Análise dinâmica não linear de cascas de dupla curvatura

Abstract

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.