We introduce to computer graphics the Pseudo-Rigid-Body Mechanism (PRBM) and the chain algorithm from mechanical engineering, with a unified tutorial from disparate source materials. The PRBM has been used successfully to simplify the simulation of non-linearly elastic beams, using deflections of an analogous spring and rigid-body linkage. It offers computational efficiency as well as an automatic parameterization in terms of physically measurable, intuitive inputs which fit naturally into existing animation work flows for character articulation. The chain algorithm is a technique for simulating the deflection of complicated elastic bodies in terms of straight elastic elements, which has recently been extended to incorporate PRBM beam-elements in three dimensions. We present a new, mathematically equivalent optimization of the 3D PRBM chain algorithm, from its former asymptotic complexity of O(n^2) in the number of elements n, to O(n). We also extend an existing PRBM for combined moment-force loads to 3D, where the existing 3D PRBM chain algorithm was limited to 3D PRBM elements for a moment-only load. This optimization and extension are validated by duplicating prior experimental results, but substituting the new optimization and combined-load elements. Finally, a loose road-map is provided with several key considerations for future extension of the techniques to dynamic simulations.

A preocupação com o impacto ambiental decorrente da implantação e operação de novas linhas metroferroviárias faz com que na elaboração dos projetos de via permanente sejam frequentemente adotados sistemas amortecedores de vibrações e ruídos secundários. As vibrações em vias de metrô são causadas principalmente pelo contato roda-trilho e são propagadas pela estrutura do túnel e pelas distintas camadas de solo podendo chegar às edificações lindeiras, onde, dependendo da intensidade, provocam desconforto aos usuários da edificação e mau funcionamento de equipamentos. Uma solução de atenuação largamente empregada atualmente em locais críticos é o \"sistema massa mola\". O sistema \"massa mola\" é composto por lajes de concreto armado, denominadas lajes flutuantes, apoiadas sobre materiais resilientes. De forma geral, quanto menor a frequência natural deste sistema, maior a atenuação das vibrações. No entanto, a utilização de apoios excessivamente flexíveis para obtenção de baixas frequências pode acarretar problemas operacionais em função de deslocamentos e acelerações excessivos das lajes flutuantes. Este projeto tem como objetivo o estudo do comportamento dinâmico das lajes flutuantes de concreto armado utilizadas em sistemas \"massa mola\" principalmente com relação à atenuação de vibrações e nível de vibrações na via permanente durante a passagem dos trens metropolitanos. A avaliação foi realizada utilizando modelos numéricos calibrados com dados experimentais obtidos nas linhas do Metrô de São Paulo. / Deploying and operating subway lines cause growing concern about environmental impact, making necessary in new lines projects the adoption of damping systems for no propagation of noise and vibration arising from traffic from trains. The vibrations in a subway track are mainly caused by wheel-rail contact and are propagated by tunnel structure and soil layers, reaching the neighboring buildings and causing annoyance residents in building. Equipment failures represent a consequence as well. A mitigation solution widely employed in critical locations is the known \"mass spring system\". The \"mass spring system\" system is composed of reinforced concrete slabs, so called floating slabs, resting on resilient materials. In general, greater attenuation of vibrations can be attained with lower natural frequency of system. However, the use of flexible supports for obtaining excessively low frequencies can cause operational problems due to excessive accelerations and displacements of the floating slab. This project aims to study the dynamic behavior of reinforced concrete floating slabs used in systems\' mass spring particularly with respect to mitigating vibrations and level of vibrations during the passage of the commuter trains. The evaluation was performed using numerical models calibrated with experimental data obtained in the lines of the São Paulo Metro.

abstract: With improvements in technology, intensive longitudinal studies that permit the investigation of daily and weekly cycles in behavior have increased exponentially over the past few decades. Traditionally, when data have been collected on two variables over time, multivariate time series approaches that remove trends, cycles, and serial dependency have been used. These analyses permit the study of the relationship between random shocks (perturbations) in the presumed causal series and changes in the outcome series, but do not permit the study of the relationships between cycles. Liu and West (2016) proposed a multilevel approach that permitted the study of potential between subject relationships between features of the cycles in two series (e.g., amplitude). However, I show that the application of the Liu and West approach is restricted to a small set of features and types of relationships between the series. Several authors (e.g., Boker & Graham, 1998) proposed a connected mass-spring model that appears to permit modeling of more general cyclic relationships. I showed that the undamped connected mass-spring model is also limited and may be unidentified. To test the severity of the restrictions of the motion trajectories producible by the undamped connected mass-spring model I mathematically derived their connection to the force equations of the undamped connected mass-spring system. The mathematical solution describes the domain of the trajectory pairs that are producible by the undamped connected mass-spring model. The set of producible trajectory pairs is highly restricted, and this restriction sets major limitations on the application of the connected mass-spring model to psychological data. I used a simulation to demonstrate that even if a pair of psychological time-varying variables behaved exactly like two masses in an undamped connected mass-spring system, the connected mass-spring model would not yield adequate parameter estimates. My simulation probed the performance of the connected mass-spring model as a function of several aspects of data quality including number of subjects, series length, sampling rate relative to the cycle, and measurement error in the data. The findings can be extended to damped and nonlinear connected mass-spring systems. / Dissertation/Thesis / Masters Thesis Psychology 2019

This thesis presents a tunable 3D real-time interactive simulator of the geometrical displacement of the thoracic diaphragm during physiological and mechanical ventilation. Particular attention is placed on capturing the heterogeneous tissue composition while maintaining computational efficiency and accuracy. The long term goal is to establish an accurate theoretical model to complement the experimental and clinical studies of the side effects associated with mechanical ventilation and to overcome the ethical difficulties of performing time resolved studies on human patients. The deformations are modelled using a commercial 3D model and a mass-spring model together with distance constraints and Verlet integration. The simulator is easily adjusted in real-time to many different cases of ventilation and validated through inspection and comparison with existing models. More research is needed to validate the model using patient specific data, as well as extending the model to include additional physiological and pathophysiological components. Long term goals includes considering the microscopic aspects of cellular mechanics to capture the underlying causes of ventilator-induced diaphragmatic dysfunction.

Computation model is presented for mass spring systems of one and two dimensional phononic band gap crystals and micro-electro-mechanical systems. The computation model is veri ed with existing work, and phononic band gap microelectro- mechanical systems are analyzed. Phononic band gap in the scienti c and industrial community is discussed. The motivation and the recent popular methods are discussed. The computation models are highlighted with their pros and cons and adequate computational applications. The one dimensional mass spring model is developed and the simulator operation is validated through comparison with the published simulation data in the original paper by J.S. Jensen et al.. Additionally, the one dimensional mass spring simulator is validated for a micro-electro-mechanical system band structure. The two dimensional mass spring model is developed, as well, the simulator operation is validated through comparison with the published simulation data in the original paper by J.S. Jensen et al.. The two-dimensional simulator is utilized to analyze solid square-shaped, hollow square-shaped, solid diamond-shaped, and hollow diamond-shaped inclusion micro-electro-mechanical band gap structures. The solid inclusion-based micro-electro-mechanical band gap results are compared with hollow inclusion-based micro-electro-mechanical structures.

Computation model is presented for mass spring systems of one and two dimensional phononic band gap crystals and micro-electro-mechanical systems. The computation model is veri ed with existing work, and phononic band gap microelectro- mechanical systems are analyzed. Phononic band gap in the scienti c and industrial community is discussed. The motivation and the recent popular methods are discussed. The computation models are highlighted with their pros and cons and adequate computational applications. The one dimensional mass spring model is developed and the simulator operation is validated through comparison with the published simulation data in the original paper by J.S. Jensen et al.. Additionally, the one dimensional mass spring simulator is validated for a micro-electro-mechanical system band structure. The two dimensional mass spring model is developed, as well, the simulator operation is validated through comparison with the published simulation data in the original paper by J.S. Jensen et al.. The two-dimensional simulator is utilized to analyze solid square-shaped, hollow square-shaped, solid diamond-shaped, and hollow diamond-shaped inclusion micro-electro-mechanical band gap structures. The solid inclusion-based micro-electro-mechanical band gap results are compared with hollow inclusion-based micro-electro-mechanical structures.

A preocupação com o impacto ambiental decorrente da implantação e operação de novas linhas metroferroviárias faz com que na elaboração dos projetos de via permanente sejam frequentemente adotados sistemas amortecedores de vibrações e ruídos secundários. As vibrações em vias de metrô são causadas principalmente pelo contato roda-trilho e são propagadas pela estrutura do túnel e pelas distintas camadas de solo podendo chegar às edificações lindeiras, onde, dependendo da intensidade, provocam desconforto aos usuários da edificação e mau funcionamento de equipamentos. Uma solução de atenuação largamente empregada atualmente em locais críticos é o \"sistema massa mola\". O sistema \"massa mola\" é composto por lajes de concreto armado, denominadas lajes flutuantes, apoiadas sobre materiais resilientes. De forma geral, quanto menor a frequência natural deste sistema, maior a atenuação das vibrações. No entanto, a utilização de apoios excessivamente flexíveis para obtenção de baixas frequências pode acarretar problemas operacionais em função de deslocamentos e acelerações excessivos das lajes flutuantes. Este projeto tem como objetivo o estudo do comportamento dinâmico das lajes flutuantes de concreto armado utilizadas em sistemas \"massa mola\" principalmente com relação à atenuação de vibrações e nível de vibrações na via permanente durante a passagem dos trens metropolitanos. A avaliação foi realizada utilizando modelos numéricos calibrados com dados experimentais obtidos nas linhas do Metrô de São Paulo. / Deploying and operating subway lines cause growing concern about environmental impact, making necessary in new lines projects the adoption of damping systems for no propagation of noise and vibration arising from traffic from trains. The vibrations in a subway track are mainly caused by wheel-rail contact and are propagated by tunnel structure and soil layers, reaching the neighboring buildings and causing annoyance residents in building. Equipment failures represent a consequence as well. A mitigation solution widely employed in critical locations is the known \"mass spring system\". The \"mass spring system\" system is composed of reinforced concrete slabs, so called floating slabs, resting on resilient materials. In general, greater attenuation of vibrations can be attained with lower natural frequency of system. However, the use of flexible supports for obtaining excessively low frequencies can cause operational problems due to excessive accelerations and displacements of the floating slab. This project aims to study the dynamic behavior of reinforced concrete floating slabs used in systems\' mass spring particularly with respect to mitigating vibrations and level of vibrations during the passage of the commuter trains. The evaluation was performed using numerical models calibrated with experimental data obtained in the lines of the São Paulo Metro.

La nécessité de simulations de tissus mous, tels que les organes internes, se pose avec le progrès des domaines scientifiques et médicaux. Le but de ma thèse est de développer un nouveau modèle générique, topologique et physique, pour simuler les organes humains. Un tel modèle doit être facile à utiliser, doit pouvoir effectuer des simulations en temps réel avec un niveau de précision permettant l'utilisation à des fins médicales. Cette thèse explore de nouvelles méthodes de simulation et propose des améliorations pour la modélisation de corps déformables. Les méthodes proposées visent à pouvoir effectuer des simulations rapides, robustes et fournissant des résultats physiquement précis. L'intérêt principal de nos solutions réside dans la simulation de tissus mous élastiques a petites et grandes déformations à des fins médicales. Nous montrons que pour les méthodes existantes, la précision pour simuler librement des corps déformables ne va pas de pair avec la performance en temps de calcul. De plus, pour atteindre l'objectif de simulation rapide, de nombreuses approches déplacent certains calculs dans une étape de pré-traitement, ce qui entraîne l'impossibilité d'effectuer des opérations de modification topologiques au cours de la simulation comme la découpe ou le raffinement. Dans cette thèse, le cadre utilisé pour les simulations s'appelle TopoSim. Il est conçu pour simuler des matériaux à l'aide de systèmes masses-ressorts (MSS) avec des paramètres d'entrée spécifiques. En utilisant un MSS, qui est connu pour sa simplicité et sa capacité à effectuer des simulations temps réel, nous présentons plusieurs améliorations basé physiques pour contrôler les fonctionnalités globales du MSS qui jouent un rôle clé dans la simulation de tissus réels. La première partie de ce travail de thèse vise à reproduire une expérience réelle de simulation physique qui a étudié le comportement du tissu porcin à l'aide d'un rhéomètre rotatif. Son objectif était de modéliser un corps viscoélastique non linéaire. A partir de l'ensemble des données acquises, les auteurs de l'expérience ont dérivé une loi de comportement visco-élastique qui a ensuite été utilisée afin de la comparer avec nos résultats de simulation. Nous définissons une formulation des forces viscoélastiques non linéaires inspirée de la loi de comportement physique. La force elle-même introduit une non linéarité dans le système car elle dépend fortement de l'amplitude de l'allongement du ressort et de trois paramètres spécifiques à chaque type de tissu. La seconde partie de la thèse présente notre travail sur les forces de correction de volume permettant de modéliser correctement les changements volumétriques dans un MSS. Ces forces assurent un comportement isotrope des solides élastiques et un comportement correct du volume quel que soit la valeur du coefficient de Poisson utilisé. La méthode nécessite de résoudre deux problèmes: l'instabilité provoquant des plis et les contraintes de Cauchy. Nos solutions à ces limitations impliquent deux étapes. La première consiste à utiliser trois types de ressorts dans un maillage entièrement hexaédrique: les arêtes, les faces diagonales et les diagonales internes. Les raideurs des ressorts dans le système ont été formulées pour obéir aux lois mécaniques de base. La deuxième étape consiste à ajouter des forces de correction linéaires calculées en fonction du changement de volume et des paramètres mécaniques du tissu simulé, à savoir le coefficient de Poisson et le module de Young [etc…] / The need for simulations of soft tissues, like internal organs, arises with the progress of the scientific and medical environments. The goal of my PhD is to develop a novel generic topological and physical model to simulate human organs. Such a model shall be easy to use, perform the simulations in the real time and which accuracy will allow usage for the medical purposes.This thesis explores novel simulation methods and improvement approaches for modeling deformable bodies. The methods aim at fast and robust simulations with physically accurate results. The main interest lies in simulating elastic soft tissues at small and large strains for medical purposes. We show however, that in the existing methods the accuracyto freely simulate deformable bodies and the real-time performance do not go hand in hand. Additionally, to reach the goal of simulating fast, many of the approaches move the necessary calculations to pre-computational part of the simulation, which results in inability to perform topological operations like cutting or refining.The framework used for simulations in this thesis is designed to simulate materials using Mass Spring Systems (MSS) with particular input parameters. Using Mass-Spring System, which is known for its simplicity and ability to perform fast simulations, we present several physically-based improvements to control global features of MSS which play the key role in simulation of real bodies

This thesis proposes a method to simulate the dynamics of an autonomous underwater vehicle towing another autonomous underwater vehicle of equivalent size using a marine cable in the vertical and horizontal plane. There is a coupling effect between the two vehicles because the towed vehicle is of equivalent size. This means that the towed vehicle cannot be modeled as just a payload but rather, must incorporate the forces and moments experienced and acting on it. In this work, only AUVs with symmetrical hulls are considered, where the towing AUV is moving at a constant velocity with a set thrust while the towed AUV has no thrust. The rope system is another important component that needs to be modeled correctly because the rope material and type significantly impact the motion of the vehicles. The rope system in this study is modeled using a numerical approach called the lumped mass spring damper method which is easy to understand and computationally inexpensive. The rope model accounts for buoyancy differences in different ropes and permits cable flexibility. This thesis enables us to study the motion of multiple combinations of different ropes and axi-symmetric types of underwater vehicles with any fixed or movable fin configuration. / M.S. / This thesis studies the motion of an autonomous underwater vehicle towing another autonomous underwater vehicle which is a large as it is. The towed vehicle cannot be assumed to be just a mass attached to the towing vehicle. There is an interaction between the two vehicle. The towed vehicle places a force on the towed vehicle and the towed vehicle likewise places a force on the towing vehicle. This interaction needs to be modeled correctly to fully capture the impact of both vehicles and their appendages. Additionally, the rope system poses a huge impact on the two vehicle depending on what type of rope is selected. Multiple factors affect the performance of a rope such as the shape and the elasticity. Some ropes may also be denser due to their material type and are less buoyant than others. These factors are considered in the modeling of the overall system and allows us to study different combinations of ropes and symmetric hulled autonomous underwater vehicles.

This thesis describes a method of modeling financial markets by utilizing concepts from mechanical vibration. The models developed represent multi-degree of freedom, mass-spring systems. The economic principles that drive the design are supply and demand, which act as springs, and shareholders, which act as masses. The primary assumption of this research is that events cannot be predicted but the responses to those events can be. In other words, economic stimuli create responses to a stock’s price that is predictable, repeatable and scientific. The approach to determining the behavior of various financial markets encompassed techniques such as Fast Fourier Transform and discretized wavelet analysis. The researched developed in three stages; first an appropriate model of causation in the stock market was established. Second, a model of steady state properties was determined. Third, experiments were conducted to determine the most effective model and to test its predictive capabilities on ten stocks. The experiments were evaluated based on the model’s hypothetical return on investment. The results showed a positive gain on capital for nine out of the ten stocks and supported the claim that stocks behave in accordance to the natural laws of vibration. As scientific approaches to modeling the stock market are beginning to develop, engineering principles are proving to be the most relevant and reliable means of financial market prediction.