A comparison of rotation-free triangular shell elements for unstructured meshes

Abstract

Many engineering applications require accurate and rapidly computed thin-shell elements. Rotation-free (RF) shell elements include the bending behaviour of thin shells without introducing any additional degrees of freedom compared to a membrane element. Instead, constant curvatures are approximated from the out-of-plane displacements of a patch of usually four triangular elements. A consequence of this is that the accuracy for irregular meshes has been unsatisfactory. The aim of this study is to find an RF shell element which is accurate also for unstructured meshes. The main difference between existing elements is whether they assume two-dimensional constant curvatures over the patch or use superposition of one-dimensional constant curvatures for the three pairs of triangles. The first assumption fulfils constant curvatures for a Kirchhoff plate exactly, whereas the second and most common assumption only approximates constant curvatures. The first assumption is significantly more resistant to element shape distortions, whereas the second assumption is slightly faster to compute and more appropriate on boundaries where one or more elements are missing or several neighbouring elements share a side. The combination is significantly more accurate for irregular meshes than other comparable RF elements for linear benchmark tests.