
- Fork the repository,
- Either submit a pull request or send your queries and contributions to the help desk.
Replies will be promptly provided.
- MATLAB (version 2009a or later)
- Comments delineating function inputs and outputs
- Consistent nomenclature as specified
N: initial node positions
n: nodal coordinate vector
C_b: bar connectivity
C_s: string connectivity
C: connectivity matrix of the structure
C_h: hinge connectivity
C_rh: rigid hinge connectivity
Ca: triangle element connectivity
E_n: transformation matrix from hinge element to total nodes
S: clustering matrix
ne: amount of members
nn: amount of nodes
n_h: amount of hinges
n_p: amount of panels
a: a vector containing the index of free nodal coordinate
b: a vector containing the index of fixed nodal coordinate
Ia: a matrix locating the free nodal coordinate
Ib: a matrix locating the fixed nodal coordinate
Gp: group matrix
l: length of members
l0_c: rest length of truss members
theta_0: initial angle of hinges
A_1: equilibrium matrix with no constraints, force density as the variable
A_1c: Equilibrium matrix with group, force density as the variable.
A_1a: equilibrium matrix with constraints, force density as the variable
A_1ac: equilibrium matrix with constraints and group, force density as the variable
A_2: equilibrium matrix with no constraints, force as variable
A_2c: Equilibrium matrix with group, force as the variable.
A_2a: equilibrium matrix with constraints, force as variable
A_2ac: equilibrium matrix with constraints and group, force as variable
phTpn: Jacobian matrix of origami
G: Hessian matrix of origami
A_o: the equilibrium matrix of the whole structure
k_h: the hinge rotational stiffness
w0: external force
q_gp: force density vector in group
q: force density vector
t_gp: force vector in group
t: force vector
index_b: number of bars
index_s: number of strings
A_b: cross-sectional area of bars
A_s: cross-sectional area of strings
A_gp: cross-sectional area of all members in a group
A_c: cross-sectional area of all members
E_c: Young's modulus of members
Kt_aa: tangent stiffness of the tensegrity
Kg_aa: geometry tangent stiffness of the tensegrity
Ke_aa: material tangent stiffness of the tensegrity
K_t_oa: tangent stiffness of the whole structure with constraints
rho: material density of members
mass: mass vector of members
substep: substeps in static analysis
w_t: external force in substeps
dnb_t: forced motion of fixed nodal coordinate in substeps
l0_ct: the changing rest length difference of truss elements
theta_0_t: the changing angle difference of hinge elements
Fhis: the load factor
t_t: the force of members in substeps
n_t: nodal coordinate vector in substeps
M_out: hinge moment in every step
l_out: truss member length in every step