Reissner–Mindlin Legendre spectral finite elements with mixed reduced quadrature

Legendre spectral finite elements (LSFEs) are examined through numerical experiments for static and dynamic Reissner–Mindlin plate bending and a mixed-quadrature scheme is proposed. LSFEs are high-order Lagrangian-interpolant finite elements with nodes located at the Gauss–Lobatto–Legendre quadrature points. Solutions on unstructured meshes are examined in terms of accuracy as a function of the number of model nodes and total operations. While nodal-quadrature LSFEs have been shown elsewhere to be free of shear locking on structured grids, locking is demonstrated here on unstructured grids. LSFEs with mixed quadrature are, however, locking free and are significantly more accurate than low-order finite-elements for a given model size or total computation time.

► Legendre spectral finite elements are examined for static and dynamic plate bending.
► Shear locking with standard nodal-quadrature is demonstrated.
► A mixed quadrature scheme is introduced that is locking free.
► The elements are dramatically more efficient than standard low-order elements.