A hierarchic family of isogeometric shell finite elements

► A hierarchic family of isogeometric shell finite elements is presented. ► The hierarchy includes Kirchhoff-Love-, Reissner-Mindlin- and 3d-shells. ► A hierarchic difference vector is used for update of the shell normal. ► The formulation is free from transverse shear locking without extra treatment. ► A new hybrid stress approach is presented to remove membrane locking.