Thin-walled metallic components have been widely used as energy absorbers. One key drawback is the high initial crippling load, which typically results in passenger injuries. It is the objective of this study to introduce taper angle to thin-walled prisms, and to examine the crushing response of thin-walled frusta. Nonlinear finite element models of thin-walled frusta of different cross-sectional geometries were developed. Experimental investigations were conducted to validate these models. The effects of key design parameters on the energy absorption characteristics of frusta were explored. Comparison between thin-walled prisms and frusta show that taper angle helps to reduce the initial crippling load and increase the resistance to global buckling. To take advantage of the interaction effects, a novel multi-frusta configuration was developed and it was shown that the energy absorption efficiency is significantly increased. The results of this work are valuable for enhancing the crashworthiness performance of thin-walled metallic energy absorber.

Thin-walled metallic components have been widely used as energy absorbers. One key drawback is the high initial crippling load, which typically results in passenger injuries. It is the objective of this study to introduce taper angle to thin-walled prisms, and to examine the crushing response of thin-walled frusta. Nonlinear finite element models of thin-walled frusta of different cross-sectional geometries were developed. Experimental investigations were conducted to validate these models. The effects of key design parameters on the energy absorption characteristics of frusta were explored. Comparison between thin-walled prisms and frusta show that taper angle helps to reduce the initial crippling load and increase the resistance to global buckling. To take advantage of the interaction effects, a novel multi-frusta configuration was developed and it was shown that the energy absorption efficiency is significantly increased. The results of this work are valuable for enhancing the crashworthiness performance of thin-walled metallic energy absorber.

The adhesive contact problems of a conical frustum punch indenting a transversely isotropic elastic half space and an orthotropic elastic half space are analytically studied in this thesis work. To solve the problem involving a transversely isotropic half space, the harmonic potential function method and the Hankel transform are employed, which lead to a general closed-form solution for the adhesive contact problem. For the case with an orthotropic half space, the problem of a point load applied on the half space is first solved by using the double Fourier transform method. The solution for the adhesive contact problem is then obtained through integrating the former solutions over the punch surface.

In this thesis, new effective and efficient implementation structures of three-dimensional (3D) spatio-temporal (ST) Finite Impulse Response (FIR) uniform and non-uniform cone and frustum filters using well-known filter banks are investigated. The performance of the proposed implementation structures for 3D ST FIR uniform and non-uniform cone and frustum filters are investigated for 3D broadband beamforming in radio astronomy applications. First, implementations of two 3D ST uniform FIR cone filters are investigated. The 3D cone filters are designed by cascading either the well-known uniform quadrature mirror – cosine-modulated (QM-CM) filter bank or directly designed filter banks (DDFBs), with 2D low-pass circularly-symmetric spatial filters. In addition, two 3D ST uniform FIR frustum filters are derived from the cone filters by implementing partial bands of the filter banks with corresponding 2D spatial filters. The performance of the proposed implementation structures for 3D ST uniform QM-CM and DDFBs cone and frustum filters are evaluated using broadband beamforming signals in radio astronomy applications. The performance of the QM-CM and DDFBs cone and frustum filters shows improvement in terms of Signal-to-Interference-plus-Noise ratio (SINRs) over existing 3D ST cone and frustum filters. In addition to their effective performance, these cone and frustum filters can be efficiently implemented with equivalent or less computational complexity compared to existing methods. Second, implementations of two 3D ST non-uniform cone and frustum filters are explored. These cone and frustum filters are obtained by cascading either QM-CM or DDFBs non-uniform filter banks, with 2D low-pass circularly-symmetric spatial filters. The motivation for the 3D ST non-uniform cone and frustum filters is to achieve better approximation at low temporal frequencies than using the uniform ones. The performance of the 3D ST non-uniform cone and frustum filters is evaluated and compared with the performance of the uniform 3D ST cone and frustum filters. Results indicate that the performance of the proposed 3D ST non-uniform QM-CM and DDFBs cone filters shows some improvement in selective filtering compared to the performance of 3D ST uniform cone filters. / Graduate / 0544 / hussamss@uvic.ca

In this thesis, multidimensional signal processing techniques to mitigate disturbances in synthetic aperture systems such as radio telescopes are investigated. Here, two computationally efficient three-dimensional (3D) spatio-temporal (ST) finite impulse response (FIR) cone filter bank structures are proposed. Furthermore, a strategy is proposed to design 3D ST FIR frustum filter banks, having double-frustum-shaped passbands oriented along the temporal axis, derived from appropriate 3D ST FIR cone filter banks. Both types of cone and frustum filter banks are almost alias free and provide near-perfect reconstruction. In the proposed cone and frustum filter banks, both temporal and spatial filtering operations can be carried out at a significantly lower rate compared to previously reported 3D ST FIR cone filter banks implying lower power consumption. Furthermore, the proposed cone and frustum filter banks require a significantly lower computational complexity than previously reported 3D ST FIR cone and frustum filter banks. Importantly, this is achieved without deteriorating the improvement in signal-to-interference-plus-noise ratio. A theoretical analysis of brightness distribution (BD) errors caused by parameter perturbations and mismatches among the transfer functions of receivers employed in synthetic aperture systems is presented. First, the BD errors caused by perturbations in the transfer functions of low noise amplifiers (LNAs) and anti-aliasing filters (AAFs) are considered, and the characteristics of the additive BD error and its effects on synthesized BDs are thoroughly analyzed. Second, the conditions that should be satisfied by the transfer functions of digital beamformers to eliminate the BD errors caused by their phase responses are examined. The sufficient condition to eliminate the BD errors is that the transfer functions are matched, and, interestingly, the phase responses are not necessary to be linear. Furthermore, the BD errors caused by typical tolerances of passive L and C elements used to implement the AAFs and those caused by the random variations of gain from LNA to LNA are quantified through numerical simulations. The simulations indicate that substantial BD errors are observed at frequencies that are close to the passband edge of the AAFs. / Graduate

This study aims to comprehend the bistable and multi-stable behaviour of flexible straws with the intention of utilising it for future engineering applications. This behaviour is achieved by the multiple inversions of conical frustum shells within the corrugation of a flexible straw. This study examined the effects of various material models, geometry variables and loading methods on the inversion of close-top and open-top conical frustum shells via experiments and FEM simulations. This thesis consists of three main parts, and the second and the third parts are complementary to each other: First, we investigated the effects of applying a uniform vertical load to the upper rim of open-top frustum shells via FEM simulations. A reference model was simulated based on the measurements of an ordinary polypropylene flexible straw specimen, using two material models - linear elastic and elastically perfectly plastic. The effects of the interactions between frusta of the corrugated segment of a flexible straw were also studied by evaluating the difference in responses between an individual frustum and conjugated models of two or three frusta. It was found that by constraining the rotation of its bottom rim, an individual frustum can fairly reproduce the complex bistable behaviour of the shorter frustum within the corrugated part of a flexible straw. Furthermore, detailed parametric studies that focused on the effects of various geometric parameters were conducted and generalised formulas that predicted the critical force were derived. A comparison between the simulated results and the analytical model in predicting progressive inversion was made to distinguish the geometric boundaries that separate the one-off snap-through to the progressive inversion of frustum shells. Next, the behaviour of close-top frustum shells in response to vertical point loading at various locations on the top surface was evaluated. A hyperelastic material was used to fabricate the physical specimens. During the experiments, the corresponding deformed shapes were recorded by 3D scanning in addition to measurements of the displacement and reaction force. We observed a close resemblance between the experimental and FEM simulated results, which validated the FEM models. Two local peaks were observed before the structure was fully inverted into its secondary stable state and the overall critical force of the structure was defined by the higher one of the two. The relationship between their magnitudes and the loading locations was analysed and an optimal loading location which gave the minimum critical force was proposed and verified by additional simulations. Furthermore, generalised formulas in predicting critical force were also acquired based on parametric studies. The optimal loading location was found to be constant in spite of variations in height and thickness. The third part of this thesis discussed the effects of lateral point loading on both close-top and open-top frustum shells at various locations on the side surface and supplemented the second part. It is found that the removal of the top surface could cause the critical force to decrease if a point load was applied laterally. Moreover, we were able to fully invert the structure with a lower critical force through lateral loading in comparison to vertical loading.

[pt] A restituição de modelos tridimensionais complexos de engenharia tem sido um desafio para a computação gráfica desde seus primórdios, pois modelos detalhados são freqüentemente compostos de milhões de polígonos, enquanto as estações gráficas atuais são capazes de exibir, em taxas interativas, apenas algo da ordem de dezenas ou centenas de milhares de polígonos. Uma das formas de melhorar o desempenho de visualizadores de modelos tridimensionais é reduzir o número de polígonos passados para a cadeia de restituição, eliminando grandes grupos de polígonos determinados como não visíveis por estarem fora do volume de visão ou escondidos por outros polígonos. Neste trabalho, realizamos um estudo do uso de volumes envolventes para determinar os conjuntos de polígonos que são potencialmente visíveis, propomos uma forma de estruturar esses polígonos numa hierarquia de forma a diminuir os cálculos necessários para esse fim e compilamos uma série de resultados que permitem nortear o uso de volumes envolventes e a estruturação de modelos. / [en] Rendering complex three-dimensional Engineering models has been a challenge for Computer Graphics ever since its origin, as detailed models are often composed of millions of polygons while current graphic stations are able to display, at interactive rates, only dozens or hundreds of thousands of polygons. A way to increase the performance of viewers of three-dimensional models is to reduce the number of polygons passed to the rendering pipeline by eliminating large groups of polygons classified as non-visible for being out of the viewing frustum or hidden by other polygons. In this work, we study the use of bounding volumes to determine sets of polygons which are potentially visible, propose a way to structure such polygons in a hierarchy so as to restrict the necessary computations for this purpose, and compile a series of results which allow us to take some conclusions on the use of bounding volumes and model structuring.

Ray tracing is a graphical technique that provides realistic simulation of light sources and complex lighting effects within three-dimensional scenes, but it is a time-consuming process that requires a tremendous amount of compute power. In order to reduce the number of calculations required to render an image, many different algorithms and techniques have been developed. One such development is the use of tree-like data structures to partition space for quick traversal when finding intersection points between rays and primitives. Even with this technique, ray-primitive intersection for large datasets is still the bottleneck for ray tracing. This thesis proposes the use of a specific spatial data structure, the K-D tree, for faster ray casting of primary rays and enables a ray-triangle culling technique that compliments view frustum and backface culling. The proposed method traverses the entire tree structure to mark nodes to be inactive if it is outside of the view frustum and skipped if the triangle is a backface. In addition, a ray frustum is calculated to test the spatial coherency of the primary ray. The combination of these optimizations reduces the average number of intersection tests per ray from 98% to 99%, depending on the data size.

Despite advancements in the analysis of statnamic load testing data, there exists uncertainty with underlying procedural assumptions. Two such assumptions are that the system mass and soil-related damping coefficient remain constant throughout the loading event. These assumptions are the culprit of aberrant predictions of the static capacity at small displacements when the overall displacement is large. An exploration of the assumptions may validate prior existing test results as well as solidify the current analysis process. However, an exploration could also reveal an overestimation or underestimation of portions of the predicted static load responses. The testing program outlined herein consists of a two-phase sequential agenda devoted toward the preparation and familiarization of a new laboratory statnamic device. The first phase involves the development of user guidelines for accurately targeting a desired statnamic test, and the second incorporates the guidelines into a preliminary testing regime specifically targeted at determining a suspected strain-dependant statnamic damping coefficient. The steps taken in this thesis are intended to launch future research endeavors toward obtaining a better understanding of the statnamic damping coefficient.

[pt] Um dos problemas mais antigos da computação gráfica tem sido a determinação de visibilidade. Vários algoritmos têm sido desenvolvidos para viabilizar modelos cada vez maiores e detalhados. Dentre estes algoritmos, destaca-se o frustum culling, cujo papel é remover objetos que não sejam visíveis ao observador. Esse algoritmo, muito comum em várias aplicações, vem sofrendo melhorias ao longo dos anos, a fim de acelerar ainda mais a sua execução. Apesar de ser tratado como um problema bem resolvido na computação gráfica, alguns pontos ainda podem ser aperfeiçoados, e novas formas de descarte desenvolvidas. No que se refere aos modelos massivos, necessita-se de algoritmos de alta performance, pois a quantidade de cálculos aumenta significativamente. Este trabalho objetiva avaliar o algoritmo de frustum culling e suas otimizações, com o propósito de obter o melhor algoritmo possível implementado em CPU, além de analisar a influência de cada uma de suas partes em modelos massivos. Com base nessa análise, novas técnicas de frustum culling serão desenvolvidas, utilizando o poder computacional da GPU (Graphics Processing Unit), e comparadas com o resultado obtido apenas pela CPU. Como resultado, será proposta uma forma de frustum culling híbrido, que tentará aproveitar o melhor da CPU e da GPU. / [en] The definition of visibility is a classical problem in Computer Graphics. Several algorithms have been developed to enable the visualization of huge and complex models. Among these algorithms, the frustum culling, which plays an important role in this area, is used to remove invisible objects by the observer. Besides being very usual in applications, this algorithm has been improved in order to accelerate its execution. Although being treated as a well-solved problem in Computer Graphics, some points can be enhanced yet, and new forms of culling may be disclosed as well. In massive models, for example, algorithms of high performance are required, since the calculus arises considerably. This work analyses the frustum culling algorithm and its optimizations, aiming to obtain the state-of-the-art algorithm implemented in CPU, as well as explains the influence of each of its steps in massive models. Based on this analysis, new GPU (Graphics Processing Unit) based frustum culling techniques will be developed and compared with the ones using only CPU. As a result, a hybrid frustum culling will be proposed, in order to achieve the best of CPU and GPU processing.