Legendre Spectral Finite Elements for Reissner-Mindlin Composite Plates

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.