GEOMETRIC MODELING AND DEPLOYMENT BEHAVIOR ANALYSIS OF CONICAL AND TOROIDAL ORIGAMI STRUCTURES

Abstract

Origami inspired structures are largely being recognized as efficient deployable structures that can serve multidisciplinary applications. The concepts of origami have been demonstrated as a valuable technique for developing different prismatic and non-prismatic deployable structural components. Recent progress has demonstrated a good amount of work on the design of origami patterns as well as their applications in multidisciplinary fields. The majority of the research work includes the origami patterns related to prismatic foldable cylinders and their applications. Although, the use of conical beams as deployable origami structures has not been investigated significantly despite their higher structural performance than prismatic cylinders. There is a wide scope of research in the design and analysis of conical and toroidal origami patterns. The research area of the analysis of cylindrical Kresling pattern has been lifted to an advanced stage. However, the research on the origami pattern design for differently shaped structures like conical and toroidal was left behind. Thus, ample opportunities are available for the researchers to explore the realm of origami inspired deployable conical and toroidal structures. In order to address these concerns, the geometric design algorithms are developed for origami based foldable conical and toroidal shaped structures; and the qualitative deployment behavior is investigated while considering geometric design parameters. The first part of this thesis deals with the design of origami folding patterns for deployable conical booms. The analytical algorithms for two type of origami patterns are presented, conical Kresling (1-6 origami) and conical Miura-ori (1-4 origami) pattern, to develop deployable conical booms. The packaging behavior of both types of patterns is investigated while considering respective design parameters. The axial truss modeling is employed to investigate the qualitative deployment behavior of conical origami structures. The bistability phenomenon is investigated using the strain energy concept. The development process of physical models of both conical origami patterns is presented to demonstrate the applicability of the proposed design algorithms. The second part of this thesis covers the geometric modeling and qualitative deployment behavior of toroidal origami structures. The mathematical modeling of the origami pattern design process is presented to develop deployable toroidal structures based on modified Kresling (1-6 origami) and modified Miura-ori patterns (1-4 origami). The packaging behavior of toroidal Kresling and toroidal Miura-ori pattern is investigated while considering respective design parameters. The numerical simulations of angular deployment are presented to investigate the qualitative deployment behavior of toroidal origami structures. The occurrence of the bistability phenomenon is discussed using the variation of strain energy of the model during deployment The development of single story as well as multi-story physical models of both toroidal origami patterns is presented to demonstrate the applicability of the proposed design algorithms. In the third part of the thesis, two experimental setups are developed to investigate the restoring force behavior of conical and toroidal origami structures considering various design parameters. The proposed experimental approach is utilized for the characterization of the origami structures based on their restoring force behavior. The experimental findings of the restoring force behavior forecast the similar qualitative behavior of the efforts required to deploy the structure obtained from analytical and numerical simulations. The proposed origami patterns advance the state of art related to origami inspired deployable structures and serves as a building block towards multi-disciplinary applications. This work is not limited to the design of thin shell deployable origami structures, whether it can be directly utilized to develop truss based deployable structures by replacing the fold lines by truss members, which enhances the domain of application of these origami patterns.