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MECSOL 2022
8th International Symposium on Solid Mechanics
A Collocation Approach for the Spectral Element Method
Submission Author:
Nivaldo Campos , SP
Co-Authors:
Nivaldo Campos, Jose Maria Campos dos Santos
Presenter: Jose Maria Campos dos Santos
doi://10.26678/ABCM.MECSOL2022.MSL22-0163
Abstract
The Spectral Element Method (SEM) belongs to a class of Trefftz methods for simulating wave problems in vibroacoustic. The matrices of displacements and forces of this method generally present ill-conditioning, which indeed is common in Trefftz methods. Besides this characteristic, precise results can still be obtained with an advantage over the Finite Element Method due to the reduced dimensions of these matrices. In its original formulation, SEM has no discretization of the boundary. In this work, a collocation approach is used instead. This approach presents results with the same level of accuracy as the original formulation, with the advantage of having faster computational processing. Also, due to the nature of the collocation technique, the boundary conditions are described only at the points chosen, not spamming its restrictions along an infinite line. The formulation implemented is suitable to model rectangular and polygonal Kirchhoff plates, allowing the consideration of several boundary conditions, including mixed ones. Very accurate results were obtained for the cases studied. These results were validated by comparing them with those from FEM models or analytical solutions when available.
Keywords
spectral element method, collocation, high frequency, Plates, Vibration
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