Mechanics Modeling of Non-rigid Origami: From Qualitative to Quantitative Accuracy

Origami, the ancient art of paper folding, has recently evolved into a design and fabrication framework for various engineering systems at vastly different scales: from large-scale deployable airframes to mesoscale biomedical devices to small-scale DNA machines. The increasingly diverse applications of origami require a better understanding of the fundamental mechanics and dynamics induced by folding. Therefore, formulating a high-fidelity simulation model for origami is crucial, especially when large amplitude deformation/rotation exists during folding. The currently available origami simulation models can be categorized into three branches: rigid-facet models, bar-hinge models, and finite element models. The first branch of models assumes that the origami facets are rigid panels and creases behaving like hinges. It is a powerful tool for kinematics analysis without unnecessary complexities. On the other hand, the bar-hinge models have become widely used for simulating nonrigid-foldable origamis. The basic idea of these models is to place stretchable bar elements along the creases and across facet diagonals, discretizing the continuous origami into a pin-jointed truss frame system. Therefore, one can analyze facet deformations, including in-plane shearing, out-of-plane bending, and twisting. Moreover, more complex crease deformations can also be captured by adding appropriate components to the bar-hinge models. Because of their simplicity and modeling capability, the bar-hinge models have been utilized with many successes in analyzing the global deformation of non-rigid origami and uncovering its mechanical principles. However, one can only achieve qualitatively accurate predictions of the bar-hinge models compared to the physical experiments, especially when complex deformation exists during origami folding. The third branch, finite element models, does not impose explicit simplification on the facet deformation using shell elements. It can accurately analyze the deformation modes of origami structures; however, their disadvantages are also evident. On the one hand, it requires a time-consuming cycle for both modeling and computing, including pre-processing and post-processing. On the other hand, the traditional shell element might experience convergence issues when large and dynamic rotations occur, as commonly observed in origami systems. This thesis investigates the mechanics modeling of non-rigid origami and proposes a new dynamic model based on Absolute Nodal Coordinate Formulation (ANCF hereafter). Firstly, we discuss the accuracy of the widely used bar-hinge model through a case study on the multi-stability behavior in a non-rigid stacked Miura-origami structure. The model successfully investigates the underpinning principles of the multi-stability behavior in non-rigid origami and finds the existence of asymmetric energy barriers for extension and compression by tailoring its crease stiffness and facet bending stiffness. This interesting phenomenon can be exploited to create a mechanical diode. Experiment results confirm the existence of asymmetric multi-stability; however, the model\u27s prediction is only qualitatively verified due to its assumption of discrete lattices. In the next part, we develop a new origami mechanics model based on ANCF, a powerful modeling tool for the nonlinear dynamic simulation of multibody systems with large rotation and deformation. The new model treats origami as ANCF thin plate elements rotating around compliant creases, and the so-called torsional spring damper connectors are developed and utilized to simulate crease folding. Finally, its modeling accuracy is experimentally validated through two case studies, including motion analysis of simple fold mechanism and dynamic deployment of Miura-ori structures. The new origami simulation model can be used to quantitatively predict the dynamic responses of non-rigid origami with complex deformations. It can help deepen our knowledge of folding-induced mechanics and dynamics and broaden the application of origami in science and engineering

GBT-based buckling analysis using the exact element method

Generalised Beam Theory (GBT), intended to analyse the structural behaviour of prismatic thin-walled members and structural systems, expresses the member local and/or global deformed configuration as a combination of cross-section deformation modes multiplied by the corresponding longitudinal amplitude functions. The determination of the latter, usually the most computer-intensive step of the analysis, is almost always performed by means of GBT-based conventional 1D (beam) finite elements, using Hermite cubic polynomials as shape functions. This paper presents the formulation, implementation and application of a new GBT-based exact element, developed in the context of member (linear) buckling analyses. This exact element, originally proposed by Eisenberger (1990), approximates the modal longitudinal amplitude functions by means of power series, whose coefficients are obtained by means of a recursive formula – since the higher-order coefficients tend to vanish, the method has the potential to become exact (up to computer precision). The buckling load parameters are the solutions of the (highly) non-linear characteristic equation associated with the buckling eigenvalue problem. A few numerical illustrative examples are presented, focusing mainly on the comparison between the combined accuracy and computational effort associated with the determination of buckling solutions with the exact and standard GBT-based (finite) elements. This comparison provides evidence that the exact element leads to equally accurate results with less degrees of freedom and, moreover, without the need to define a (longitudinal) mesh the relative efficiency of the exact element is higher when the buckling modes exhibit larger half-wave numbers.Fundação para a Ciência e Tecnologia (FCT) através do Projeto nº SFRH/BPD/98111/2013

Developing Advanced Shape Sensing Methodologies for Aerospace Applications

L'abstract è presente nell'allegato / the abstract is in the attachmen

Long-span cold-formed steel single C-section portal frames

This thesis presents a comprehensive study of long-span cold-formed steel single C-section portal frames. The study includes the formulation of a nonlinear beam finite element for thin-walled sections, a series of full-scale frame tests and component tests, finite element modelling and advanced analysis followed by the formulation of design guidelines. The study was aimed at exploring the structural behaviour through experiment and numerical analysis towards developing provisions for the design of cold-formed steel portal frames using Advanced Analysis. A nonlinear thin-walled beam element for general open cross-sections was formulated, incorporating warping effect and non-coincident location of the shear centre and the centroid. It was successfully implemented in the geometric nonlinear analysis framework of the OpenSees finite element software. Towards investigating the behaviour and determining the ultimate strength, six full-scale tests on cold-formed steel single C-section portal frames were conducted. Separate tests were performed on frame connections, point-fastener connections and coupons to obtain the material parameters required for numerical modelling. Advanced shell finite element models of the full-scale frames and frame connections were created and validated against experimental results. The bolts and screws used for the connections between components were represented by point-based deformable fasteners. The force-deformation characteristics of the deformable fasteners were incorporated and successfully implemented in the Advanced Analysis. The strength of cold-formed steel single C-section portal frames determined by the Direct Strength Method and the Direct Design Method were compared. To account for inherent uncertainties in the strength of CFS portal frames, system resistance factors were derived. It was concluded that the Direct Design Method using Advanced Analysis is the likely future method for the design of cold-formed steel portal frames

Development of three-dimensional finite element software for curved plate girder and tub girder bridges during construction

Because of its ability to be easily shaped, steel is an attractive material for curved girders. Plate girder and tub girder bridges, for example, are often the preferred solution for direct connectors in highway networks. This flexibility in fabrication, however, presents challenges for structural engineers because of the difficulties associated with accounting for combined bending and torsion with curved geometry. The potential presence of skewed supports is a further source of complexity. In fact, no commercial structural engineering program currently addresses the evaluation of plate girder and tub girder bridges while modeling them to the full extent of their three-dimensional configuration. Most engineers, for example, use a two-dimensional bridge representation, which is often accurate for typical design of a complete bridge but may also be unconservative in many cases. The few programs that allow a full three-dimensional representation require extensive knowledge of finite element theory as well as significant time to model any complex structure. This dissertation presents the assumptions, methodology and calculations involved in the programming of a new structural engineering program designed to assess the behavior and stability or curved plate girder and tub girder bridges during erection or deck placement. It then illustrates the capabilities of the program for various structural systems subjected to a variety of loads, from self-weight to wind and temperature loads. In addition to a linear elastic analysis, multiple types of analysis are offered to the engineer: a geometrically nonlinear analysis provides a more accurate behavior for flexible systems, a linearized buckling analysis yields an upper bound evaluation of the stability of the structure, while a modal dynamic analysis estimates the free vibration modes of that structure.Civil, Architectural, and Environmental Engineerin

A finite element method for geometrically nonlinear large displacement problems in thin, elastic plates and shells

A finite element method is presented for geometrically nonlinear large displacement problems in thin, elastic plates and shells of arbitrary shape and boundary conditions subject to externally applied concentrated or distributed loading. The initially flat plate or curved shell is idealized as an assemblage of flat, triangular plate, finite elements representing both membrane and flexural properties. The \u27geometrical\u27 stiffness of the resulting eighteen degree-of-freedom triangular element is derived from a purely geometrical standpoint. This stiffness in conjunction with the standard small displacement \u27elastic\u27 stiffness is used in the linear-incremental approach to obtain numerical solutions to the large displacement problem. Only stable equilibrium configurations are considered and engineering strains are assumed to remain small. Four examples are presented to demonstrate the validity and versatility of the method and to point out its deficiencies --Abstract, page ii

Direct Strength Method for the Design of Cold-Formed Steel Sections Under Localised Loading

The main objective of the thesis is the development of the Direct Strength Method (DSM) for the design of cold-formed steel sections under general localised loading. In order to calibrate the DSM equations, it is necessary to have three main input variables which are the buckling load, the yield load and the experimental data. The first objective of this research is the development of the Finite Strip Method (FSM) theory for analysis of thin-walled sections under localised loading with general end boundary conditions to determine the buckling load as described in Chapters 3 and 4 of the thesis. The theory is included in Version 2.0 of the THIN-WALL-2 program which can be used for analysing structural members under generalised loading conditions as described in Chapter 5. The second objective is the formulation of plastic mechanism models to estimate the yield load of thin-walled sections subjected to localised loading. In order to establish these models, observations are performed from experiments to ascertain the failure modes of structural members under localised loading with different cross-sections, load cases and flange fastening conditions. From the data, new simple plastic mechanism models are built-up based on the concept of the balance between the internal energy of the structural member and the external energy of the applied loads to estimate the yield load as described in Chapter 6. The third objective is collating the experimental data of thin-walled sections under localised loading. The data is collected from previous literature for different types of cross-sections: un-lipped plain-C, lipped plain-C, SupaCee and Dimond Hi-Span channel (DHS) sections subjected to all load cases. In addition, both flange fastened and unfastened conditions are assembled in the experimental database as described in Chapter 6. From these three input variables, the DSM design equations are proposed for structural members under general localised loading. The method is a consistent and simplified model generalised for all localised load cases. It includes both an inelastic reserve component as observed in testing and a yield load component. Also, a reliability analysis calibration is performed to validate the accuracy of the DSM predictions with the collected experimental data as described in Chapter 7

Research in structural and solid mechanics, 1982

Advances in structural and solid mechanics, including solution procedures and the physical investigation of structural responses are discussed