Isogeometric analysis of Free Form Shells and Accurate calculation of direction vectors using Kirchhoff-Love and Reissner-Mindlin theories

This paper presents isogeometric analysis of free form shells based on Kirchhoff-Love and Reissner-Mindlin theories. The isogeometric approach utilizes Non-Uniform Rational B-Splines (NURBS) for different order approximation of the variables defining the geometry as well as the unknown functions. The geometry is defined for both theories by the NURBS technique for surface generation. In the employed Reissner-Mindlin shell theory, by making use of the anchor point concept the normal vector is calculated accurately. The Kirchhoff-Love shell theory uses three displacements degrees of freedom per node, but the Reissner-Mindlin theory uses five degrees of freedom, three displacements and two rotations. Also, for Kirchhoff-Love shell theory C1 continuity of the NURBS basis functions is needed, while for the Reissner-Mindlin shell theory C0 continuity is sufficient. Several standard benchmark examples with available analytical solutions are presented to demonstrate the performance and accuracy of the approaches. Also, a new benchmark problem is designed to study the performance of the methods as well as the convergence behavior of the presented approach when applied to completely free form shells.