An extended isogeometric thin shell analysis based on Kirchhoff–Love theory

• An extended isogeometric element formulation (XIGA) for analysis of through-the-thickness cracks in thin shell structures.
• XIGA can reproduce the singular field near the crack tip and the discontinuities across the crack.
• NURBS basis possesses C1C1-continuity required by Kirchhoff–Love theory without additional rotational degrees of freedom.

An extended isogeometric element formulation (XIGA) for analysis of through-the-thickness cracks in thin shell structures is developed. The discretization is based on Non-Uniform Rational B-Splines (NURBS). The proposed XIGA formulation can reproduce the singular field near the crack tip and the discontinuities across the crack. It is based on the Kirchhoff–Love theory where C1C1-continuity of the displacement field is required. This condition is satisfied by the NURBS basis functions. Hence, the formulation eliminates the need of rotational degrees of freedom or the discretization of the director field facilitating the enrichment strategy. The performance and validity of the formulation is tested by several benchmark examples.