Active Origami (eBook)

Modeling, Design, and Applications

Edwin A. Peraza Hernandez, Darren J. Hartl, Dimitris C. Lagoudas (Autoren)

eBook Download: PDF

2018 | 1st ed. 2019
XXI, 464 Seiten
Springer International Publishing (Verlag)
978-3-319-91866-2 (ISBN)

Infos

Origami structures have the ability to be easily fabricated from planar forms, enable the deployment of large structures from small volumes, and are potentially reconfigurable. These characteristics have led to an increased interest in theoretical and computational origami among engineers from across the world. In this book, the principles of origami, active materials, and solid mechanics are combined to present a full theory for origami structures. The focus is on origami structures morphed via active material actuation and formed from sheets of finite thickness. The detailed theoretical derivations and examples make this an ideal book for engineers and advanced students who aim to use origami principles to develop new applications in their field.

Edwin A. Peraza Hernandez is a postdoctoral researcher in the Department of Aerospace Engineering at Texas A&M University. He obtained his B.S. and Ph.D. degrees in Aerospace Engineering from Texas A&M University in 2012 and 2016, respectively. His research interests include structural mechanics, design optimization, active materials, origami, and tensegrity. Edwin is the author of more than 28 technical publications in archival journals and conference proceedings and has received two best paper awards.

Darren J. Hartl received his BS in Aerospace Engineering in 2004 and Ph.D. in Aerospace Engineering in 2009, both from Texas A&M University. He currently holds an Assistant Professor position at Texas A&M in his home department, and his work bridges the topics of advanced multifunctional material systems and their integration into aerospace platforms. After over three years as a Research Assistant Professor at Texas A&M, Dr. Hartl held joint appointments at the Air Force Research Laboratory (AFRL) in the Materials and Manufacturing Directorate and Aerospace Systems Directorate. At Texas A&M, Dr. Hartl maintains an active research team consisting of graduate, undergraduate, and postdoctoral researchers. He has over 16 years of experience working with shape memory alloys and morphing structures and his efforts have included both experimental and theoretical studies. Since 2006, Darren has co-authored 146 technical publications on the topics of active materials modeling, testing, and integration into morphing structures. He has given over 25 invited talks or seminars (9 international) and has taught short courses on SMA theories in the US and Europe. Since 2014, he has served as an Associate Editor for the Journal of Intelligent Material Systems and Structures. He was recently selected as the 2016 recipient of the ASME Gary Anderson Early Achievement Award.

Dimitris C. Lagoudas is currently the Associate Vice Chancellor for Engineering Research, Senior Associate Dean for Research, Deputy Director of Texas A&M Engineering Experiment Station (TEES), the inaugural recipient of the John and Bea Slattery Chair in Aerospace Engineering, and a Distinguished University Professor at Texas A&M University. D.C. Lagoudas' research involves the design, characterization, and modeling of multifunctional material systems at nano, micro, and macro levels with averaging micromechanics methods developed to bridge the various length scales and functionalities including mechanical, thermal, and electrical properties of nanocomposites. His research team is one of the most recognized internationally in the area of modeling and characterization of shape memory alloys. He has co-authored more than 450 scientific publications in archival journals and conference proceedings. He has published extensively on the subject of shape memory alloys with his students, postdoctoral associates and colleagues and several of his journal papers are now considered classic papers in the field. The theoretical models that his research group developed have been implemented and integrated into finite element analysis software, which have been used by academic institutions around the world and also by industry and government laboratories. D.C. Lagoudas received the 2006 ASME Adaptive Structures and Material Systems Prize in recognition of his contributions to the modeling and characterization of shape memory alloys and their use in aerospace structures and he is the 2011 recipient of the SPIE Smart Structure and Materials Lifetime Achievement Award.

Inhalt

Preface 6
Contents 9
List of Symbols 13
1 Introduction to Active Origami Structures 20
1.1 Origami Structures 20
1.2 Active Origami Structures 32
1.2.1 Active Materials 33
1.2.2 Review of Active Origami Structures 34
1.2.2.1 Thermally Activated Origami Structures 35
1.2.2.2 Chemically Activated Origami Structures 40
1.2.2.3 Electromagnetically Activated Origami Structures 43
1.3 Origami Design 45
1.4 Simulation and Visualization of Origami Structures 49
Chapter Summary 53
Problems 53
References 56
2 Kinematics of Origami Structures with Creased Folds 73
2.1 Introduction 73
2.2 Fundamental Concepts 75
2.3 Fold Pattern Description 78
2.4 Kinematic Constraints for Origami with Creased Folds 87
2.4.1 Developability Constraint 87
2.4.2 Loop Closure Constraint 88
2.5 Folding Map Formulation 99
2.5.1 Parameters Required to Derive the Folding Map 100
2.5.2 Folding Map Formulation 104
2.6 Computational Implementation of the Model 111
2.7 Simulation Examples of the Kinematic Model 116
Chapter Summary 122
Problems 122
References 126
3 Unfolding Polyhedra Method for the Design of Origami Structures with Creased Folds 129
3.1 Introduction 129
3.2 Unfolding Polyhedra Method Considering Creased Folds 131
3.2.1 Problem Definition 132
3.2.2 Goal Mesh Description 133
3.2.3 Determination of Spanning Trees 143
3.2.4 Formulation of the Unfolding Map 147
3.2.5 Determination of Folding Motion 157
3.2.6 Limitations of the Unfolding Polyhedra Method 159
3.3 Examples of the Unfolding Polyhedra Method 162
Chapter Summary 162
Problems 165
References 171
4 Tuck-Folding Method for the Design of Origami Structures with Creased Folds 174
4.1 Introduction 174
4.2 Tuck-Folding Method Considering Creased Folds 176
4.2.1 Problem Definition 176
4.2.2 Goal Mesh Description 179
4.2.3 Edge Module Parameterization and Constraints 181
4.2.3.1 Loop Closure Constraints 183
4.2.3.2 Constraints for Valid Edge Module Geometry 187
4.2.3.3 Constraints to Prevent Intersections Among Tuck-Folded Edge Modules 189
4.2.3.4 Summary of Design Constraints 191
4.2.4 Edge Module Trimming 191
4.2.5 Determination of Design Variables 194
4.2.6 Determination of Folding Motion 196
4.2.7 Design Requirements of the Tuck-Folding Method 198
4.3 Examples of the Tuck-Folding Method 200
Chapter Summary 212
Problems 212
References 215
5 Kinematics of Origami Structures with Smooth Folds 217
5.1 Introduction 217
5.2 Fundamental Concepts 220
5.3 Shape Formulation of Smooth Folds 224
5.3.1 Continuity Conditions for Smooth Folds 229
5.3.2 Fold Parameterization Examples 233
5.4 Fold Pattern Description 234
5.5 Kinematic Constraints for Origami with Smooth Folds 241
5.5.1 Developability Constraint 241
5.5.2 Loop Closure Constraints 242
5.6 Folding Map Formulation 257
5.6.1 Parameters Required to Derive the Folding Map 258
5.6.2 Folding Map Formulation 262
5.7 Computational Implementation of the Model 264
5.8 Simulation Examples of the Kinematic Model 268
Chapter Summary 278
Problems 280
References 282
6 Unfolding Polyhedra Method for the Design of Origami Structures with Smooth Folds 285
6.1 Introduction 285
6.2 Unfolding Polyhedra Method Considering Smooth Folds 286
6.2.1 Problem Definition 286
6.2.2 Face Trimming Step 290
6.3 Examples of the Unfolding Polyhedra Method 294
Chapter Summary 300
Problems 301
References 306
7 Tuck-Folding Method for the Design of Origami Structures with Smooth Folds 309
7.1 Introduction 309
7.2 Tuck-Folding Method Considering Smooth Folds 310
7.2.1 Problem Definition 310
7.2.2 Face Trimming Step 313
7.2.3 Edge Module Parameterization and Constraints 316
7.2.3.1 Loop Closure Constraints 316
7.2.3.2 Constraints for Valid Edge Module Geometry 321
7.2.3.3 Constraints to Prevent Intersections Among Tuck-Folded Edge Modules 321
7.2.3.4 Summary of Design Constraints 323
7.3 Examples of the Tuck-Folding Method 323
7.3.1 Design and Fabrication of Shape Memory Polymer Self-Folding Sheets 335
7.3.1.1 Fabrication of Shape Memory Polymer Active Folds 335
7.3.1.2 Self-Folding Behavior of Shape Memory Polymer Sheets 337
Chapter Summary 341
Problems 342
References 345
8 Structural Mechanics and Design of Active Origami Structures 347
8.1 Introduction 347
8.2 Kinematics of Origami Structures with Smooth Folds of Non-Zero Thickness 348
8.3 Structural Mechanics Modeling Approach 355
8.3.1 Conservation of Linear and Angular Momentum 355
8.3.2 Constitutive Equations 357
8.3.3 Boundary Value Problem 358
8.3.4 Variational Formulation 358
8.4 Structural Mechanics Model Formulation 359
8.4.1 Model Development 359
8.4.2 Numerical Implementation 363
8.4.2.1 Quadrature Rules for Numerical Integration 368
8.5 Examples of the Implemented Model 370
8.5.1 Examples of Structures Having One Fold 370
8.5.2 Examples of Structures Having One Fold Intersection 375
8.5.3 Examples of Structures Having Multiple Fold Intersections 377
8.5.4 Computational Efficiency Comparison 379
8.6 Unfolding Polyhedra Method for the Design of Self-Folding Structures 381
8.7 Tuck-Folding Method for the Design of Self-Folding Structures 394
8.7.1 Design of a Self-Folding Parabolic Antenna Using the Tuck-Folding Method 404
8.7.1.1 Antenna Design Problem 405
8.7.1.2 Results of the Antenna Design Exploration Study 410
Chapter Summary 416
Problems 416
References 421
Appendix A Notation and Useful Formulas 426
A.1 Vectors in Three-Dimensional Space 426
A.2 Vectors of Arbitrary Dimensions 432
A.3 Matrices of Arbitrary Dimensions 433
A.4 Block Matrices 435
A.5 Systems of Linear Equations 437
Problems 439
Appendix B Examples of Implementation Codes 441
B.1 Implementation of the Kinematic Model for Origami with Creased Folds (Chap.2) 441
B.2 Implementation of the Unfolding Polyhedra Method for Origami with Creased Folds (Chap.3) 445
B.3 Implementation of the Tuck-Folding Method for Origami with Creased Folds (Chap.4) 448
B.4 Implementation of the Kinematic Model for Origami with Smooth Folds (Chap.5) 454
B.5 Implementation of the Unfolding Polyhedra Method for Origami with Smooth Folds (Chap.6) 460
B.6 Implementation of the Tuck-Folding Method for Origami with Smooth Folds (Chap.7) 463
Appendix C Constitutive Models 469
C.1 Linear Elastic Materials 469
C.2 Thermoelastic Materials 470
C.3 Piezoelectric Materials 470
C.4 Phase Transforming Materials 471
References 476
Index 477

Produkt-Details

• Erscheint lt. Verlag: 12.7.2018
• Zusatzinfo: XXI, 464 p. 263 illus., 38 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Active materials • Adaptive origami structures • Chemically-activated self-folding structures • Design parametrization and constraints • Electrically-activated self-folding structures • Individual fold analysis • Magnetically-activated self-folding structures • numerical implementation • Origami with creased folds • Origami with smooth folds • Self-folding structures • Structural mechanics model formulation • Thermally-activated self-folding structures
• ISBN-10: 3-319-91866-4 / 3319918664
• ISBN-13: 978-3-319-91866-2 / 9783319918662