A compatible hierarchical adaptive scheme is proposed which allows to control both density and geometrical properties of meshes with four-node linear finite shell elements. The algorithm produces a sequence of meshes with two aims, nearly equal distribution of the local error in each element and a mesh with regular elements, thus internal element angles near 90° and length ratios of adjacent element sides near unity. This goal is achieved in an efficient manner imposing a combination of a local smoothing algorithm with the adaptive mesh generation.
New created nodes are positioned on the real shell surface and shell boundaries which may be given e.g. by CAD data. Also the shell directors are determined from the normals on the real geometry. Shell intersections are detected automatically as common curves of two adjacent shell parts. As a shell continuum cannot be assumed for these intersections and thus simple standard adaptive schemes fail, shell intersections have to be treated in a way similar to shell boundaries. For some numerical examples the developed algorithms are demonstrated and the resulting meshes are shown.