Origami as a Tool for Mathematical Investigation and Error Modelling in Origami Construction

Origami is the ancient Japanese art of paper folding. It has inspired applications in industries ranging from Bio-Medical Engineering to Architecture. This thesis reviews ways in which Origami is used in a number of fields and investigates unexplored areas providing insight and new results which may lead to better understanding and new uses. The OSME conference series arguably covers most of the research activities in the field of Origami and its links to Science and Mathematics. The thesis provides a comprehensive review of the work that has been presented at these conferences and published in their proceedings. The mathematics of Origami has been explored before and much of the fundamental work in this field is presented in chapter 3. Here an attempt is made to push the bounds of this field by suggesting ways in which Origami can be used as a mathematical tool for in-depth exploration of non trivial problems. A particular problem we consider is the 4-colour theorem and its proof. Looking at some well known methods for producing angles and lengths mathematically the thesis also explores how accurate these might be. This leads to the surprisingly unstudied field of error modelling in Origami. Errors in folding processes have not previously been looked at from a mathematical point of view. The thesis develops a model for error estimation in crease patterns and a framework for error modelling in Origami applications. By introducing a standardised error into alignments, uniform error bounds for each of the one-fold constructions are generated. This defines a region in which a crease could lie in order to satisfy the alignments of a given fold within a specified tolerance. Analysis of this method on some examples provides insight into how this might be used in multi-fold constructions. An algorithm to that effect is introduced

Modeling and Programming Shape-Morphing Structured Media

Shape-morphing and self-propelled locomotion are examples of mechanical behaviors that can be "programmed" in structured media by designing geometric features at micro- and mesostructural length scales. This programmability is possible because the small-scale geometry often imposes local kinematic modes that are strongly favored over other deformations. In turn, global behaviors are influenced by local kinematic preferences over the extent of the structured medium and by the kinematic compatibility (or incompatibility) between neighboring regions of the domain. This considerably expands the design space for effective mechanical properties, since objects made of the same bulk material but with different internal geometry will generally display very different behaviors. This motivates pursuing a mechanistic understanding of the connection between small-scale geometry and global kinematic behaviors. This thesis addresses challenges pertaining to the modeling and design of structured media that undergo large deformations. The first part of the thesis focuses on the relation between micro- or mesoscale patterning and energetically favored modes of deformation. This is first discussed within the context of twisted bulk metallic glass ribbons whose edges display periodic undulations. The undulations cause twist concentrations in the narrower regions of the structural element, delaying the onset of material failure and permitting the design of structures whose deployment and compaction emerge from the ribbons' chirality. Following this discussion of a periodic system, we study sheets with non-uniform cut patterns that buckle out-of-plane. Motivated by computational challenges associated with the presence of geometric features at disparate length scales, we construct an effective continuum model for these non-periodic systems, allowing us to simulate their post-buckling behavior efficiently and with good accuracy. The second part of the thesis discusses ways to leverage the connection between micro/mesoscale geometry and energetically favorable local kinematics to create "programmable matter" that undergo prescribed shape changes or self-propelled locomotion when exposed to an environmental stimulus. We first demonstrate the capabilities of an inverse design method that automates the design of structured plates that morph into target 3D geometries over time-dependent actuation paths. Finally, we present devices made of 3D-printed liquid crystal elastomer (LCE) hinges that change shape and self-propel when heated.</p

Kinematics, Structural Mechanics, and Design of Origami Structures with Smooth Folds

Origami provides novel approaches to the fabrication, assembly, and functionality of engineering structures in various fields such as aerospace, robotics, etc. With the increase in complexity of the geometry and materials for origami structures that provide engineering utility, computational models and design methods for such structures have become essential. Currently available models and design methods for origami structures are generally limited to the idealization of the folds as creases of zeroth-order geometric continuity. Such an idealization is not proper for origami structures having non-negligible thickness or maximum curvature at the folds restricted by material limitations. Thus, for general structures, creased folds of merely zeroth-order geometric continuity are not appropriate representations of structural response and a new approach is needed. The first contribution of this dissertation is a model for the kinematics of origami structures having realistic folds of non-zero surface area and exhibiting higher-order geometric continuity, here termed smooth folds. The geometry of the smooth folds and the constraints on their associated kinematic variables are presented. A numerical implementation of the model allowing for kinematic simulation of structures having arbitrary fold patterns is also described. Examples illustrating the capability of the model to capture realistic structural folding response are provided. Subsequently, a method for solving the origami design problem of determining the geometry of a single planar sheet and its pattern of smooth folds that morphs into a given three-dimensional goal shape, discretized as a polygonal mesh, is presented. The design parameterization of the planar sheet and the constraints that allow for a valid pattern of smooth folds and approximation of the goal shape in a known folded configuration are presented. Various testing examples considering goal shapes of diverse geometries are provided. Afterwards, a model for the structural mechanics of origami continuum bodies with smooth folds is presented. Such a model entails the integration of the presented kinematic model and existing plate theories in order to obtain a structural representation for folds having non-zero thickness and comprised of arbitrary materials. The model is validated against finite element analysis. The last contribution addresses the design and analysis of active material-based self-folding structures that morph via simultaneous folding towards a given three-dimensional goal shape starting from a planar configuration. Implementation examples including shape memory alloy (SMA)-based self-folding structures are provided

Development of a window system with optimised ventilation and noise-reduction performance: an approach using metamaterials.

Noise transmission is a key factor regarding indoor comfort and energy-smart Architecture and Engineering. In most cases, occupants of the building must choose between a naturally ventilated indoor environment or a quiet one. On the other hand, the acoustic metamaterials (AMMs) allow more customisable physical properties according to their spatial configurations, proving significant merits over traditional architecture and engineering materials. This PhD study will investigate AMMs techniques to develop a window system that can control the incoming noise while allowing natural ventilation. This is a crucial point for AMMs research. So far, even if many solutions have been developed to pursue this objective, they still lack ergonomics and human perception analysis. Through a multi-disciplinary methodology, the author first a) highlighted which are the ergonomic principles that add value to the window system from the users perspective, then b) investigated a series of suitable AMMs techniques to be applied for noise reduction and natural ventilation, c) developed a specific AMM design suitable to follow those ergonomic principles previously highlighted and assessed it through human perception, and finally d) optimised a full-scale prototype for a broad acoustic range and customisable ergonomic application. Social science, ergonomic, numerical, analytical and experimental studies were used throughout the PhD project to draw a full-scale window prototype using AMMs to allow natural ventilation independently from the outdoor noise situation. The so-called acoustic metawindow (AMW) allows Transmission Loss (TL) of 10-80dB on a significant frequency range for human hearing (50-5000Hz) in an open configuration while allowing sufficient natural ventilation. In addition, the AMW is proved to positively impact the indoor environment from both physical and human perception points of view thanks to its ergonomic nature. This project will open a new AMMs field of investigation that is not limited to noise reduction but also includes outdoor stimuli optimisation towards a more comprehensive indoor comfort

Modeling of High Pressure Confined Inflatable Structures

Safety of transportation tunnels is a top priority among transportation agencies and public administrators and a very important aspect in the daily operation of a tunnel system. However, it is always a challenge to create and integrate protection systems in existing tunnels to prevent or at least mitigate the occurrence of hazardous events such as spread of smoke or noxious fumes, flooding, among others. Typically there two ways for preventing or mitigating the occurrence of hazardous events: one is the implementation of permanent solutions and, the second one, is the use of temporary solutions. Permanent solutions usually have relatively high sealing efficiency due to their solid and rigid sealing mechanisms such as bulkheads and floodgates. However, they can be extremely expensive and sometimes difficult to build or install due to physical, economical or operational constraints. On the other hand, temporary solutions, which can be relatively low cost and easy to install, offer a temporary countermeasure while permanent repairs are implemented. The development of flexible structures, such as inflatable plugs for temporary solutions is becoming a viable alternative for protection of transportation tunnels and other similar critical civil infrastructure.;The Resilient Tunnel System (RTS) is a passive tunnel protection system developed at West Virginia University (WVU). This system is intended to prevent or minimize the damage induced by hazardous events by creating a compartment to contain the threat. The Resilient Tunnel System implements inflatable structures at specific locations of the tunnel to seal up the tunnel and create a compartment to isolate the compromised region. WVU has conducted several validation tests on full scale inflatable structures designed to mitigate flooding in an actual rail transportation tunnel and in specially built testing facilities. However, testing at full scale either in an actual tunnel or in specially built testing facilities, is a very complex and resource demanding task. It can take several iterations to achieve desired results which cannot be accurately predicted in advance. Therefore, the development of numerical models using Finite Element Analysis becomes imperative in order to: first, reproduce experimental work done at WVU using different prototypes at different scales; and then use the calibrated models as predicting tool that can anticipate the outcome of experiments and eventually reduce its number due to the intrinsic complexity and cost.;This dissertation aims to present the results of the development of Finite Element Models of confined inflatable structures designed to withstand flooding pressures. Models of different prototypes were created and analyzed in order to reproduce experimental results. Numerical results show that the adjusted models can reproduce experimental results, ranging from deployment, full pressurization and induced failure, with a great degree of accuracy providing a reliable predicting tool for evaluation of alternative configurations and parametric studies

Folded Sandwich Protective Structures against Blast and Impact Loads

In this thesis, novel folded truncated pyramid structures and a bi-directional load-self-cancelling square dome structure are proposed as the core of light-weight protective sandwich structures to resist blast and impact loads. Analytical derivations, numerical simulations, quasi-static and dynamic crushing tests are carried out to examine the dynamic crushing behaviours and energy absorption capacities of various designs for developing the best-performing core structures for blast and impact load resistance

4D printing of shape-changing thermo-responsive textiles

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonThis research reviews the state-of-the-art literature on the two-emerging material-driven Additive Manufacturing (AM) strategies, Functionally Graded Additive Manufacturing (FGAM) and 4D Printing (4DP) to recognise, select and implement the appropriate materials, design and fabrication methods to produce shape-changing thermo-responsive textiles. Shapememory polymers (SMPs) are required to provide the active properties required to sense and self-actuate when subjected to an appropriate stimulus over time. The current availability of SMPs for AM in the commercial market is limited and expensive. To ensure a wider uptake of 4DP, the aim of this research is to develop a material selection framework to discover, define and select commercially available thermoplastics as potential SMPs for use in material extrusion (ME) 4DP. The theoretical and practical knowledge to create a thermally actuated dual-state mechanism (DSM) active structure is described at a feasible level for users with different backgrounds and knowledge levels in 4DP. The experiments showed that commercial AM filaments could be used for 4DP, but not all materials exhibit shape memory properties despite belonging to the same material type. The shape recovery performance and repeatability of an SMP would also vary according to the programming condition. The next stage of this research details the development and testing of polymertextile composites using direct ME of PLA filaments on synthetic mesh fabrics. T-peel test results revealed that the compatibility between the printing material and the textile substrate fibre type has a dominant effect on the peel resistance of ME polymer-textile composite. The research demonstrated the use of 4DP as an alternative and novel technique for the 3D manipulation of textile fabrics. The shape transformation studies presented a proof-ofconcept that the accuracy of deformation and the shape-shifting patterns of the thermoresponsive textiles can be controlled by the geometrical dimensions and structural arrangement of the printed SMP structure on the textile substrate. The findings will enable researchers and designers to take advantage of the optimum parameters to discover new shape transformations and to create potential applications in the AM fashion and textile industry

Development of new approaches for characterising DNA origami-based nanostructures with atomic force microscopy and super-resolution microscopy

DNA nanotechnology has developed a versatile set of methods to utilise DNA self-assembly for the bottom-up construction of arbitrary two- and three-dimensional DNA objects in the nanometre size range, and to functionalise the structures with unprecedented site-specificity with nanoscale objects such as metallic and semiconductor nanoparticles, proteins, fluorescent dyes, or synthetic polymers. The advances in structure assembly have resulted in the application of functional DNA-based nanostructures in a gamut of fields from nanoelectronic circuitry, nanophotonics, sensing, drug delivery, to the use as host structure or calibration standard for different types of microscopy. However, the analytical means for characterising DNA-based nanostructures drag behind these advances. Open questions remain, amongst others in quantitative single-structure evaluation. While techniques such as atomic force microscopy (AFM) or transmission electron microscopy (TEM) offer feature resolution in the range of few nanometres, the number of evaluated structures is often limited by the time-consuming manual data analysis. This thesis has introduced two new approaches to quantitative structure evaluation using AFM and super-resolution fluorescence microscopy (SRM). To obtain quantitative data, semi-automated computational image analysis routines were tailored in both approaches. AFM was used to quantify the attachment yield and placement accuracy of poly(3-tri(ethylene glycol)thiophene)-b-oligodeoxynucleotide diblock copolymers on a rectangular DNA origami. This work has also introduced the first hybrid of DNA origami and a conjugated polymer that uses a highly defined polythiophene derivative synthesised via state-of-the-art Kumada catalyst-transfer polycondensation. Among the AFM-based studies on polymer-origami-hybrids, this was the first to attempt near-single molecule resolution, and the first to introduce computational image analysis. Using the FindFoci tool of the software ImageJ revealed attachment yields per handle between 26 - 33%, and determined a single block copolymer position with a precision of 80 - 90%. The analysis has pointed out parameters that potentially influence the attachment yield such as the handle density and already attached objects. Furthermore, it has suggested interactions between the attached polymer molecules. The multicolour SRM approach used the principles of single-molecule high-resolution co-localisation (SHREC) to evaluate the structural integrity and the deposition side of the DNA origami frame “tPad” based on target distances and angles in a chiral fluorophore pattern the tPads were labelled with. The computatinal routine that was developed for image analysis utilised clustering to identify the patterns in a sample’s signals and to determine their characteristic distances and angles for hundreds of tPads simultaneously. The method excluded noise robustly, and depicted the moderate proportion of intact tPads in the samples correctly. With a registration error in the range of 10 -15 nm after mapping of the colour channels, the precision of a single distance measurements on the origami appeared in the range of 20 - 30 nm. By broadening the scope of computational AFM image analysis and taking on a new SRM approach for structure analysis, this work has presented working approaches towards new tools for quantitative analysis in DNA nanotechnology. Furthermore, the work has presented a new approach to constructing hybrid structures from DNA origami and conjugated polymers, which will open up new possibilities in the construction of nanoelectronic and nanophotonic structures