An isogeometric continuum shell element for non-linear analysis

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 also interpolated using an arbitrary 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. This yields a complete isogeometric representation of the continuum shell formulation. The proposed shell element is implemented in a standard finite element code using Bezier extraction which facilitates numerical integration on the ereference 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 delamination buckling in composite materials is also demonstrated.