Three dimensional non-conforming 8-node solid elements with rotational degrees of freedom

A new three-dimensional 8-node solid element with rotational degrees of freedom is presented. The proposed element is established by adding rotational degrees of freedom to the basic X-node solid element. Thus the element has three translations and three rotational degrees of freedom per node. The corner rotations are introduced by transforming the hierarchical mid-edge displacements which are parabolic shape along an edge. The derivation of the element is based on the mixed variational principles in which the rotations are introduced as independent variables. Several types of non-conforming modes are selectively added to the displacement fields to obtain a series of improved elements. The resulting elements do not have the spurious-zero energy modes and Poisson\'s ratio locking and pass patch test. Numerical examples show that presented non-conforming solid elements with rotational degrees of freedom show good performance even in the highly distorted meshes.