Stabilization schemes for 12-node to 21-node brick elements based on orthogonal and consistently assumed stress modes

Abstract

In this paper, hybrid 13-node to 21-node elements are devised by assuming a set of lower order and a set of higher order stress modes. The lower order modes are so chosen that the resulting elements in the absence of the higher order modes are equivalent to the respective sub-integrated elements. To identify the higher order modes for stabilizing the sub-integrated elements, spurious mechanisms of the sub-integrated elements are first derived. The higher order stress modes, being orthogonal to all the lower modes, are then modified from the strain derived from the spurious mechanisms. To reduce computational cost, simplification is introduced to the flexibility matrix associated with the higher order stress modes. Numerical examples of the stabilized 20- and 21-node elements are presented, their accuracy is close to the state-of-the-art hybrid elements, yet the former elements are much more efficient. © 1994.