Legendre spectral finite elements for Reissner–Mindlin composite plates

Abstract

Legendre spectral finite elements (LSFEs) are examined in their application to Reissner–Mindlin composite plates for static and dynamic deformation on unstructured grids. LSFEs are high-order Lagrangian-interpolant finite elements whose nodes are located at the Gauss–Lobatto–Legendre quadrature points. Nodal quadrature is employed for mass-matrix calculations, which yields diagonal mass matrices. Full quadrature or mixed-reduced quadrature is used for stiffness-matrix calculations. Solution accuracy is examined in terms of model size, computation time, and memory storage for LSFEs and for quadratic serendipity elements calculated in a commercial finite-element code. Linear systems for both model types were solved with the same sparse-system direct solver. At their best, LSFEs provide many orders of magnitude more accuracy than the quadratic elements for a fixed measure (e.g., computation time). At their worst, LSFEs provide the same accuracy as the quadratic elements for a given measure. The LSFEs were insensitive to shear locking and were shown to be more robust in the thin-plate limit than their low-order counterparts.