Mixed formulated 13-node hexahedral elements with rotational degrees of freedom

A new three-dimensional 13-node hexahedral element with rotational degrees of freedom,<br />which is designated as MR-H13 element, is presented. The proposed element is established by adding five<br />nodes to one of the six faces of basic 8-node hexahedral element. The new element can be effectively<br />used in the connection between the refined mesh and the coarser mesh. The derivation of the current<br />element in this paper is based on the variational principles in which the rotation and skew-symmetric<br />stress are introduced as independent variables. Numerical examples show that the performance of the new<br />element is satisfactory.