Legendre Spectral Finite Elements for Reissner-Mindlin Plates

This is to certify that I have examined a copy of a technical report by Kazh Brito and found it satisfactory in all respects, and that any and all revisions required by the examining committee have been made. Abstract This is an exploration of Legendre spectral finite-element (LSFE) formulations for Reissner-Mindlin plates. The goal was to compare high-order LSFEs with standard low-order finite elements in terms of computational efficiency, and determine an optimal formulation for thin-walled elastic media. Simulations using various LSFE and standard FE formulations were carried out. Model performance is compared by examining the error as a function of both model size (DoF) and model efficiency (FLOPs) for the various formulations. Results showed that LSFEs using a mixed formulation consisting of nodal Gauss-Lobatto-Legendre quadrature for the bending matrix, and reduced Gauss-Legendre quadrature for the shear matrix were most computationally efficient of all elements tested.