pq-Adaptive solid finite elements for three-dimensional plates and shells

This article presents a pq-adaptive finite element procedure for three-dimensional computation of thin-walled structures like plates and shells. The approach is based on a hexahedral element with high-order shape functions. The polynomial degree of the shape functions in the three spatial directions of the element is adjusted by means of an adaptive procedure. To this end, a hierarchical error indicator is applied to automatically control the polynomial degree q in thickness and p in the in-plane direction of plate- and shell-like structures. The efficiency and reliability of the proposed adaptive method is demonstrated using two numerical examples.