Tires serve as important components of wheeled vehicles and their analytical modeling has drawn the attention of many researches in the past decades. A high-resolution finite element (FE) tire model contains detailed structural and material characteristics of a tire that exhibit degrees-of-freedom (DoF) in the order of 10⁵ or greater. However, such high-resolution models in their full detail are not practically applicable in multibody dynamic analysis of vehicles and a reduction in their order becomes necessary. In this research different formulations to construct condensed FE tire models suitable for multibody simulations are developed and their characteristics are discussed. In addition, two new and novel forms of substructuring are presented that aim at isolating the contact region of a tire without the need for keeping the boundary DoF which otherwise remain in the reduced system in the standard substructuring procedures. The new substructuring methods provide a great tool in constructing condensed FE tire models with much less total number of DoF compared to cases where a standard substructuring is used. In order to increase the computational efficiency of the condensed FE tire models even further, the possibility of model condensation in the contact region is studied. This research also addresses the applicability of available friction models into the condensed FE tire models. Different formulations of a condensed tire model presented in this research are used to construct several computational models. These models are utilized to simulate certain scenarios and the results are discussed.

Methods of component mode synthesis, such as Craig and Bampton reduction, are known to generally yield more accurate results in deformable multibody dynamics. The main shortcoming of those methods is that they are intuitively based. Recently Nikravesh developed a reduction method called mode condensation which is derived from the equations of motion and yields the same results as Craig and Bampton reduction. In this dissertation, it is proven that these two methods span the same column space; therefore, they should yield identical results. We propose that mode condensation provides an analytical justification for Craig and Bampton reduction. Test results suggest that Craig and Bampton reduction and mode condensation are appropriate for a broader range of applications because their column space matches up well with the conditions under which the deformable body is restrained. Although Guyan reduction preserves exact solutions for static problems, its applications shall be limited to low frequency excitation because of raised eigen-frequencies. Modal truncation is not recommended for use in multibody dynamic settings because it lacks the ability to receive forces and displacements at the moving boundary. Another issue addressed in this dissertation is the misconception that if mean axes are adopted as the moving reference frame, only free-free modes should be used for model reduction. It was not clear how a restrained deformable body with mean axes can be condensed properly. We have shown that the conventional (nodal-fixed) mode shapes can be used with mean axes as long as the transformation matrix has full rank and contains complete rigid-body mode shapes.

Die Mehrkörpersimulation (MKS) kommt in immer mehr Bereichen zum Einsatz. Bis vor einigen Jahren war das Thema fast ausschließlich im Automobilbereich wichtig. Heute wird der Ansatz in fast allen Bereichen der Technik, in dem „Bewegungsabläufe“ eine Rolle spielen, eingesetzt. Im Gegensatz zur Finite Elemente (FE)-Methode, für die eine detaillierte Bauteiltopologie mit einer Vielzahl von Elementen nötig ist, können mit MKS-Systemen selbst komplexe mechanische Systeme mit einer relativ geringen Anzahl an Freiheitsgraden abgebildet werden. Das Programm Adams hat diese Entwicklung maßgeblich mit gestaltet. Neben den Erweiterungen im Bereich der Solver und anderer mathematischer Formulierungen war immer die einfache Benutzerführung, die Integration von weiteren Simulationstechnologien und auch die Entwicklung von Spezialanwendungen ein wichtiges Thema der Entwicklung. Im Rahmen dieses Vortrages wird der Einsatz von Adams an Hand von Beispielen demonstriert. Weiterer Schwerpunkt ist die Erweiterung der Modelle durch Berücksichtigung der elastischen Materialeigenschaften einzelner Bauteile. Die Kopplung zur Lebensdauerberechnung an Hand von Beispielen schließt den Beitrag ab.

Musculoskeletal dynamics is a branch of biomechanics that takes advantage of interdisciplinary models to describe the relation between muscle actuators and the corresponding motions of the human body. Muscle forces play a principal role in musculoskeletal dynamics. Unfortunately, these forces cannot be measured non-invasively. Measuring surface EMGs as a non-invasive technique is recognized as a surrogate to invasive muscle force measurement; however, these signals do not reflect the muscle forces accurately. Instead of measurement, mathematical modelling of the musculoskeletal dynamics is a well established tool to simulate, predict and analyse human movements. Computer simulations have been used to estimate a variety of variables that are difficult or impossible to measure directly, such as joint reaction forces, muscle forces, metabolic energy consumption, and muscle recruitment patterns. Musculoskeletal dynamic simulations can be divided into two branches: inverse and forward dynamics. Inverse dynamics is the approach in which net joint moments and/or muscle forces are calculated given the measured or specified kinematics. It is the most popular simulation technique used to study human musculoskeletal dynamics. The major disadvantage of inverse dynamics is that it is not predictive and can rarely be used in the cause-effect interpretations. In contrast with inverse dynamics, forward dynamics can be used to determine the human body movement when it is driven by known muscle forces. The musculoskeletal system (MSS) is dynamically under-determinate, i.e., the number of muscles is more than the degrees of freedom (dof) of the system. This redundancy will lead to infinite solutions of muscle force sets, which implies that there are infinite ways of recruiting different muscles for a specific motion. Therefore, there needs to be an extra criterion in order to resolve this issue. Optimization has been widely used for solving the redundancy of the force-sharing problem. Optimization is considered as the missing consideration in the dynamics of the MSS such that, once appended to the under-determinate problem, \human-like" movements will be acquired. \Human-like" implies that the human body tends to minimize a criterion during a movement, e.g., muscle fatigue or metabolic energy. It is commonly accepted that using those criteria, within the optimization necessary in the forward dynamic simulations, leads to a reasonable representation of real human motions. In this thesis, optimal control and forward dynamic simulation of human musculoskeletal systems are targeted. Forward dynamics requires integration of the differential equations of motion of the system, which takes a considerable time, especially within an optimization framework. Therefore, computationally efficient models are required. Musculoskeletal models in this thesis are implemented in the symbolic multibody package MapleSim that uses Maple as the leverage. MapleSim generates the equations of motion governing a multibody system automatically using linear graph theory. These equations will be simplified and highly optimized for further simulations taking advantage of symbolic techniques in Maple. The output codes are the best form for the equations to be applied in optimization-based simulation fields, such as the research area of this thesis. The specific objectives of this thesis were to develop frameworks for such predictive simulations and validate the estimations. Simulating human gait motion is set as the end goal of this research. To successfully achieve that, several intermediate steps are taken prior to gait modelling. One big step was to choose an efficient strategy to solve the optimal control and muscle redundancy problems. The optimal control techniques are benchmarked on simpler models, such as forearm flexion/extension, to study the efficacy of the proposed approaches more easily. Another major step to modelling gait is to create a high-fidelity foot-ground contact model. The foot contact model in this thesis is based on a nonlinear volumetric approach, which is able to generate the experimental ground reaction forces more effectively than the previously used models. Although the proposed models and approaches showed strong potential and capability, there is still room for improvement in both modelling and validation aspects. These cutting-edge future works can be followed by any researcher working in the optimal control and forward dynamic modelling of human musculoskeletal systems.

The main focus of this research is to use graph-theoretic formulations to develop an automated algorithm for the generation of sensitivity equations. The idea is to combine the benefits of direct differentiation with that of graph-theoretic formulation. The primary deliverable of this work is the developed software module which can derive the system equations and the sensitivity equations directly from the linear graph of the system. Sensitivity analysis refers to the study of changes in system behaviour brought about by the changes in model parameters. Due to the rapid increase in the sizes and complexities of the models being analyzed, it is important to extend the capabilities of the current tools of sensitivity analysis, and an automated, efficient, and accurate method for the generation of sensitivity equations is highly desirable. In this work, a graph-theoretic algorithm is developed to generate the sensitivity equations. In the current implementation, the proposed algorithm uses direct differentiation to generate sensitivity equations at the component level and graph-theoretic methods to assemble the equation fragments to form the sensitivity equations. This way certain amount of control can be established over the size and complexity of the generated sensitivity equations. The implementation of the algorithm is based on a commercial software package \verb MapleSim[Multibody] and can generate governing and sensitivity equations for multibody models created in MapleSim. In this thesis, the algorithm is tested on various mechanical, hydraulic, electro-chemical, multibody, and multi-domain systems. The generated sensitivity information are used to perform design optimization and parametric importance studies. The sensitivity results are validated using finite difference formulations. The results demonstrate that graph-theoretic sensitivity analysis is an automated, accurate, algorithmic method of generation for sensitivity equations, which enables the user to have some control over the form and complexity of the generated equations. The results show that the graph-theoretic method is more efficient than the finite difference approach. It is also demonstrated that the efficiency of the generated equations are at par or better than the equation obtained by direct differentiation.

This paper was presented at CJK-OSM 7, 18–21 June 2012, Huangshan, China.

Many engineering applications make use of fiber assemblies under compression. Unfortunately, this compression behavior is difficult to predict, due to nonlinear compliance, hysteresis, and anelasticity. The main objective of this research is to develop an algorithm which is capable of incorporating the microscale features of the fiber network into macroscopic scale applications, particularly the modeling of contact mechanics in multibody systems. In micromechanical approaches, the response of a fiber assembly to an external force is related to the response of basic fiber units as well as the interactions between these units, i.e. the mechanical properties of the constituent fibers and the architecture of the assembly will both have a significant influence on the overall response of the assembly to compressive load schemes. Probabilistic and statistical principles are used to construct the structure of the uniformly-distributed random network. Different micromechanical approaches in modeling felt, as a nonwoven fiber assembly with unique mechanical properties, are explored to gain insight into the key mechanisms that influence its compressive response. Based on the deformation processes and techniques in estimating the number of fiber contacts, three micromechanical models are introduced: (1) constitutive equations for micromechanics of three-dimensional fiberwebs under small strains, in which elongation of the fibers is the key deformation mechanism, adapted for large deformation ranges; (2) micromechanical model based on the rate theory of granular media, in which bending and torsion of fibers are the predominant elemental deformations used to calculate compliances of a particular contact; and (3) a mechanistic model developed using the general deformation theory of the fiber networks with fiber bending at the micro level and a binomial distribution of fiber contacts. A well-established mechanistic model, based on fiber-to-fiber friction at the micro level, is presented for predicting the hysteresis in compression behavior of wool fiberwebs. A novel algorithm is introduced to incorporate a hysteretic micromechanical model - a combination of the mechanistic model with microstructural fiber bending, which uses a binomial distribution of the number of fiber-to-fiber contacts, and the friction-based hysteresis idea - into the contact mechanics of multibody simulations with felt-lined interacting bodies. Considering the realistic case in which a portion of fibers slides, the fiber network can be treated as two subnetworks: one from the fibers with non-sliding contact points, responsible for the elastic response of the network, and the other consisting of fibers that slide, generating irreversible hysteresis phenomenon in the fiberweb compression. A parameter identification is performed to minimize the error between the micromechanical model and the elastic part of the loading-unloading experimental data for felt, then contribution of friction was added to the obtained mechanistic compression-recovery curves. The theoretical framework for constructing a mechanistic multibody dynamic model of a vertical piano action is developed, and its general validity is established using a prototype model. Dynamic equations of motion are derived symbolically for the piano action using a graph-theoretic formulation. The model fidelity is increased by including hammer-string interaction, backcheck wire and hammer shank flexibility, a sophisticated key pivot model, nonlinear models of bridle strap and butt spring, and a novel mathematical contact model. The developed nonlinear hysteretic micromechanical model is used for the hammer-string interaction to affirm the reliability and applicability of the model in general multibody dynamic simulations. In addition, dynamic modeling of a flexible hub-beam system with an eccentric tip mass including nonlinear hysteretic contact is studied. The model represents the mechanical finger of an actuator for a piano key. Achieving a desired finger-key contact force profile that replicates that of a real pianist's finger requires dynamic and vibration analysis of the actuator device. The governing differential equations for the dynamic behavior of the system are derived using Euler-Bernoulli beam theory along with Lagrange's method. To discretize the distributed parameter flexible beam in the model, the finite element method is utilized. Excessive vibration due to the arm flexibility and also the rigid-body oscillations of the arm, especially during the period of key-felt contact, is eliminated utilizing a simple grounded rotational dashpot and a grounded rotational dashpot with a one-sided relation. The effect on vibration behavior attributed to these additional components is demonstrated using the simulated model.

Os acidentes com veículos ferroviários podem ter origem em muitos fatores, mas os principais são relacionados com a dinâmica do veículo e carga, via permanente em péssimas condições e operações inseguras nos trens. Os acidentes causam mortes, danos materiais e ao meio ambiente e prejuízos para as operadoras e seus clientes. Para avaliar a dinâmica dos veículos ferroviários, um sistema multicorpos foi desenvolvido (programa computacional) para representar matematicamente um típico veículo ferroviário com seus principais graus de liberdade. As equações de movimento foram desenvolvidas utilizando a equação de Lagrange de movimento, a qual considera princípios da mecânica como: energia cinética, energia potencial e a dissipação de energia do sistema. As equações acopladas e desacopladas são programadas e resolvidas para acelerações, estas são integradas duas vezes, obtendo-se as velocidades e deslocamentos. A partir das repostas do sistema o comportamento do veículo pode ser avaliado em várias condições de operação. A verificação do programa é realizada através de comparações com resultados de outros programas publicados na literatura, onde se verifica uma adequada correlação. Avaliações nos principais regimes de operação são realizadas de forma a simular condições determinadas pela norma AAR e condições extras originadas por irregularidades aperiódicas da via do tipo cusp e jog. Dois tipos de veículos são simulados para representar as condições típicas das ferrovias brasileiras: veículos operando em bitola métrica e em bitola larga. Os resultados das simulações apresentam valores de amplitude e fase que estão de acordo com resultados expostos nas normas e na literatura ferroviária de referência utilizada neste trabalho. A avaliação dinâmica de veículos ferroviários através de um programa computacional é importante, pois considera as principais características dos veículos e via permanente. A possibilidade de representar o veículo com uma configuração simples em relação a programas comerciais permite uma simulação rápida e confiável para determinar respostas em regimes como: hunting, twist e roll, pitch e bounce e yaw e sway. / The accidents with rail vehicles has origin due to many factors, but the main ones are related to the dynamics of the vehicle and load, the spoiled railway and unsafe operations on the trains. Accidents causing deaths, damage to property and the environment and damage to operators and their customers. In order to evaluate the railway vehicles dynamics, it was developed a multibody system (computer program) to mathematically represent a typical railway vehicle with its main degrees of freedom. The motion equations were developed using Lagrange's equation of motion, which takes into consideration the principles of mechanical, as: kinetic energy, potential energy and energy dissipation of the system. The coupled and uncoupled equations are programmed and solved for accelerations, which are twice integrated, in order to have the speeds and displacements. From the system’s responses, the vehicle behavior can be evaluated in several operating conditions. The comparison of the program is accomplished through confrontations with results from other programs in the literature, in which a good correlation is verified. The evaluations in the main regimes of operation are made in a way simulate the conditions determined by the standard conditions and extra conditions caused by aperiodic irregularities of the track. Two types of vehicles are simulated to represent the typical conditions of Brazilian railways: vehicles operating on meter gauge and large gauge. The simulation results show that amplitude and phase values are consistent with results presented in the standards and in the railway literature of reference of this work. The rail vehicles dynamic evaluation through a computer program was important because it considers the main characteristics of vehicles and permanent way. The possibility of representing the vehicle with a simple configuration in relation to commercial softwares allows a fast and reliable simulation to determine responses in regimes as: hunting, twist and roll, pitch and bounce and yaw and sway.

Devido as severas condições as quais veículos militares blindados de esteira são submetidos, o desenvolvimento de modelos que representam o comportamento dinâmico destes veículos torna-se imprescindível, para além da possibilidade de avaliação das intensidades das vibrações ocorrendo na cabine, ser possível criar veículos que tenham vantagens na mobilidade, fator esse que engloba tanto a transposição de obstáculos, como a rodagem em condições menos severas, e por fim, no tempo e na exatidão dos disparos, afetada pelas respostas dinâmicas que o veículo fornece. Para ser possível encontrar um veículo que desempenhe tais condições de forma satisfatória, apenas modelos que representem adequadamente as suas propriedades, apresentando respostas das acelerações e deslocamentos, não são suficientes. O objetivo deste trabalho é o desenvolvimento de um modelo numérico que tenha a capacidade de simular as condições dinâmicas extremas as quais um veículo de esteira é induzido, e também, otimizar o modelo, com a finalidade de encontrar molas e amortecedores capazes de proporcionar respostas adequadas às funções custo desenvolvidas. Estas funções objetivo são definidas como a combinação linear da aceleração e deslocamento, verticais e rotacionais, em conjunto de restrições impostas, objetivando encontrar uma combinação ideal para mobilidade, tempo e exatidão nos disparos e por fim, molas e amortecedores adequados as condições de logística Para proposta deste estudo, um modelo matemático 2D e um 3D, de um veículo de esteira, foi desenvolvido. O modelo possibilita a avaliação dos graus de liberdade de deslocamento vertical das massas não suspensas e do deslocamento vertical, arfagem e rolagem da massa suspensa. Os efeitos da esteira são modelados como molas verticais lineares exercendo uma força de restauração para alinhar as rodas de rodagem, proporcional ao deslocamento relativo entre essas rodas. A otimização é feita através de ferramentas numéricas presentes no software comercial Simulink, sendo necessário o desenvolvimento das funções custo que caracterizem os objetivos ideais para cada tipo de análise. Os resultados de simulações numéricas sob a forma de cursos de deslocamento de pontos característicos do casco e deslocamentos dos eixos de rodas em um sistema de coordenadas de referência assumido, também estão incluídos, bem como as quantidades de valor RMS de cada uma das respostas, comparando um veículo padrão, com o veículo com a suspensão otimizada. / Due to the severe conditions in which armored military vehicles are submitted, the development of models that represent the dynamic behavior of these vehicles becomes essential, besides the possibility of evaluating the vibration intensities occurring in the cabin, to be possible to create vehicles that have mobility a factor that encompasses both the transposition of obstacles, and the shooting in less severe conditions, and finally, in the time and accuracy of the shots, affected by the dynamic responses that the vehicle provides. In order to be able to find a vehicle that fulfills these conditions satisfactorily, only models that adequately represent its properties, presenting responses of the accelerations and displacements, are not enough. The objective of this work is the development of a numerical model that has the ability to simulate extreme dynamic conditions such as a tracked vehicle is induced, and also to optimize the model with the purpose of finding springs and shock absorbers capable of adequate alternative answers cost functions developed. These are the goals defined as a linear combination of acceleration and displacement, vertical and rotational, together imposed constraints, aiming to find an ideal combination for mobility, time and precision in the shots and, finally, springs and dampers suitable as logistics conditions To propose this study, a 2D and 3D mathematical model of a tracked vehicle were developed. The model allows the evaluation of the degrees of freedom of vertical displacement of the non-suspended masses and the vertical displacement, pitch and roll of the suspended mass. The effects of the track are modeled as linear vertical springs exerting a restoring force to align the road wheels, proportional to the relative displacement between these wheels. The optimization is done through numerical tools present in Simulink software, and it is necessary to develop cost functions that characterize the ideal objectives for each type of analysis. The results of numerical simulations in the form of displacement courses of characteristic hull points and wheel axle displacements in an assumed reference coordinate system are also included, as well as the RMS value quantities of each of the responses, comparing a standard vehicle with the optimized suspension.

Os acidentes com veículos ferroviários podem ter origem em muitos fatores, mas os principais são relacionados com a dinâmica do veículo e carga, via permanente em péssimas condições e operações inseguras nos trens. Os acidentes causam mortes, danos materiais e ao meio ambiente e prejuízos para as operadoras e seus clientes. Para avaliar a dinâmica dos veículos ferroviários, um sistema multicorpos foi desenvolvido (programa computacional) para representar matematicamente um típico veículo ferroviário com seus principais graus de liberdade. As equações de movimento foram desenvolvidas utilizando a equação de Lagrange de movimento, a qual considera princípios da mecânica como: energia cinética, energia potencial e a dissipação de energia do sistema. As equações acopladas e desacopladas são programadas e resolvidas para acelerações, estas são integradas duas vezes, obtendo-se as velocidades e deslocamentos. A partir das repostas do sistema o comportamento do veículo pode ser avaliado em várias condições de operação. A verificação do programa é realizada através de comparações com resultados de outros programas publicados na literatura, onde se verifica uma adequada correlação. Avaliações nos principais regimes de operação são realizadas de forma a simular condições determinadas pela norma AAR e condições extras originadas por irregularidades aperiódicas da via do tipo cusp e jog. Dois tipos de veículos são simulados para representar as condições típicas das ferrovias brasileiras: veículos operando em bitola métrica e em bitola larga. Os resultados das simulações apresentam valores de amplitude e fase que estão de acordo com resultados expostos nas normas e na literatura ferroviária de referência utilizada neste trabalho. A avaliação dinâmica de veículos ferroviários através de um programa computacional é importante, pois considera as principais características dos veículos e via permanente. A possibilidade de representar o veículo com uma configuração simples em relação a programas comerciais permite uma simulação rápida e confiável para determinar respostas em regimes como: hunting, twist e roll, pitch e bounce e yaw e sway. / The accidents with rail vehicles has origin due to many factors, but the main ones are related to the dynamics of the vehicle and load, the spoiled railway and unsafe operations on the trains. Accidents causing deaths, damage to property and the environment and damage to operators and their customers. In order to evaluate the railway vehicles dynamics, it was developed a multibody system (computer program) to mathematically represent a typical railway vehicle with its main degrees of freedom. The motion equations were developed using Lagrange's equation of motion, which takes into consideration the principles of mechanical, as: kinetic energy, potential energy and energy dissipation of the system. The coupled and uncoupled equations are programmed and solved for accelerations, which are twice integrated, in order to have the speeds and displacements. From the system’s responses, the vehicle behavior can be evaluated in several operating conditions. The comparison of the program is accomplished through confrontations with results from other programs in the literature, in which a good correlation is verified. The evaluations in the main regimes of operation are made in a way simulate the conditions determined by the standard conditions and extra conditions caused by aperiodic irregularities of the track. Two types of vehicles are simulated to represent the typical conditions of Brazilian railways: vehicles operating on meter gauge and large gauge. The simulation results show that amplitude and phase values are consistent with results presented in the standards and in the railway literature of reference of this work. The rail vehicles dynamic evaluation through a computer program was important because it considers the main characteristics of vehicles and permanent way. The possibility of representing the vehicle with a simple configuration in relation to commercial softwares allows a fast and reliable simulation to determine responses in regimes as: hunting, twist and roll, pitch and bounce and yaw and sway.