An isogeometric continuum shell element for non-linear analysis

•Formulation of a complete isogeometric continuum shell element including geometric non-linearity.•Use of NURBS for the in-plane displacements in the reference surface of the shell.•Innovative use of a B-spline for the interpolation in the thickness direction.•Use of the B-spline to capture weak and strong discontinuities in the thickness direction, including delamination.

An isogeometric continuum shell formulation is proposed in which NURBS basis functions are used to construct the reference surface of the shell. Through-the-thickness behavior is interpolated using a higher-order B-spline which is in contrast to the standard continuum shell (solid-like shell) formulation where a linear Lagrange shape function is typically used in the thickness direction. The present formulation yields a complete isogeometric representation of the continuum shell. The shell element is implemented in a standard finite element code using Bézier extraction which facilitates numerical integration on the reference surface of the shell. Through-the-thickness integration is done using a connectivity array which determines the support of a B-spline basis function over an element. The formulation has been verified using different linear and geometrically non-linear examples. The ability of the formulation in modelling buckling of static delaminations in composite materials is also demonstrated.