A análise de compósitos laminados apresenta grandes desafios, pois, diferentemente dos materiais isotrópicos homogêneos, os compósitos laminados são constituídos de materiais heterogêneos e anisotrópicos. Além disso, as distribuições de tensões interlaminares obtidas com as formulações convencionais são descontínuas e imprecisas. Sua melhoria, portanto, é imprescindível para buscar e modelar critérios de falha relacionados às estruturas formadas por compósitos laminados. Diante disso, este trabalho se concentrou no desenvolvimento e implementação computacional de um elemento finito posicional de pórtico plano laminado cuja cinemática é descrita ao longo da espessura do laminado de acordo com a teoria Layerwise. A formulação do elemento considera a não linearidade geométrica, originada pela ocorrência de grandes deslocamentos e rotações, e admite deformações moderadas, em função da lei constitutiva de Saint-Venant-Kirchhoff. O desenvolvimento deste trabalho se iniciou com uma preparação teórica sobre mecânica dos sólidos deformáveis e métodos numéricos para que fossem adquiridos os subsídios teóricos necessários ao desenvolvimento de códigos computacionais, à interpretação dos resultados e à tomada de decisões quando das análises numéricas. A formulação desenvolvida é Lagrangiana total com emprego do método dos elementos finitos baseado em posições. Inicialmente o elemento finito posicional de pórtico plano homogêneo é proposto, uma vez que sua cinemática possibilita uma expansão natural para o caso laminado. Os graus de liberdade são compostos por posições nodais e por vetores generalizados que representam o giro e a variação na altura da seção transversal. A eficiência do elemento é constatada através de análises realizadas em problemas de pórtico sujeitos a grandes deslocamentos e rotações. Os resultados obtidos apresentaram excelente concordância com soluções numéricas e analíticas disponíveis na literatura. Uma expansão natural da cinemática é empregada na formulação do elemento laminado. Os graus de liberdade do elemento são as posições nodais e as componentes de vetores generalizados associados às seções transversais de cada lâmina. Dessa forma, as lâminas têm liberdade para variação de espessura e giro independente das demais, mas com as posições compatibilizadas nas interfaces. Os resultados de análises numéricas realizadas em vários exemplos demonstram a eficiência da formulação proposta, pois as distribuições de deslocamentos e tensões ao longo da espessura do laminado apresentaram excelente concordância com as obtidas a partir de análises numéricas utilizando um elemento finito bidimensional em uma discretização bastante refinada. Os exemplos analisados contemplam problemas com seção laminada fina ou espessa. / The analysis of laminated composites presents challenges because, unlike homogeneous isotropic materials, the laminated composites are made up of heterogeneous and anisotropic materials. Moreover, the distribution of interlaminar stresses obtained with conventional formulations are discontinuous and inaccurate. His improvement is therefore essential to check and modeling failure criteria related to structures formed by laminates. Thus, this work focused on developing and computational implementation of a positional finite element of laminated plane frame whose kinematics is described throughout the thickness of the laminate according to Layerwise theory. The formulation element considers the geometric nonlinearity, caused by the occurrence of large displacements and rotations, and admits moderate deformation, in the constitutive law function of Saint-Venant-Kirchhoff. The development of this work began with a theoretical preparation on mechanics of deformable solids and numerical methods for the acquired of the theoretical support needed for the development of computational codes, interpretation of results and decision-making when of the numerical analyzes. The developed formulation is total Lagrangian with use of the finite element method based on positions. Initially the positional finite element of homogeneous plane frame is proposed, since their kinematic enables a natural expansion for the laminate case. The degrees of freedom are composed of nodal positions and generalized vectors representing the spin and the variation in the height of the cross section. The efficiency of the element is verified through analyzes performed in frame problems subject to large displacements and rotations. The results showed excellent agreement with numerical and analytical solutions available in the literature. A natural expansion of the kinematics is used in the formulation of the laminate element. The degrees of freedom of the element are the nodal positions and components of the generalized vectors associated to cross-sections of each lamina. Thus, the laminas are free for the thickness variation and for independent spin, but with the positions matched in the interfaces. The results of numerical analysis performed in various examples show the effectiveness of the proposed formulation, since the distributions of displacements and stresses through the thickness of the laminate agreed well with those obtained from numerical analysis using a discretization with two-dimensional finite elements in a very refined. The examples discussed include problems with thin or thick laminated section.

Fiber reinforced composite materials are widely used in aerospace, mechanical, civil and other industries because of their high strength-to-weight and stiffness-to-weight ratios. However, composite structures are highly prone to impact damage. Possible types of defect or damage in composite include matrix cracking, fiber breakage, and delamination between plies. In addition, delamination in a laminated composite is usually invisible. It is very diffcult to detect it while the component is in service and this will eventually lead to catastrophic failure of the structure. Such damages may be caused by dropped tools and ground handling equipments. Damage in a composite structure normally starts as a tiny speckle and gradually grows with the increase in load to some degree. However, when such damage reaches a threshold level, serious accident can occur. Hence, it is important to have up-to-date information on the integrity of the structure to ensure the safety and reliability of composite components, which require frequent inspections to identify and quantify damage that might have occurred even during manufacturing, transportation or storage. How to identify a damage using the obtained information from a damaged composite structure is one of the most pivotal research objectives. Various forms of structural damage cause variations in structural mechanical characteristics, and this property is extensively employed for damage detection. Existing traditional non-destructive inspection techniques utilize a variety of methods such as acoustic emission, C-scan, thermography, shearography and Moir interferometry etc. Each of these techniques is limited in accuracy and applicability. Most of these methods require access to the structure.They also require a significant amount of equipment and expertise to perform inspection. The inspections are typically based on a schedule rather than based on the condition of the structure. Furthermore, the cost associated with these traditional non-destructive techniques can be rather prohibitive. Therefore, there is a need to develop a cost-effective, in-service, diagnostic system for monitoring structural integrity in composite structures. Structural health monitoring techniques based on dynamic response is being used for several years. Changes in lower natural frequencies and mode shapes with their special derivatives or stiffness/ exibility calculation from the measured displacement mode shapes are the most common parameters used in identification of damage. But the sensitivity of these parameters for incipient damage is not satisfactory. On the other hand, for in service structural health monitoring, direct use of structural response histories are more suitable. However, they are very few works reported in the literature on these aspects, especially for composite structures, where higher order modes are the ones that get normally excited due to the presence of flaws. Due to the absence of suitable direct procedure, damage identification from response histories needs inverse mapping; like artificial neural network. But, the main diffculty in such mapping using whole response histories is its high dimensionality. Different general purpose dimension reduction procedures; like principle component analysis or indepen- dent component analysis are available in the literature. As these dimensionally reduced spaces may loose the output uniqueness, which is an essential requirement for neural network mapping, suitable algorithms for extraction of damage signature from these re- sponse histories are not available. Alternatively, fusion of trained networks for different partitioning of the damage space or different number of dimension reduction technique, can overcome this issue efficiently. In addition, coordination of different networks trained with different partitioning for training and testing samples, training algorithms, initial conditions, learning and momentum rates, architectures and sequence of training etc., are some of the factors that improves the mapping efficiency of the networks. The applications of smart materials have drawn much attention in aerospace, civil, mechanical and even bioengineering. The emerging field of smart composite structures offers the promise of truly integrated health and usage monitoring, where a structure can sense and adapt to their environment, loading conditions and operational requirements, and materials can self-repair when damaged. The concept of structural health monitoring using smart materials relies on a network of sensors and actuators integrated with the structure. This area shows great promise as it will be possible to monitor the structural condition of a structure, throughout its service lifetime. Integrating intelligence into the structures using such networks is an interesting field of research in recent years. Some materials that are being used for this purpose include piezoelectric, magnetostrictive and fiber-optic sensors. Structural health monitoring using, piezoelectric or fiber-optic sensors are available in the literature. However, very few works have been reported in the literature on the use of magnetostrictive materials, especially for composite structures. Non contact sensing and actuation with high coupling factor, along with other prop- erties such as large bandwidth and less voltage requirement, make magnetostrictive materials increasingly popular as potential candidates for sensors and actuators in structural health monitoring. Constitutive relationships of magnetostrictive material are represented through two equations, one for actuation and other for sensing, both of which are coupled through magneto-mechanical coefficient. In existing finite element formulation, both the equations are decoupled assuming magnetic field as proportional to the applied current. This assumption neglects the stiffness contribution coming from the coupling between mechanical and magnetic domains, which can cause the response to deviate from the time response. In addition, due to different fabrication and curing difficulties, the actual properties of this material such as magneto-mechanical coupling coefficient or elastic modulus, may differ from results measured at laboratory conditions. Hence, identification of the material properties of these embedded sensor and actuator are essential at their in-situ condition. Although, finite element method still remains most versatile, accurate and generally applicable technique for numerical analysis, the method is computationally expensive for wave propagation analysis of large structures. This is because for accurate prediction, the finite element size should be of the order of the wavelength, which is very small due to high frequency loading. Even in health monitoring studies, when the flaw sizes are very small (of the order of few hundred microns), only higher order modes will get affected. This essentially leads to wave propagation problem. The requirement of cost-effective computation of wave propagation brings us to the necessity of spectral finite element method, which is suitable for the study of wave propagation problems. By virtue of its domain transfer formulation, it bypasses the large system size of finite element method. Further, inverse problem such as force identification problem can be performed most conveniently and efficiently, compared to any other existing methods. In addition, spectral element approach helps us to perform force identification directly from the response histories measured in the sensor. The spectral finite element is used widely for both elementary and higher order one or two dimensional waveguides. Higher order waveguides, normally gives a behavior, where a damping mode (evanescent) will start propagating beyond a certain frequency called the cut-off frequency. Hence, when the loading frequencies are much beyond their corresponding cut-off frequencies, higher order mo des start propagating along the structure and should be considered in the analysis of wave propagations. Based on these considerations, three main goals are identified to be pursued in this thesis. The first is to develop the constitutive relationship for magnetostrictive sensor and actuator suitable for structural analysis. The second is the development of different numerical tools for the modelling the damages. The third is the application of these developed elements towards solving inverse problems such as, material property identification, impact force identification, detection and identification of delamination in composite structure. The thesis consists of four parts spread over six chapters. In the first part, linear, nonlinear, coupled and uncoupled constitutive relationships of magnetostrictive materials are studied and the elastic modulus and magnetostrictive constant are evaluated from the experimental results reported in the literature. In uncoupled model, magnetic field for actuator is considered as coil constant times coil current. The coupled model is studied without assuming any explicit direct relationship with magnetic field. In linear coupled model, the elastic modulus, the permeability and magnetostrictive coupling are assumed as constant. In nonlinear-coupled model, the nonlinearity is decoupled and solved separately for the magnetic domain and mechanical domain using two nonlinear curves,’ namely the stress vs. strain curve and magnetic flux density vs. magnetic field curve. This is done by two different methods. In the first, the magnetic flux density is computed iteratively, while in the second, artificial neural network is used, where a trained network gives the necessary strain and magnetic flux density for a given magnetic field and stress level. In the second part, different finite element formulations for composite structures with embedded magnetostrictive patches, which can act both as sensors and actuators, is studied. Both mechanical and magnetic degrees of freedoms are considered in the formulation. One, two and three-dimensional finite element formulations for both coupled and uncoupled analysis is developed. These developed elements are then used to identify the errors in the overall response of the structure due to uncoupled assumption of the magnetostrictive patches and shown that this error is comparable with the sensitivity of the response due to different damage scenarios. These studies clearly bring out the requirement of coupled analysis for structural health monitoring when magnetostrictive sensor and actuator are used. For the specific cases of beam elements, super convergent finite element formulation for composite beam with embedded magnetostrictive patches is introduced for their specific advantages in having superior convergence and in addition, these elements are free from shear locking. A refined 2-node beam element is derived based on classical and first order shear deformation theory for axial-flexural-shear coupled deformation in asymmetrically stacked laminated composite beams with magnetostrictive patches. The element has an exact shape function matrix, which is derived by exactly solving the static part of the governing equations of motion, where a general ply stacking is considered. This makes the element super convergent for static analysis. The formulated consistent mass matrix, however, is approximate. Since the stiffness is exactly represented, the formulated element predicts natural frequency to greater level of accuracy with smaller discretization compared to other conventional finite elements. Finally, these elements are used for material property identification in conjunction with artificial neural network. In the third part, frequency domain analysis is performed using spectrally formulated beam elements. The formulated elements consider deformation due to both shear and lateral contraction, and numerical experiments are performed to highlight the higher order effects, especially at high frequencies. Spectral element is developed for modelling wave propagation in composite laminate in the presence of magnetostrictive patches. The element, by virtue of its frequency domain formulation, can analyze very large domain with nominal cost of computation and is suitable for studying wave propagation through composite materials. Further more, identification of impact force is performed form the magnetostrictive sensor response histories using these spectral elements. In the last part, different numerical examples for structural health monitoring are directed towards studying the responses due to the presence of the delamination in the structure; and the identification of the delamination from these responses using artificial neural network. Neural network is applied to get structural damage status from the finite element response using its mapping feature, which requires output uniqueness. To overcome the loss of output uniqueness due to the dimension reduction, damage space is divided into different overlapped zones and then different networks are trained for these zones. Committee machine is used to co ordinate among these networks. Next, a five-stage hierarchy of networks is used to consider partitioning of damage space, where different dimension reduction algorithms and different partitioning between training and testing samples are used for better mapping fro the identification procedure. The results of delamination detection for composite laminate show that the method developed in this thesis can be applied to structural damage detection and health monitoring for various industrial structures. This thesis collectively addresses all aspects pertaining to the solution of inverse problem and specially the health monitoring of composite structures using magnetostric tive sensor and actuator. In addition, the thesis discusses the necessity of higher order theory in the high frequency analysis of wavw propagation. The thesis ends with brief summary of the tasks accomplished, significant contribution made to the literature and the future applications where the proposed methods addressed in this thesis can be applied.

A análise de compósitos laminados apresenta grandes desafios, pois, diferentemente dos materiais isotrópicos homogêneos, os compósitos laminados são constituídos de materiais heterogêneos e anisotrópicos. Além disso, as distribuições de tensões interlaminares obtidas com as formulações convencionais são descontínuas e imprecisas. Sua melhoria, portanto, é imprescindível para buscar e modelar critérios de falha relacionados às estruturas formadas por compósitos laminados. Diante disso, este trabalho se concentrou no desenvolvimento e implementação computacional de um elemento finito posicional de pórtico plano laminado cuja cinemática é descrita ao longo da espessura do laminado de acordo com a teoria Layerwise. A formulação do elemento considera a não linearidade geométrica, originada pela ocorrência de grandes deslocamentos e rotações, e admite deformações moderadas, em função da lei constitutiva de Saint-Venant-Kirchhoff. O desenvolvimento deste trabalho se iniciou com uma preparação teórica sobre mecânica dos sólidos deformáveis e métodos numéricos para que fossem adquiridos os subsídios teóricos necessários ao desenvolvimento de códigos computacionais, à interpretação dos resultados e à tomada de decisões quando das análises numéricas. A formulação desenvolvida é Lagrangiana total com emprego do método dos elementos finitos baseado em posições. Inicialmente o elemento finito posicional de pórtico plano homogêneo é proposto, uma vez que sua cinemática possibilita uma expansão natural para o caso laminado. Os graus de liberdade são compostos por posições nodais e por vetores generalizados que representam o giro e a variação na altura da seção transversal. A eficiência do elemento é constatada através de análises realizadas em problemas de pórtico sujeitos a grandes deslocamentos e rotações. Os resultados obtidos apresentaram excelente concordância com soluções numéricas e analíticas disponíveis na literatura. Uma expansão natural da cinemática é empregada na formulação do elemento laminado. Os graus de liberdade do elemento são as posições nodais e as componentes de vetores generalizados associados às seções transversais de cada lâmina. Dessa forma, as lâminas têm liberdade para variação de espessura e giro independente das demais, mas com as posições compatibilizadas nas interfaces. Os resultados de análises numéricas realizadas em vários exemplos demonstram a eficiência da formulação proposta, pois as distribuições de deslocamentos e tensões ao longo da espessura do laminado apresentaram excelente concordância com as obtidas a partir de análises numéricas utilizando um elemento finito bidimensional em uma discretização bastante refinada. Os exemplos analisados contemplam problemas com seção laminada fina ou espessa. / The analysis of laminated composites presents challenges because, unlike homogeneous isotropic materials, the laminated composites are made up of heterogeneous and anisotropic materials. Moreover, the distribution of interlaminar stresses obtained with conventional formulations are discontinuous and inaccurate. His improvement is therefore essential to check and modeling failure criteria related to structures formed by laminates. Thus, this work focused on developing and computational implementation of a positional finite element of laminated plane frame whose kinematics is described throughout the thickness of the laminate according to Layerwise theory. The formulation element considers the geometric nonlinearity, caused by the occurrence of large displacements and rotations, and admits moderate deformation, in the constitutive law function of Saint-Venant-Kirchhoff. The development of this work began with a theoretical preparation on mechanics of deformable solids and numerical methods for the acquired of the theoretical support needed for the development of computational codes, interpretation of results and decision-making when of the numerical analyzes. The developed formulation is total Lagrangian with use of the finite element method based on positions. Initially the positional finite element of homogeneous plane frame is proposed, since their kinematic enables a natural expansion for the laminate case. The degrees of freedom are composed of nodal positions and generalized vectors representing the spin and the variation in the height of the cross section. The efficiency of the element is verified through analyzes performed in frame problems subject to large displacements and rotations. The results showed excellent agreement with numerical and analytical solutions available in the literature. A natural expansion of the kinematics is used in the formulation of the laminate element. The degrees of freedom of the element are the nodal positions and components of the generalized vectors associated to cross-sections of each lamina. Thus, the laminas are free for the thickness variation and for independent spin, but with the positions matched in the interfaces. The results of numerical analysis performed in various examples show the effectiveness of the proposed formulation, since the distributions of displacements and stresses through the thickness of the laminate agreed well with those obtained from numerical analysis using a discretization with two-dimensional finite elements in a very refined. The examples discussed include problems with thin or thick laminated section.

L’objet de cette thèse est de proposer et d’identifier un modèle de comportement mécanique en fatigue écrit à l’échelle du pli ou de la couche composite élémentaire. Le modèle doit permettre de prédire l’évolution des dégradations mais également la résistance résiduelle. Les matériaux concernés par cette étude sont des composites renforcés par des tissus de fibres de verre bi ou tri axiaux. Ce travail exclue les zones de liaisons ou de reprise de pli où des contraintes hors plan engendrent des couplages forts entre endommagement intra et inter laminaires. Les principaux objectifs de la thèse sont de : - Identifier sur le matériau de l’étude les mécanismes d’endommagement et leur couplage en quasi-statique et en fatigue - Caractériser et modéliser la perte de rigidité engendrée par les mécanismes d’endommagement - Caractériser et modéliser les cinétiques d’endommagement en fatigue - Caractériser et modéliser les pertes de résistance engendrées par les mécanismes d’endommagement - Implémenter et tester le modèle proposé (ou celui retenu de la littérature et qui sera modifié si besoin) dans un code de calcul EF / The purpose of this thesis is to propose and identify a model of mechanical fatigue behavior written for the lamina level. The model would be able to predict damage evolution but also residual strength. Studied materials are bi or tri axial glass fibre reinforced plastics fabrics. This work excluded joints areas where out of plane stresses generate strong coupling between intra and inter laminar damage. The main goals of the thesis are: - Identify on the material of the study damage mechanisms and their coupling in quasi-static and fatigue - Characterize and model residual stiffness caused by damage mechanisms - Characterize and model fatigue damage - Characterize and model residual strength caused by damage mechanisms - Implement and test the proposed model (or the one chosen in the literature and changed if necessary) in a computer FE code

Composite laminates are being more employed as fundamental structures due to its low weight and high stiffness. An example of this innovation is the primary structures of modern aircraft, which are lighter than the material formerly used. To predict the material response as load gradually increases can be quite demanding due to composite\'s complex failure mechanism. Hence superior computational models should be further investigated to precisely predict the mechanical behavior of composite media. This dissertation addresses an extended finite element procedure based on the layerwise displacement theory to simulate purely mode I delamination failure in composite laminates. The present model has the potential to perform structural analyzes in a pre-delaminated structure and also considering progressive failure. The type of element to be employed at the discretion of the model is the rectangular 4-node iso-parametric homogeneous element whose displacement field is approximated based in the layerwise theory. There are four types of degrees of freedom, one displacement in each direction, and one degree of freedom associated to the strong discontinuity. Numerical examples already solved in the bibliography are suggested in this dissertation, which demonstrate the potential of the model developed to accurately simulate pure mode I delamination in case of the investigation here is further elaborated. In addition, one possibility of future development of this dissertation is the modeling of fracture mode I without the need to discretize the cohesive planes as realized in traditional Cohesive Zone Methods. / Compósitos laminados estão sendo mais empregados como estruturas fundamentais devido ao seu baixo peso e alta rigidez. Um exemplo dessa inovação são as estruturas primárias das aeronaves modernas, que são mais leves do que as os materiais empregados antigamente. Prever a resposta do material à medida que a carga aumenta gradualmente pode ser difícil devido ao complexo mecanismo de falha dos compósitos. Portanto, modelos computacionais mais refinados devem ser investigados a fim de se prever um comportamento mecânico mais preciso. Esta dissertação aborda um procedimento de elementos finitos estendido baseado na teoria de deslocamento layerwise para simular falhas de delaminação modo I em laminados compósitos. O modelo abordado tem potencial para realizar análises em uma estrutura prédelaminada além de falha progressiva. O tipo de elemento a ser empregado na discrição do modelo é o isoparamétrico, homogêneo de 4 nós, retangular, e o campo de deslocamento é baseado na teoria layerwise. Existem quatro tipos de graus de liberdade, um deslocamento em cada direção, e um grau de liberdade associado à forte. Sugere-se nesse trabalho, exemplos, que são comparados com a bibliografia, e que apontam que o modelo desenvolvido nesta dissertação tem o potencial de simular o fenômeno de delaminação em modo I com acurácia, caso o estudo nessa dissertação seja estendido. Além disso, uma possibilidade de desenvolvimento futuro desse trabalho é a modelagem da fratura modo I sem a necessidade de discretizar os planos coesivos entre as lâminas, como realizado em métodos coesivos tradicionais.

O trabalho de pesquisa realizado trata do comportamento dinâmico e aeroelástico em compósitos laminados de rigidez variável (LCRV). Em virtude dos avanços das técnicas de manufatura de laminados, este tema tem ganhado notoriedade internacional e sua importância se justifica pelo crescente número de trabalhos na área. Neste contexto, foram analisados dois tipos distintos de LCRV: o primeiro diz respeito a laminados fabricados com espaçamento variável entre as fibras paralelas; e o segundo trata de laminados fabricados com deposição das fibras por caminhos curvilíneos, termo em inglês tow steering. Com objetivo de explorar as características dos LCRV, foi desenvolvido um modelo aeroelástico baseado no método dos modos admitidos (Rayleigh-Ritz), utilizando as hipóteses da teoria clássica de laminação (TCL), e foi utilizado o modelo aerodinâmico baseado na teoria das faixas quase estacionária para as análises em escoamentos subsônicos, e na teoria dos pistões, para escoamentos supersônicos nas análises de flutter de painel. Assim, foi investigada a influência do efeito de diferentes funções de distribuição do volume de fibras no comportamento aeroelástico e nas três primeiras frequências naturais, constatando-se uma significativa influência nos resultados, justificando um tratamento adequado para modelagem microestrutural dos laminados com espaçamento variável. Por outro lado, com objetivo de analisar o efeito de incertezas no processo de fabricação nos LCRV fabricados com a tecnologia de tow steering, foi desenvolvida uma estratégia de identificação de incertezas e sua propagação no modelo numérico, além da otimização para obtenção de um projeto robusto. Constatou-se que a melhor configuração obtida pela otimização determinística apresentou grande dispersão quando perturbado o ângulo de definição da trajetória das fibras, diferentemente da configuração selecionada de maneira robusta, que apresentou resultados menos sensíveis a perturbações nos ângulos de deposição das fibras. Foi investigada também a viabilidade da utilização de LCRV do ponto de vista dinâmico, visando aumentar a frequência natural fundamental, e com aplicação em flutter de painel. Em ambas as aplicações foi otimizada a trajetória da deposição das fibras, com base nos polinômios interpoladores de Lagrange, sendo encontrados ganhos razoáveis quando comparados com os laminados de material composto tradicionais de rigidez constante (LCRC). Adicionalmente, foi verificado que os resultados obtidos para o LCRC e o LCRV analisados experimentalmente corroboraram os resultados obtidos numericamente no que diz respeito às frequências naturais e aos modos de vibrar. / The developed research work is related to the dynamic and aeroelastic behaviors of variable stiffness composite laminate plates (VSCL). Due to the advances in the manufacturing techniques, this research theme has been gaining international relevance and its importance is justified by the increasing number of research works in this area. In this context, two different types of VSCL are analyzed: the first regards variable fiber spacing laminates, and the second is manufactured using curvilinear paths (tow steering). In order to explore the VSCL characteristics, it was developed an aeroelastic model based on the assumed modes approach (Rayleigh-Ritz), using the hypotheses of “classical lamination theory” (CLT). Moreover, it was used the aerodynamic model based on the quasi-steady strip theory in the subsonic analyses, and the piston theory, for supersonic flows used in the evaluation of panel flutter. It was investigated the influence of different fiber volume distribution on the aeroelastic behavior and on the first three natural frequencies; it has been found that those influences are significant, which justifies the adequate treatment for the micro -structural model of VSCL. Also, to cope with uncertainties during manufacturing of steered composite laminates, it was developed a strategy for identification of those uncertainties and their propagation through the numerical model; also, an optimization procedure was proposed to achieve robust designs. It was noticed that the response of the optimal configuration obtained from deterministic optimization presented a large dispersion when the tow steering angles were perturbed, in contrast with the selected configuration obtained from robust optimization, in which the results were much less sensible to perturbations in the tow steering angles. Also, it was investigated the viability to use LCRV from the dynamic standpoint, aiming at increasing the fundamental frequency, and with application in flutter panel. For both applications, the fiber placement trajectory was optimized based on Lagrange polynomials. Reasonable gains were found with respect to constant stiffness composite laminates (CSCL). Additionally, it was verified that the obtained experimental results for VSCL and CSCL corroborate the counterparts obtained from numerical simulations regarding natural frequencies and mode shapes. / Tese (Doutorado)

Composite laminates are being more employed as fundamental structures due to its low weight and high stiffness. An example of this innovation is the primary structures of modern aircraft, which are lighter than the material formerly used. To predict the material response as load gradually increases can be quite demanding due to composite\'s complex failure mechanism. Hence superior computational models should be further investigated to precisely predict the mechanical behavior of composite media. This dissertation addresses an extended finite element procedure based on the layerwise displacement theory to simulate purely mode I delamination failure in composite laminates. The present model has the potential to perform structural analyzes in a pre-delaminated structure and also considering progressive failure. The type of element to be employed at the discretion of the model is the rectangular 4-node iso-parametric homogeneous element whose displacement field is approximated based in the layerwise theory. There are four types of degrees of freedom, one displacement in each direction, and one degree of freedom associated to the strong discontinuity. Numerical examples already solved in the bibliography are suggested in this dissertation, which demonstrate the potential of the model developed to accurately simulate pure mode I delamination in case of the investigation here is further elaborated. In addition, one possibility of future development of this dissertation is the modeling of fracture mode I without the need to discretize the cohesive planes as realized in traditional Cohesive Zone Methods. / Compósitos laminados estão sendo mais empregados como estruturas fundamentais devido ao seu baixo peso e alta rigidez. Um exemplo dessa inovação são as estruturas primárias das aeronaves modernas, que são mais leves do que as os materiais empregados antigamente. Prever a resposta do material à medida que a carga aumenta gradualmente pode ser difícil devido ao complexo mecanismo de falha dos compósitos. Portanto, modelos computacionais mais refinados devem ser investigados a fim de se prever um comportamento mecânico mais preciso. Esta dissertação aborda um procedimento de elementos finitos estendido baseado na teoria de deslocamento layerwise para simular falhas de delaminação modo I em laminados compósitos. O modelo abordado tem potencial para realizar análises em uma estrutura prédelaminada além de falha progressiva. O tipo de elemento a ser empregado na discrição do modelo é o isoparamétrico, homogêneo de 4 nós, retangular, e o campo de deslocamento é baseado na teoria layerwise. Existem quatro tipos de graus de liberdade, um deslocamento em cada direção, e um grau de liberdade associado à forte. Sugere-se nesse trabalho, exemplos, que são comparados com a bibliografia, e que apontam que o modelo desenvolvido nesta dissertação tem o potencial de simular o fenômeno de delaminação em modo I com acurácia, caso o estudo nessa dissertação seja estendido. Além disso, uma possibilidade de desenvolvimento futuro desse trabalho é a modelagem da fratura modo I sem a necessidade de discretizar os planos coesivos entre as lâminas, como realizado em métodos coesivos tradicionais.

V současnosti jedna z metod spojování zejména tlustých a vysoce zatížených kompozitních komponent je šroubový spoj, který je možné rozebrat pro případ opravy na rozdíl od lepeného spoje. Kompozitní konstrukce se tradičně dimenzují tak, aby během provozu nedošlo k porušení první vrstvy laminátu, nicméně důležité je taky poznat chování laminátu po porušení první vrstvy. Pro strukturální analýzu nejenom spojů, ale také dalších komponent se používá metoda konečných prvků a protože moderní nelineání řešiče jsou schopné modelovat chování laminátu po porušení první vrstvy, tato schopnost jednoho z nich byla využita v této práci při zkoumaní chování sklolaminátu spojeného s hliníkovou částí šrouby. Konečno-prvkové modely dvou spojů kovové a kompozitní části konstrukce schopné popsat progresivní porušování laminátu byly postaveny s využitím tří různých poruchových kritérií – kritéria maximálního napětí, kritéria Hill a kritéria Tsai-Wu. Problém byl řešen s využitím řešiče Nastran. Křivky síla-posuv, tuhost-posuv a hodnoty zatížení při hraničním posuvu byly porov-nány s výsledky experimentů. Jelikož faktor zbytkové tuhosti ovlivňuje výsledky ana-lýzy progresivního porušování, byly provedeny citlivostní studie zkoumajíci vliv faktoru na přesnost a stabilitu výpočtu. Shoda výpočtu s experimentem v případe prvního šroubového spoje je méně uspokojivá, nicméně shoda v případě druhého spoje, který má zesilující tenkou ocelovou destičku na spodní straně, je podstatně lepší. Vý-borná shoda je zejména při použití interaktivních kritérií Hill a Tsai-Wu.

In response to serious environmental and economic concerns, the design and production of aircrafts have been changing profoundly over the past decades with the nose-to-tail switch from metallic materials to lightweight composite materials such as carbon fibre reinforced plastic (CFRP). In this context, the present doctoral research work aimed to contribute to the development of a CFRP booster casing, a real innovation in the field initiated and conducted by Safran Aero Boosters. More specifically, this thesis addresses the matter of joining metal/CFRP hybrid structures, which are prone to possibly detrimental residual stresses.The issue is treated with an approach combining experimental characterisation and finite element (FE) simulations. The multi-layered system’s state of damage was systematically examined on hundreds of micrographs, and the outcome of this study is presented under the form of a statistical analysis. Further, the defects’ 3D morphology is investigated by incremental polishing. A number of thermal and mechanical properties are measured by diverse physical tests on part of the constituent materials, i.e. the aerospace grade RTM6 epoxy resin, the structural Redux 322 epoxy film adhesive, and AISI 316L stainless steel. They are used as input data in a FE model of the multilayer that is developed and progressively refined to obtain detailed residual stress fields after thermal loading. These results are compared to experimental data acquired by X-ray diffraction stress analysis and with the curvature-based Stoney formula. Cohesive elements are placed at specific locations within the FE model to allow simulating progressive damage. Peel tests, mode I, mode II and mixed mode I/II fracture tests are thus performed in view of measuring the joint toughness. The results of these tests are discussed and the presence of residual stress in the fracture specimens is highlighted. Key information for the calibration of the cohesive law is finally identified via inverse FE analysis of the mode I test, this being a significant step in the process of building a damage predictive FE model of the multi-layered system. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished