On improved hybrid finite elements with rotational degrees of freedom

A set of three new hybrid elements with rotational degrees‐of‐freedom (d.o.f.'s) is introduced. The solid, 8‐node, hexahedron element is developed for solving three‐dimensional elasticity problems. This element has three translational and three rotational d.o.f.'s at each node and is based on a 42‐parameter. three‐dimensional stress field in the natural convected co‐ordinate system. For two‐dimensional, plane elasticity problems, an improved triangular hybrid element and a quadrilateral hybrid element are presented. These elements use two translational and one rotational d.o.f. at each node. Three different sets of five‐parameter stress fields defined in a natural convected co‐ordinate system for the entire element are used for the mixed triangular element. The mixed quadrilateral element is based on a nine‐parameter complete linear stress field in natural space. The midside translational d.o.f.'s are expressed in terms of the corner nodal translations and rotations using appropriate transformations. The stiffness matrix is derived based on the Hellinger–Reissner variational principle. The elements pass the patch test and demonstrate an improved performance over the existing elements for prescribed test examples.