Geometrically nonlinear analysis of thin-shell deployable structures: NURBS-based isogeometric elements are slower than standard Lagrange polynomial finite element formulations

Abstract

Isogeometric formulations of thin shells provide accurate geometric descriptions and deformation fields with higher-order continuity. They use only translational degrees of freedom and require smaller-sized models than standard finite elements with bilinear shape functions, which include both displacement and rotational degrees of freedom. This paper analyses the folding of a prototypical thin-shell deployable structure, a tape spring, using both NURBS-based and bilinear Reissner-Mindlin finite elements available in the software LS-DYNA. It is found that the analysis with isogeometric elements is three times slower than the analysis with bilinear Lagrange polynomial elements. Use of high aspect ratio meshes in the regions of the tape spring that do not deform significantly during folding leads to significant improvements in speed for both types of elements, but the difference in performance remains.