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

The thesis presents a novel computational method for analysing the static and dynamic behaviour of a multi-damaged beam using local and non-local elasticity theories. Most of the lumped damage beam models proposed to date are based on slender beam theory in classical (local) elasticity and are limited by inaccuracies caused by the implicit assumption of the Euler-Bernoulli beam model and by the spring model itself, which simplifies the real beam behaviour around the crack. In addition, size effects and material heterogeneity cannot be taken into account using the classical elasticity theory due to the absence of any microstructural parameter. The proposed work is based on the inhomogeneous Euler-Bernoulli beam theory in which a Dirac's delta function is added to the bending flexibility at the position of each crack: that is, the severer the damage, the larger is the resulting impulsive term. The crack is assumed to be always open, resulting in a linear system (i.e. nonlinear phenomena associated with breathing cracks are not considered). In order to provide an accurate representation of the structure's behaviour, a new multi-cracked beam element including shear effects and rotatory inertia is developed using the flexibility approach for the concentrated damage. The resulting stiffness matrix and load vector terms are evaluated by the unit-displacement method, employing the closed-form solutions for the multi-cracked beam problem. The same deformed shapes are used to derive the consistent mass matrix, also including the rotatory inertia terms. The two-node multi-damaged beam model has been validated through comparison of the results of static and dynamic analyses for two numerical examples against those provided by a commercial finite element code. The proposed model is shown to improve the computational efficiency as well as the accuracy, thanks to the inclusion of both shear deformations and rotatory inertia. The inaccuracy of the spring model, where for example for a rotational spring a finite jump appears on the rotations' profile, has been tackled by the enrichment of the elastic constitutive law with higher order stress and strain gradients. In particular, a new phenomenological approach based upon a convenient form of non-local elasticity beam theory has been presented. This hybrid non-local beam model is able to take into account the distortion on the stress/strain field around the crack as well as to include the microstructure of the material, without introducing any additional crack related parameters. The Laplace's transform method applied to the differential equation of the problem allowed deriving the static closed-form solution for the multi-cracked Euler-Bernoulli beams with hybrid non-local elasticity. The dynamic analysis has been performed using a new computational meshless method, where the equation of motions are discretised by a Galerkin-type approximation, with convenient shape functions able to ensure the same grade of approximation as the beam element for the classical elasticity. The importance of the inclusion of microstructural parameters is addressed and their effects are quantified also in comparison with those obtained using the classical elasticity theory.