Accurate calculation of nodal vectors in isogeometric analysis of shell structures, using Greville points

In this paper, the isogeometric analysis of shell structures along with the optimal method for accurate calculation of nodal vectors is proposed. The Nurbs surface with maximum regularity is used for shell mid-surface description. According to the Reisner- Mindlin hypothesis, the director vectors at control points are needed for the interpolation of the rotations. The calculated nodal direct vectors must lead to exact interpolated director vectors on the shell surface. Hence, a method has been proposed in which the components of director vectors at control points are obtained by solving a system of equations on the whole patch. The system of equations is formed using known values of direction vectors at the Greville points. The accuracy of the proposed method has been investigated by using the results of the most common problem in shell analysis. Convergence behavior for displacement at the loading points has been studied in all solved problems for different order of NURBS and net of control points. The deformation results show better convergence behavior with increasing the regularity and order of NURBS. The knot averages are in a one-to-one correspondence with control points. Thus, the system of equations on these points leads to a unique solution for the nodal direction vectors, and the time to solve equations is significantly reduced.