Esta é a tradução da segunda e última parte do texto de Arquimedes sobre os corpos flutuantes. A primeira parte deste texto está publicada na Revista da Sociedade Brasileira de História da Ciência, v. 16, p. 69-80, 1996. Nesta segunda parte, Arquimedes discute as condições de equilíbrio para um paraboloide de revolução flutuando em um líquido.
Modeling beam reinforced thin plates at mid and high frequencies through the most commonly used methods such as finite and boundary element methods frequently leads to unsatisfactory results, since the accuracy of these methods depends on the relation between the dimensions of the elements in which the structure was discretized and the wavelength. Due to this characteristic, the modeling using these techniques will require that the size of the elements becomes smaller as the frequency increases, while its number needs to be increased. For structures that are usual in some areas, like the aerospace industry, this will be possible only with an unreasonable computational effort, which is responsible for restricting the use of these methods practically to low-frequency applications. Semi-analytical methods such as the spectral element method do not need mesh refinement at higher frequencies, but they were very limited in the geometries and boundary conditions that can be treated. This paper presents a spectral element for rectangular thin plates reinforced symmetrically along the sides with Euler beams, which can be used to model plates with arbitrary boundary conditions. The method was verified by comparing its results with those obtained from a Finite Element model.
This work studies the influence that the shape of the section of a column immersed in a watercourse has in relation to the hydrodynamic forces that arise due to fluid-structure interaction. The data about São Paulo state rivers’ flows and bridges were revised in order to determine a critical flow rate and choose the cross sections study cases. The simulations made with the ANSYS Fluent software allowed it to obtain the parameters of pressure and drag present in the surface of the column, and these values were used as a criterion to analyze the performance of different cross sections. The model was validated by comparison with the results from other authors in order to guarantee reliability to the study. The values obtained for different cross sections were compared to standardized values recommended by the Brazilian code NBR 7187/2003, when available.
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