Análise dinâmica não linear de cascas de dupla curvatura
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Data
2023-12-13
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Universidade Federal de Goiás
Resumo
In the literature, the analytical and semi-analytical formulations used for shell analysis are pri marily based on theories designed for shells parameterized by orthogonal surfaces. In this work,
tensor theories, especially Koiter’s theory, capable of dealing with non-orthogonal surfaces as
well, are employed for analyzing shells with double curvature: spherical panels, elliptical and
hyperbolic paraboloids, and parabolic conoids. The shells, made of linear elastic material, are
analyzed using a semi-analytical model derived from the Rayleigh-Ritz method. Due to the
complexity of the geometry and boundary conditions of the analyzed shells – and consequen tly, the displacement fields – the constructed models require a significant number of degrees of
freedom to achieve numerical convergence. Thus, two order-reduction techniques were used
for shell analysis, the Proper Orthogonal Decomposition and the Spectral Submanifolds. The
natural frequencies, vibration modes, non-linear static responses, and non-linear free and for ced vibrations of shallow and non-shallow doubly curved shells were determined. The results
show that the tensor formulation is superior to the orthogonal formulations for shallow and non shallow shells. The order-reduction techniques used were effective in reducing computational
effort and processing time, without compromising the results of the analyses, within the load
and displacement limits of their formulations. The results contribute to the understanding of
nonlinear phenomena present in these structures.
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Citação
PINHO, F. A. X. C. Análise dinâmica não linear de cascas de dupla curvatura. 2024. 279 f. Tese (Doutorado em Geotecnia, Estruturas e Construção Civil) - Escola de Engenharia Civil e
Ambiental, Universidade Federal de Goiás, Goiânia, 2023.