Improved numerical integration for locking treatment in isogeometric structural elements. Part II: Plates and shells

B-spline reduced quadrature rules are proposed in the context of isogeometric analysis. When performing a full Gaussian integration, the high regularity provided by spline basis functions strengthens the locking phenomena and deteriorates the performance of Reissner-Mindlin elements. The uni-dimensional B-spline-based quadrature rules, given in a previous paper (part I), are extended to multi-dimensional problems such as plates and shells. The improved reduced integration schemes are constructed using a tensor product of the uni-dimensional schemes. A single numerical quadrature is performed for bending, transverse shear and membrane terms, without introducing Hourglass modes. The proposed isogeometric reduced elements are free from membrane and transverse shear locking. Convergence is first assessed in plate problems with several aspect ratios and then in the shell obstacle course problems. The resulting under-integrated elements exhibit better accuracy and computational efficiency.