L’étude analytique proposée porte sur le comportement en vibration de nanotubes de carbone et de nanoplaques de graphène. Pour ce faire, il s’agira dans un premier temps d’étudier les traditionnelles théories de Bresse-Timoshenko pour les poutres et de Uflyand-Mindlin pour les plaques. Des modèles de cisaillement alternatifs sont développés, notamment basés sur des approches asymptotiques issues du milieu élastique tri-dimensionnel. Les interactions interatomiques, ne pouvant pas être négligées à une échelle nanoscopique, seront ensuite prises en compte dans les modèles à travers la présence de paramètres non locaux. Ainsi, différentes approches continues seront considérées : phénoménologiques, asymptotiques et continualisées. Ce dernier type d’approche est récent et est basé sur le développement de modèles continus à partir des équations discrètes de poutres et plaques épaisses et de l’utilisation des approximants de Padé et des développements en séries de Taylor. Pour chaque modèle développé au cours de cette étude, les fréquences propres seront déterminées pour différentes conditions aux limites. Il s’agira ainsi de définir le meilleur cadre pour l’utilisation de chaque modèle et de déterminer l’éventuelle supériorité d’un modèle sur les autres. / This thesis deals with the analytical study of vibration of carbon nanotubes and graphene plates. First, a brief overview of the traditional Bresse-Timoshenko models for thick beams and Uflyand- Mindlin models for thick plates will be conducted. It has been shown in the literature that the conventionally utilized mechanical models models overcorrect the shear effect and that of rotary inertia. To improve the situation, two alternative versions of theories of beams and plates are proposed. The first one is derived through the use of equilibrium equations and leads to a truncated governing differential equation in displacement. It is shown, by considering a power series expansion of the displacement, that this is asymptotically consistent at the second order. The second theory is based on slope inertia and results in the truncated equation with an additional sixth order derivative term. Then, these theories will be extended in order to take into account some scale effects such as interatomic interactions that cannot be neglected for nanomaterials. Thus, different approaches will be considered: phenomenological, asymptotic and continualized. The basic principle of continualized models is to build continuous equations starting from discrete equations and by using Taylor series expansions or Padé approximants. For each of the different models derived in this study, the natural frequencies will be determined, analytically when the closed-form solution is available, numerically when the solution is given through a characteristic equation. The objective of this work is to compare the models and to establish the eventual superiority of a model on others.

Fundações do tipo radier estaqueado são aquelas formadas pelos elementos estruturais de placa e estacas (elementos de barras) e o solo . Ao contrário de outras tipos de fundações, onde a carga da superestrutura é transferida ao solo pelo radier ou pelas estacas apenas, no radier estaqueado a contribuição das estacas, bem como a do radier são consideradas. As estacas transferem as cargas da superestrutura ao solo e, assim, permitem a redução dos recalques de uma forma muito econômica. O objetivo do presente trabalho é a análise da interação solo-estrutura através do acoplamento MEC-MEF. O solo é considerado um semi-espaço homogêneo, elástico e linear governado pela equação de Navier e modelado pelo Método dos Elementos de Contorno (MEC), admitindo a solução fundamental de Mindlin. As estacas são modeladas pelo Método dos Elementos Finitos (MEF) e cada elemento possui quatro nós. Além disso, as estacas podem receber forças horizontais, verticais e momentos. A tensão de cisalhamento ao longo da estaca é aproximada por um polinômio do segundo grau e as forças na direção horizontal são aproximadas por um polinômio do quarto grau. O elemento de fundação que faz a ligação do pilar com a estaca é representado por uma placa de grande rigidez, que apresenta o comportamento de um bloco. A interação entre o radier estaqueado e o solo é feita através da reação resultante da interação estaca-solo, nos nós com estaca. A interface radier-solo é dividida em elementos triangulares e para a reação do solo considera-se a variação linear ao longo de cada elemento. A superestrutura é modelada pelo MEF. Vários exemplos de interação solo-estrutura são estudados nesta tese, e mostram que as soluções obtidas a partir do programa computacional desenvolvido no presente trabalho denominado SSI estão de acordo com outros autores. / Piled raft foundations are structures consisting of piles, the raft and the soil. Unlike classical foundation design where the building load is either transferred by the raft or the piles alone, in a piled raft foundation the contribution of the piles as well as the raft is taken into account. The piles transfer a part of the building loads into the soil and thereby allow the reduction of settlement in a very economic way. The objective of the present work is the analysis of soil-structure interaction using BEM-FEM coupling. The soil, assumed to be an elastic linear homogeneous half space is governed by Navier\'s equation and it is modeled by the Boundary Elements Method (BEM) using Mindlin\'s fundamental solution. The piles are modeled by the Finite Element Method (FEM) with four nodes each. In addition, the piles can received horizontal and vertical forces and bending moments. The shear traction along the pile is approximated by a second-degree polynomial and the tractions in the horizontal direction are approximated by a fourth degree polynomial. The cap of the pile group is assumed to be rigid. The interaction between the raft and soil is made through the subgrade reaction. The soil-cap interface is divided into triangular elements and the subgrade reaction is assumed to vary linearly across each element. The building\'s structure is modeled by FEM. Several soil structure interaction examples are studied in this thesis, and they show that the solutions obtained from program SSI are in good agreement with others authors.

Inscrite dans le cadre du projet national FOREVER, l'étude proposée s'articule autour des essais en vraie grandeur réalisés à Saint Rémy-lès-Chevreuse par le CEBTP sur neuf micropieux isolés et deux groupes (2x2, 2 diamètres d'entre-axe) chargés axialement, puis transversalement dans du sable de Fontainebleau. Elle comprend l'introduction dans un code de calcul facile d'utilisation pour l'ingénieur, de l'effet de groupe de manière automatique et tridimensionnelle; le programme "GOUPEG-3D" repose sur la théorie couplée des modèles hybrides, utilisant les fonctions de transfert de charge (courbes "p-y" et "t-z") pour l'estimation de l'interaction pieu-sol et l'interaction pieu-sol-pieu intervenant par le biais de coefficients multiplicateurs de déplacement et réducteurs de pression ultime évalués à partir des équations de Mindlin (théorie du continuum élastique). Pour l'analyse des essais, les hypothèses ont porté principalement sur la construction des courbes de réaction du sol en s'appuyant sur les recommandations en vigueur (TA 95, Fascicule 62, règle simplifiée de BUSTAMANTE & DOIX [1985]) reposant sur les essais pressiométriques et sur l'influence du mode de fabrication des micropieux (gravitaire ou à l'aide du perforateur pneumatique R-SOL). Une étude paramétrique portant sur le module de cisaillement intervenant dans les équations de Mindlin, a mis en évidence la forte sensibilité du logiciel à ce paramètre élastique difficile à appréhender et encore sujet à de nombreuses controverses quant à son estimation.

Fundações do tipo radier estaqueado são aquelas formadas pelos elementos estruturais de placa e estacas (elementos de barras) e o solo . Ao contrário de outras tipos de fundações, onde a carga da superestrutura é transferida ao solo pelo radier ou pelas estacas apenas, no radier estaqueado a contribuição das estacas, bem como a do radier são consideradas. As estacas transferem as cargas da superestrutura ao solo e, assim, permitem a redução dos recalques de uma forma muito econômica. O objetivo do presente trabalho é a análise da interação solo-estrutura através do acoplamento MEC-MEF. O solo é considerado um semi-espaço homogêneo, elástico e linear governado pela equação de Navier e modelado pelo Método dos Elementos de Contorno (MEC), admitindo a solução fundamental de Mindlin. As estacas são modeladas pelo Método dos Elementos Finitos (MEF) e cada elemento possui quatro nós. Além disso, as estacas podem receber forças horizontais, verticais e momentos. A tensão de cisalhamento ao longo da estaca é aproximada por um polinômio do segundo grau e as forças na direção horizontal são aproximadas por um polinômio do quarto grau. O elemento de fundação que faz a ligação do pilar com a estaca é representado por uma placa de grande rigidez, que apresenta o comportamento de um bloco. A interação entre o radier estaqueado e o solo é feita através da reação resultante da interação estaca-solo, nos nós com estaca. A interface radier-solo é dividida em elementos triangulares e para a reação do solo considera-se a variação linear ao longo de cada elemento. A superestrutura é modelada pelo MEF. Vários exemplos de interação solo-estrutura são estudados nesta tese, e mostram que as soluções obtidas a partir do programa computacional desenvolvido no presente trabalho denominado SSI estão de acordo com outros autores. / Piled raft foundations are structures consisting of piles, the raft and the soil. Unlike classical foundation design where the building load is either transferred by the raft or the piles alone, in a piled raft foundation the contribution of the piles as well as the raft is taken into account. The piles transfer a part of the building loads into the soil and thereby allow the reduction of settlement in a very economic way. The objective of the present work is the analysis of soil-structure interaction using BEM-FEM coupling. The soil, assumed to be an elastic linear homogeneous half space is governed by Navier\'s equation and it is modeled by the Boundary Elements Method (BEM) using Mindlin\'s fundamental solution. The piles are modeled by the Finite Element Method (FEM) with four nodes each. In addition, the piles can received horizontal and vertical forces and bending moments. The shear traction along the pile is approximated by a second-degree polynomial and the tractions in the horizontal direction are approximated by a fourth degree polynomial. The cap of the pile group is assumed to be rigid. The interaction between the raft and soil is made through the subgrade reaction. The soil-cap interface is divided into triangular elements and the subgrade reaction is assumed to vary linearly across each element. The building\'s structure is modeled by FEM. Several soil structure interaction examples are studied in this thesis, and they show that the solutions obtained from program SSI are in good agreement with others authors.

Orientador: Leandro Palermo Jr / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-09T15:27:34Z (GMT). No. of bitstreams: 1 Sakanaka_SandraHiromi_M.pdf: 2300706 bytes, checksum: bf530823f185b6dbee7f56dd83d01a67 (MD5) Previous issue date: 2006 / Resumo: A análise de vibração livre e de instabilidade de placas finas e placas moderadamente espessas é apresentada através do método dos elementos de contorno (MEC) considerando o efeito da deformação pela força cortante e, particularmente para o cálculo de freqüências naturais, o efeito da inércia rotatória é também considerado. A formulação da solução fundamental é baseada na teoria de Mindlin (1951) mas resultados para a teoria de Kirchhoff (1850) também podem ser obtidos [Palermo Jr. (2000)]. O presente trabalho usa a técnica da iteração inversa através do coeficiente de Rayleigh para a determinação das menores freqüências naturais e cargas críticas de instabilidade das placas. A implementação numérica emprega elementos de contorno isoparamétricos lineares contínuos e descontínuos. Elementos constantes de domínio são usados. Os parâmetros nodais são posicionados nos extremos dos elementos e os pontos de carregamento dos elementos descontínuos são deslocados para o interior a uma distância igual a um quarto do comprimento do elemento. Expressões analíticas das integrais de contorno são desenvolvidas para os casos em que o elemento contém o ponto de carregamento e integração numérica de Gauss-Legendre é feita nos outros casos. As integrais de domínio foram transformadas em integrais de contorno para cada célula e foram tratadas como cargas de superfície atualizadas através de um processo iterativo. Os resultados obtidos foram comparados com valores encontrados na literatura para demonstrar a precisão do presente trabalho / Abstract: Free-vibration analysis and static buckling loads analysis of thin and thick plates considering the shear deformation effects using the Boundary Element Method (BEM) is presented. For the calculation of natural frequencies, the rotatory inertia is also counted. The formulation of the fundamental solution considers Mindlin¿s plates but results according to the classic theory can also be obtained [Palermo Jr. (2000)]. The present article makes use of the inverse iteration with Rayleigh coefficient to determine the smallest natural frequencies and the smallest static buckling loads of the plates. The numerical implementation employed continuous or discontinuous isoparametric linear boundary elements according to the characteristics of the problem to be solved. Constant domain elements are used. Nodal parameters have been placed at the ends of the elements and the source point of the discontinuous elements were positioned at a distance equal to one quarter of the element length. Analytical expressions have been employed in the integration on elements containing the source point and Gauss-Legendre numerical integration scheme otherwise. The domain integrals containing the inertia effects or nonlinear effect have been transformed into boundary integrals for each cell and were treated as surface loads updated in an iterative process. The obtained results were compared to those in literature to demonstrate the precision of this proposal / Mestrado / Estruturas / Mestre em Engenharia Civil

Es werden die vorgestellten Fehlerindikatoren in Bezug auf die Netzsteuerung anhand von drei Beispielen analysiert. Im weiteren werden auch die einzelen MITC-Elemente und ihre Besonderheiten bei dieser Analyse der Netzsteuerung mit berücksichtigt. Als Abschluss werden einige spezielle Fehlerindikatoren vorgestellt, die für die weitere Entwicklung einige interessante Eigenschaften aufzeigen. Im zweiten Teil geht es um die Auswertung mit dem speziellen Ziel der Findung einer optimalen Netzsteuerung. Dabei wird auf die Besonderheiten der Elemente eingegangen sowie auf die Plattendicke und auf ihre Wirkung bei den Fehlerindikatoren. Mit diesen Erkenntnissen wird ein spezieller Fehlerindikator vorgestellt, der die Vorteile aller Fehlerindikatoren aus Teil I vereint.

The present work describes the construction of a semi-analytical model for prediction of buckling loads in simply supported corrugated paperboard panels. The model accounts for transverse shear, due to the weakness of the core in such plates compared to the facings. This was done utilizing energy relations and rst order transverse shear. The panel was homogenised using laminate theory. A detailed model using FEM was derived in order to validate the predictive capabilities of the analytical model. Experimental testing was performed to estimate the accuracy of both theoretical models, and assess the limitation of the analytical model. All modes of analysis showed good agreement for cubic boxes. Further investigation into expanding the scope of the analytical model was carried out and commented on.

This thesis focuses on the development and convergence study of finite element methods for eigenvalue analysis of arbitrarily shaped domains with multi-material and material-void interfaces. Such configurations can be found in problems with evolving discontinuities and interfaces as in fluid-structure interaction or topology optimization problems. The differential equations considered in this thesis include the elliptic operator, Timoshenko beam and Mindlin plate. The compatibility conditions at the interface are weakly imposed using either Nitsche's method or Lagrange multipliers. The variational statements are derived for each case. The analysis results are benchmarked using Galerkin finite element discretization with bodyitted grids. Nitsche's method shows a direct dependence on a penalty term and for Lagrange multipliers method, additional degrees of freedom are added to the solution vector. The convergence rate of the discretized forms is computationally determined and is shown to be optimal for both Timoshenko beams and Mindlin plates.

The aerospace industry is increasingly coming to the conclusion that physics-based high-fidelity models need to be used as early as possible in the design of its products. At the preliminary design stage of wing structures, though highly desirable for its high accuracy, a detailed finite element analysis(FEA) is often not feasible due to the prohibitive preparation time for the FE model data and high computation cost caused by large degrees of freedom. In view of this situation, often equivalent beam models are used for the purpose of obtaining global solutions. However, for wings with low aspect ratio, the use of equivalent beam models is questionable, and using an equivalent plate model would be more promising. An efficient method, Equivalent Plate Analysis or simply EPA, using an equivalent plate model, is developed in the present work for studying the static and free-vibration problems of built-up wing structures composed of skins, spars, and ribs. The model includes the transverse shear effects by treating the built-up wing as a plate following the Reissner-Mindlin theory (FSDT). The Ritz method is used with the Legendre polynomials being employed as the trial functions. Formulations are such that there is no limitation on the wing thickness distribution. This method is evaluated, by comparing the results with those obtained using MSC/NASTRAN, for a set of examples including both static and dynamic problems. The Equivalent Plate Analysis (EPA) as explained above is also used as a basis for generating other efficient methods for the early design stage of wing structures, such that they can be incorporated with optimization tools into the process of searching for an optimal design. In the search for an optimal design, it is essential to assess the structural responses quickly at any design space point. For such purpose, the FEA or even the above EPA, which establishes the stiffness and mass matrices by integrating contributions spar by spar, rib by rib, are not efficient enough. One approach is to use the Artificial Neural Network (ANN), or simply called Neural Network (NN) as a means of simulating the structural responses of wings. Upon an investigation of applications of NN in structural engineering, methods of using NN for the present purpose are explored in two directions, i.e. the direct application and the indirect application. The direct method uses FEA or EPA generated results directly as the output. In the indirect method, the wing inner-structure is combined with the skins to form an "equivalent" material. The constitutive matrix, which relates the stress vector to the strain vector, and the density of the equivalent material are obtained by enforcing mass and stiffness matrix equities with regard to the EPA in a least-square sense. Neural networks for these material properties are trained in terms of the design variables of the wing structure. It is shown that this EPA with indirect application of Neural Networks, or simply called an Equivalent Skin Analysis (ESA) of the wing structure, is more efficient than the EPA and still fairly good results can be obtained. Another approach is to use the sensitivity techniques. Sensitivity techniques are frequently used in structural design practices for searching the optimal solutions near a baseline design. In the present work, the modal response of general trapezoidal wing structures is approximated using shape sensitivities up to the second order, and the use of second order sensitivities proved to be yielding much better results than the case where only first order sensitivities are used. Also different approaches of computing the derivatives are investigated. In a design space with a lot of design points, when sensitivities at each design point are obtained, it is shown that the global variation in the design space can be readily given based on these sensitivities. / Ph. D.

Dans le domaine du génie civil et de la construction, ainsi que de l'industrie, les structures hétérogènes multicouches sont très utilisées. L'une des demandes formulées par les ingénieurs pour concevoir de telles structures est aussi la connaissance des charges limites qu'elles peuvent supporter. Des méthodes d'homogénéisation des plaques et poutres multicouches en analyse limite ont ainsi été développées. Elles conduisent respectivement à des cinématiques de Love-Kirchhoff ou d'Euler-Bernoulli pour la structure homogène équivalente. Afin de prendre en compte les effets de cisaillement, de nouveaux modèles de plaques et de poutres multiparticulaires ont été proposés et justifiés. Après une validation par éléments finis de ces modèles, on les applique au cas des poutres en béton armé renforcées. Ils permettent d'avoir une estimation rapide des chargements maximaux supportables et de construire ainsi un outil de dimensionnement à l'Etat Limite Ultime pour de telles structures.