Este trabalho aborda os conceitos básicos da teoria de segunda ordem das placas elásticas delgadas, utilizando o Método dos Elementos Finitos (introduzido através do Método dos Resíduos Ponderados, na variante de Galerkin). São deduzidas as matrizes de rigidez geométrica, de rigidez secante e de rigidez tangente, relativas ao problema em consideração. É proposta ainda uma conduta notavelmente simplificada, que facilita sobremaneira a construção da matriz de rigidez tangente. / This paper delas with the basic concepts of the secondf order theory of thin elastic plates, through the use of the Finite Element Method 9introcuced through the Weighted Residual Method, in Galerkin\'s approach). The matrices of geometric stiffness, secant stiffness, and tangent stiffness for the problem under consideration are deduced. It is also proposed an outstandingly simplified conduct, which will greatly easen the construction of the tangent stiffness matrix.

A interação dinâmica resultante do impacto de esferas de aço contra chapas de alumínio é estudada através da representação numérica de testes experimentais, os quais imitam freqüentes colisões de pequenos fragmentos contra a fuselagem de aeronaves. Importância é dada à modelagem do comportamento visco-plástico do material da chapa, o que conduz à proposição de uma modificação no método de caracterização dinâmica mecânica de material, realizado através de um equipamento denominado Barra de Hopkinson. Adicionalmente, a influência de possíveis erros na seleção de parâmetros de simulação, relacionados ao contato, amortecimento estrutural e principalmente ao material, é discutida através de análises numéricas de sensibilidade. Testes de impacto foram conduzidos de forma a se obter a velocidade balística das chapas. O deslocamento máximo permanente das chapas a baixas velocidades também foi medido. O método de caracterização dinâmica de material proposto é então avaliado pela comparação dos resultados de simulações numéricas frente aos dados experimentais obtidos nos testes de impacto. As predições de deslocamento máximo permanente, para testes sem perfuração da chapa, e de velocidade balística, para testes de perfuração total, indicaram uma boa concordância numérico-experimental, respeitadas as observações realizadas acerca dos parâmetros envolvidos. / Dynamic interaction present on impact of steel spheres against aluminum panels is studied through a numerical model of experimental tests, which reproduce common collisions of small debris against airplane fuselages. This thesis emphasizes the panel-material visco-plastic behaviour modeling, which leads to a modification of the material dynamic characterization method, based on a Split Hopkinson Pressure Bar. Influence of possible errors in some numerical simulations parameters, related to contact, structural damping and material behaviour is also discussed by sensitivity numerical analyses. Impact tests were conducted to obtain the ballistic velocity of the panels. Also, the final maximum plate deformation at low velocities was measured. The proposed dynamic characterization method is explored by comparing the numerical simulation and the impact tests. The predicted maximum impact point displacement, for no perforation cases, and the ballistic velocity, for total perforation tests, present a good numerical-experimental agreement, bearing in mind the observations about the various used parameters.

O tema desta pesquisa refere-se ao tratamento numérico de estruturas de pavimentos, dando ênfase à utilização do método dos elementos de contorno - MEC para o tratamento de elementos planos, enquanto os elementos lineares serão tratados através do método dos elementos finitos - MEF. Busca-se contribuir com uma série de trabalhos realizados nesta área, principalmente com a consideração do efeito da excentricidade do eixo neutro das barras em relação à superfície neutra da placa somando-o, portanto, ao fenômeno de flexão desta última. A técnica de acoplamento dos elementos estruturais utilizada foi a técnica das sub-regiões, que facilita a visualização do problema da combinação e viabiliza o uso da técnica de condensação estática na resolução do sistema de equações. / This research refers to the numeric analysis of structures, emphasizing the use of the boundary element method - BEM - in the discretization of the plates, while the linear elements wil be formulated through the finite element method - FEM. The aim is to contribute with a number of works related to this subject, specially in the consideration of the effect of the stiffeners eccentricity in relation to the plates neutral surface, in addition to its bending state. The tool adopted to fulfill the coupling among these kinds of structural elements is the well-known sub region or multi-domain technique, which works well with the static condensation technique for solving the sparse system of equation generated.

Aerospace structures comprising of metals and composites are exposed to extreme loading and environmental conditions which necessitates regular inspection and maintenance to verify and monitor overall structural integrity. The timely and accurate detection, characterization and monitoring of structural cracking, corrosion, delaminating, material degradation and other types of damage are of major concern in the operational environment. Along with these, stringent requirements of safety and operational reliability have lead to evolutionary methods for evaluation of structural integrity. As a result, conventional nondestructive evaluation methods have moved towards a new concept, Structural Health Monitoring (SHM). SHM provides in-situ information a bout the occurrence of damage if any, location and severity of damage and residual life of the structure and also helps in improving the safety, reliability and confidence levels of critical engineering structures. While the concepts underlying SHM are well understood, development of methods is still in a nascent stage which requires extensive research that is challenging and has been the main motivating factor for undertaking the work reported in the thesis. Under the scope of the investigations carried out in this thesis, an integrated approach using Ultrasonic (active) and Acoustic Emission (passive) methods has been explored for SHM of metallic and composite plate structures using a distributed array of surface bonded circular piezoelectric wafer active sensors(PWAS). In ultrasonic method, PWAS is used for actuation and reception of Lamb waves in plate structures. The damage detection is based on the interaction of waves with defects resulting in reflection, mode conversion and scattering. In acoustic emission (AE) technique, the same sensor is used to pick up the stress waves generated by initiation or growth of defects or damage. Thus, both the active and passive damage detection methods are used in this work for detection, location and characterization of defects and damage in metallic and composite plates with complex geometries and structural discontinuities. And, thus the strategy adopted is to use time-frequency analysis and time reversal technique to extract the information from Lamb wave signals for damage detection and a geodesic based Lamb wave approach for location of the damage in the structure. To start with experiments were conducted on aluminum plates to study the interaction of Lamb waves with cracks oriented at different angles and on a titanium turbine blade of complex geometry with a fine surface crack. Further, the interaction of Lamb wave modes with multiple layer delaminations in glass fiber epoxy composite laminates was studied. The data acquired from these experiments yielded complex sets of signals which were not easily discern able for obtaining the information required regarding the defects and damage. So, to obtain a basic understanding of the wave patterns, Spectral finite element method has been employed for simulation of wave propagation in composite beams with damages like delamination and material degradation. Following this, time-frequency analysis of a number of simulated and experimental signals due to elastic wave scattering from defects and damage were performed using wavelet transform (WT) and Hilbert-Huang transform(HHT).And, a comparison of their performances in the context of quantifying the damages has given detailed insight into the problem of identifying localized damages, dispersion of multi-frequency non-stationary signals after their interaction with different types of defects and damage, finally leading to quantification. Conventional Lamb wave based damage detection methods look for the presence of defects and damage in a structure by comparing the signal obtained with the baseline signal acquired under healthy conditions. The environmental conditions like change in temperature can alter the Lamb wave signals and when compared with baseline signals may lead to false damage prediction. So, in order to make Lamb wave based damage detection baseline free, in the present work, the time reversal technique has been utilized. And, experiments were conducted on metallic and composite plates to study the time reversal behavior ofA0 andS0Lamb wave modes. Damage in the form of a notch was introduced in an aluminum plate to study the changes in the characteristics of the time reversed Lamb wave modes experimentally. This experimental study showed that there is no change in the shape of the time reversed Lamb wave in the presence of defect implying no breakage of time reversibility. Time reversal experiments were further carried out on a carbon/epoxy composite T-pull specimen representing a typical structure. And, the specimen was subjected to a tensile loading in a Universal testing machine. PWAS sensor measurements were carried out at no load as also during different stages of delamination due to tensile loading. Application of time reversed A 0 and S0 modes for both healthy and delaminated specimens and studying the change in shape of the time reversed Lamb wave signals has resulted in successful detection of the presence of delamination. The aim of this study has been to show the effectiveness of Lamb wave time reversal technique for damage detection in health monitoring applications. The next step in SHM is to identify the damage location after the confirmation of presence of damage in the structure. Wave based acoustic damage detection methods (UT and AE) employing triangulation technique are not suitable for locating damage in a structure which has complicated geometry and contains structural discontinuities. And, the problem further gets compounded if the material of the structure is anisotropic warranting complex analytical velocity models. In this work, a novel geodesic approach using Lamb waves is proposed to locate the AE source/damage in plate like structures. The approach is based on the fact that the wave takes minimum energy path to travel from the source to any other point in the connected domain. The geodesics are computed numerically on the meshed surface of the structure using Dijkstra’s algorithm. By propagating the waves in reverse virtually from these sensors along the geodesic path and by locating the first inter section point of these waves, one can get the AE source/damage location. Experiments have been conducted on metallic and composite plate specimens of simple and complex geometry to validate this approach. And, the results obtained using this approach has demonstrated the advantages for a practicable source location solution with arbitrary surfaces containing finite discontinuities. The drawback of Dijkstra’s algorithm is that the geodesics are allowed to travel along the edges of the triangular mesh and not inside them. To overcome this limitation, the simpler Dijkstra’s algorithm has been replaced by a Fast Marching Method (FMM) which allows geodesic path to travel inside the triangular domain. The results obtained using FMM showed that one can accurately compute the geodesic path taken by the elastic waves in composite plates from the AE source/damage to the sensor array, thus obtaining a more accurate damage location. Finally, a new triangulation technique based on geodesic concept is proposed to locate damage in metallic and composite plates. The performances of triangulaton technique are then compared with the geodesic approach in terms of damage location results and their suitability to health monitoring applications is studied.

L’objectif de cette thèse est de concevoir et de réaliser un mobile piézoélectrique pour utilisation coopérative. Le terme mobile piézoélectrique est utilisé dans cette thèse pour décrire un robot piézoélectrique miniature. Ce robot miniature mobile est actionné par des matériaux piézoélectriques. L’objectif de la thèse est donc la conception et la réalisation d’un robot pouvant être miniaturisé et qui pourrait donc être utilisé dans le cadre du mimétisme des essaims biologiques (fourmis, abeilles…) pour un fonctionnement coopératif.Le robot réalisé est constitué d'un support mince et de patchs piézoélectriques. Les patchs piézoélectriques sont collés sur le support de façon intelligente afin de déplacer le support en milieu terrestre. Dans ce contexte, la thèse est divisée en trois parties.La première partie est consacrée à la modélisation d’un tel système (support mince avec des patches piézoélectriques sur une seule de ses faces). Une modélisation par la méthode des éléments finis est développée pour ce système en se basant sur le principe variationnel d’Hamilton et en considérant l'hypothèse de Love-Kirchhoff. L’originalité de cette modélisation réside dans l’utilisation de la notion du plan neutre pour modéliser ce système asymétrique. Cela permet de ne modéliser le système étudié que par un modèle éléments finis à deux dimensions (2D) tout en tenant compte de la troisième dimension dans le calcul. La deuxième partie présente le principe de fonctionnement du robot qui est inspiré des moteurs linéaire ultrasoniques à ondes progressive. Cette partie présente toutes les étapes de la conception optimale afin de créer les mouvements nécessaires. La conception optimale est étudiée en utilisant la modélisation par éléments finis obtenue dans la première partie. La troisième partie de cette thèse est dédiée à la réalisation d’un prototype expérimental. Le processus de fabrication ainsi que l’électronique associée au robot sont présentés dans cette partie. Le robot est caractérisé expérimentalement en mesurant la vitesse en fonction de la tension appliquée, la vitesse en fonction de masses embarquées par le robot et la vitesse en fonction de la force fournie par le robot. Ce robot est, par ailleurs, comparé avec d’autres systèmes de même nature. / The objective of this thesis is to design and realize a piezoelectric mobile for cooperative use. The term piezoelectric mobile is used in this thesis to describe a piezoelectric miniature robot. This mobile miniature robot is actuated by piezoelectric materials. The aim of the thesis is the design and the realization of a robot that can be miniaturized and could therefore be used in the context of biological mimicry swarms (ants, bees ...) for a cooperative operation.The realized robot consists of a thin support and piezoelectric patches. Piezoelectric patches are bonded on the support on an intelligent manner in order to move the support on land. In this context, the thesis is divided into three parts.The first part is devoted to the modeling of such a system (thin support with piezoelectric patches on one of its faces). Modeling by the finite element method is developed for this system based on the variational principle of Hamilton and considering the Love-Kirchhoff hypothesis. The originality of this model lies in the use of the concept of the neutral plane to model this asymmetric system. This allows modeling the system studied by a finite element model in two dimensions (2D), taking into account the third dimension in the calculation.The second part presents the operating principle of the robot which is inspired by the linear traveling wave ultrasonic motors. This section presents all the stages of the optimal design to create the necessary movements. The optimal design is investigated using finite element modeling obtained in the first part.The third part of this thesis is devoted to the realization of an experimental prototype. The manufacturing process and the associated electronics for the robot are presented in this section. The robot is characterized experimentally by measuring the speed according to the applied voltage, the speed versus mass loaded by the robot and the speed according to the force provided by the robot. This robot is also compared with other similar systems.