On the development of NURBS-based isogeometric solid shell elements: 2D problems and preliminary extension to 3D

This work deals with the development of 2D solid shell non-uniform rational B-spline elements. We address a static problem, that can be solved with a 2D model, involving a thin slender structure under small perturbations. The plane stress, plane strain and axisymmetric assumption can be made. \(\overline{B}\) projection and reduced integration techniques are considered to deal with the locking phenomenon. The use of the \(\overline{B}\) approach leads to the implementation of two strategies insensitive to locking: the first strategy is based on a 1D projection of the mean strain across the thickness; the second strategy undertakes to project all the strains onto a suitably chosen 2D space. Conversely, the reduced integration approach based on Gauss points is less expensive, but only alleviates locking and is limited to quadratic approximations. The performance of the various 2D elements developed is assessed through several numerical examples. Simple extensions of these techniques to 3D are finally performed.