Geometry-based structural analysis and design via discrete stress functions

This PhD thesis proposes a direct and unified method for generating global static equilibrium for 2D and 3D reciprocal form and force diagrams based on reciprocal discrete stress functions. This research combines and reinterprets knowledge from Maxwell’s 19th century graphic statics, projective geometry and rigidity theory to provide an interactive design and analysis framework through which information about designed structural performance can be geometrically encoded in the form of the characteristics of the stress function. This method results in novel, intuitive design and analysis freedoms. In contrast to contemporary computational frameworks, this method is direct and analytical. In this way, there is no need for iteration, the designer operates by default within the equilibrium space and the mathematically elegant nature of this framework results in its wide applicability as well as in added educational value. Moreover, it provides the designers with the agility to start from any one of the four interlinked reciprocal objects (form diagram, force diagram, corresponding stress functions). This method has the potential to be applied in a wide range of case studies and fields. Specifically, it leads to the design, analysis and load-path optimisation of tension-and compression 2D and 3D trusses, tensegrities, the exoskeletons of towers, and in conjunction with force density, to tension-and-compression grid-shells, shells and vaults. Moreover, the abstract nature of this method leads to wide cross-disciplinary applicability, such as 2D and 3D discrete stress fields in structural concrete and to a geometrical interpretation of yield line theory

Structure formation and identification in geometrically driven soft matter systems

Subdividing space through interfaces leads to many space partitions that are relevant to soft matter self-assembly. Prominent examples include cellular media, e.g. soap froths, which are bubbles of air separated by interfaces of soap and water, but also more complex partitions such as bicontinuous minimal surfaces. Using computer simulations, this thesis analyses soft matter systems in terms of the relationship between the physical forces between the system’s constituents and the structure of the resulting interfaces or partitions. The focus is on two systems, copolymeric self-assembly and the so-called Quantizer problem, where the driving force of structure formation, the minimisation of the free-energy, is an interplay of surface area minimisation and stretching contributions, favouring cells of uniform thickness. In the first part of the thesis we address copolymeric phase formation with sharp interfaces. We analyse a columnar copolymer system “forced” to assemble on a spherical surface, where the perfect solution, the hexagonal tiling, is topologically prohibited. For a system of three-armed copolymers, the resulting structure is described by solutions of the so-called Thomson problem, the search of minimal energy configurations of repelling charges on a sphere. We find three intertwined Thomson problem solutions on a single sphere, occurring at a probability depending on the radius of the substrate. We then investigate the formation of amorphous and crystalline structures in the Quantizer system, a particulate model with an energy functional without surface tension that favours spherical cells of equal size. We find that quasi-static equilibrium cooling allows the Quantizer system to crystallise into a BCC ground state, whereas quenching and non-equilibrium cooling, i.e. cooling at slower rates then quenching, leads to an approximately hyperuniform, amorphous state. The assumed universality of the latter, i.e. independence of energy minimisation method or initial configuration, is strengthened by our results. We expand the Quantizer system by introducing interface tension, creating a model that we find to mimic polymeric micelle systems: An order-disorder phase transition is observed with a stable Frank-Caspar phase. The second part considers bicontinuous partitions of space into two network-like domains, and introduces an open-source tool for the identification of structures in electron microscopy images. We expand a method of matching experimentally accessible projections with computed projections of potential structures, introduced by Deng and Mieczkowski (1998). The computed structures are modelled using nodal representations of constant-mean-curvature surfaces. A case study conducted on etioplast cell membranes in chloroplast precursors establishes the double Diamond surface structure to be dominant in these plant cells. We automate the matching process employing deep-learning methods, which manage to identify structures with excellent accuracy

Arbitrary views of high-dimensional space and data

Computer generated images of three dimensional scenes objects are the result of parallel/perspective projections of the objects onto a two dimensional plane. The computational techniques may be extended to project n-dimensional hyperobjects onto (n-1) dimensions, for n \u3e 3. Projection to one less dimension may be applied recursively for data of any high dimension until that data is two-dimensional, when it may be directed to a computer screen or to some other two-dimensional output device. Arbitrary specification of eye location, target location, field-of-view angles and other parameters provide flexibility, so that data may be viewed-and hence perceived-in previously unavailable ways. However, arbitrary views may also increase the computational requirements, and may complicate the user\u27s task in preparing and interpreting a view. Data with a dimension greater than three are difficult to perceive geometrically, yet may be invaluable to the observer. This study designs and implements a data visualisation system which incorporates arbitrary views of high-dimensional objects using repeated hyperplanar projection

Applications of Non-Orthogonal Waveforms and Artificial Neural Networks in Wireless Vehicular Communications

Ph. D. ThesisWe live in an ever increasing world of connectivity. The need for highly robust, highly efficient wireless communication has never been greater. As we seek to squeeze better and better performance from our systems, we must remember; even though our computing devices are increasing in power and efficiency, our wireless spectrum remains limited. Recently there has been an increasing trend towards the implementation of machine learning based systems in wireless communications. By taking advantage of a neural networks powerful non-linear computational capability, communication systems have been shown to achieve reliable error free transmission over even the most dispersive of channels. Furthermore, in an attempt to make better use of the available spectrum, more spectrally efficient physical layer waveforms are gathering attention that trade increased interference for lower bandwidth requirements. In this thesis, the performance of neural networks that utilise spectrally efficient waveforms within harsh transmission environments are assessed. Firstly, we investigate and generate a novel neural network for use within a standards compliant vehicular network for vehicle-to-vehicle communication, and assess its performance practically in several of the harshest recorded empirical channel models using a hardware-in-the-loop testing methodology. The results demonstrate the strength of the proposed receiver, achieving a bit-error rate below 10−3 at a signal-to-noise ratio (SNR) of 6dB. Secondly, this is then further extended to utilise spectrally efficient frequency division multiplexing (SEFDM), where we note a break away from the 802.11p vehicular communication standard in exchange for a more efficient use of the available spectrum that can then be utilised to service more users or achieve a higher data throughput. It is demonstrated that the proposed neural network system is able to act as a joint channel equaliser and symbol receiver with bandwidth compression of up to 60% when compared to orthogonal frequency division multiplexing (OFDM). The effect of overfitting to the training environment is also tested, and the proposed system is shown to generalise well to unseen vehicular environments with no notable impact on the bit-error rate performance. Thirdly, methods for generating inputs and outputs of neural networks from complex constellation points are investigated, and it is reasoned that creating ‘split complex’ neural networks should not be preferred over ‘contatenated complex’ neural networks in most settings. A new and novel loss function, namely error vector magnitude (EVM) loss, is then created for the purposes of training neural networks in a communications setting that tightly couples the objective function of a neural network during training to the performance metrics of transmission when deployed practically. This loss function is used to train neural networks in complex environments and is then compared to popular methods from the literature where it is demonstrated that EVM loss translates better into practical applications. It achieved the lowest EVM error, thus bit-error rate, across all experiments by a margin of 3dB when compared to its closest achieving alternative. The results continue and show how in the experiment EVM loss was able to improve spectral efficiency by 67% over the baseline without affecting performance. Finally, neural networks combined with the new EVM loss function are further tested in wider communication settings such as visible light communication (VLC) to validate the efficacy and flexibility of the proposed system. The results show that neural networks are capable of overcoming significant challenges in wireless environments, and when paired with efficient physical layer waveforms like SEFDM and an appropriate loss function such as EVM loss are able to make good use of a congested spectrum. The authors demonstrated for the first time in practical experimentation with SEFDM that spectral efficiency gains of up to 50% are achievable, and that previous SEFDM limitations from the literature with regards to number of subcarriers and size of the transmit constellation are alleviated via the use of neural networksEPSRC, Newcastle Universit

Modelling and characterisation of porous materials

Porous materials possessing random microstructures exist in both organic (e.g. polymer foam, bone) and in-organic (e.g. silica aerogels) forms. Foams and aerogels are two such materials with numerous engineering and scientific applications such as light-weight cores in sandwich structures, packaging, impact and crash structures, filters, catalysts and thermal and electrical insulators. As such, design and manufacture using these materials is an important task that can benefit significantly from the use of computer aided engineering tools. With the increase in computational power, multi-scale modelling is fast becoming a powerful and increasingly relevant computational technique. Ultimately, the aim is to employ this technique to decrease the time and cost of experimental mechanical characterisation and also to optimise material microstructures. Both these goals can be achieved through the use of multi-scale modelling to predict the macro-mechanical behaviour of porous materials from their microstructural morphologies, and the constituent materials from which they are made. The aim of this work is to create novel software capable of generating realistic randomly micro-structured material models, for convenient import into commercial finite element software. An important aspect is computational efficiency and all techniques are developed paying close attention to the computation time required by the final finite element simulations. Existing methods are reviewed and where required, new techniques are devised. The research extensively employs the concept of the Representative Volume Element (RVE), and a Periodic Boundary Condition (PBC) is used in conjunction with the RVEs to obtain a volume-averaged mechanical response of the bulk material from the micro-scale. Numerical methods such as Voronoi, Voronoi-Laguerre and Diffusion Limited Cluster-Cluster Aggregation are all employed in generating the microstructures, and where necessary, enhanced in order to create a wide variety of realistic microstructural morphologies, including mono-disperse, polydisperse and isotropic microstructures (relevant to gas-expanded foam materials) as well as diffusion-based microstructures (relevant for aerogels). Methods of performing large strain simulations of foams microstructures, up to and beyond the onset strain of densification are developed and the dependence of mechanical response on the size of an RVE is considered. Both mechanical and morphological analysis of the RVEs is performed in order to investigate the relationship between mechanical response and internal microstructural morphology of the RVE. The majority of the investigation is limited to 2-d models though the work culminates in extending the methods to consider 3-d microstructures