Axisymmetric solid-of-revolution finite elements with rotational degrees of freedom

Two new solid-of-revolution axisymmetric finite elements, which account for hoop fibre rotations, are introduced. The first is based on an irreducible formulation, with only displacement and rotation fields assumed independently. The second element, based on a Hellinger–Reissner like formulation, possesses an additional assumed stress field. Furthermore, an element correction, often employed in membrane elements with drilling degrees of freedom to alleviate membrane-bending locking, is adapted to the axisymmetric case. The supplemental nodal rotations introduced herein enhance modelling capability, facilitating for instance the connection between axisymmetric shell and solid models. The new elements are shown to be accurate and stable on a number of popular benchmark problems when compared with previously proposed elements. In fact, for cylinders under internal pressure analysed with a regular mesh, our mixed elements predict displacement exactly, a phenomenon known as superconvergence. The new elements are also shown to be robust and accurate on a number of bending dominated problems.