A reconstructed local B̄ formulation for isogeometric Kirchhoff-Love shells

An efficient assumed strain formulation for avoiding the membrane locking of non polar shells is developed in the context of B-spline interpolation. Assumed membrane strains are introduced locally in each element with a local L2-projection, and then a spline reconstruction algorithm, developed by Thomas et al. (2015), is employed for reconstructing the membrane strain at the global patch level. In this way, a banded stiffness matrix is obtained that strongly reduces the computational cost with respect to the standard B̄ formulation for isogeometric analysis. The main advantages of the proposed method are: the reproduction of regular membrane strain fields, an accurate membrane locking-free solution and an high computational efficiency with respect to standard B̄ formulation. The method can be applied for any polynomial degree of the B-spline interpolation. The effectiveness of the proposed method is demonstrated analyzing some bending and membrane dominated problem, commonly employed as benchmark in the shell literature.