A hybrid brick element with rotational degrees of freedom

Abstract

An 8-node brick element using Allman's displacement interpolation is proposed. The optimal number of 36 stress modes is identified. The six equal-rotation strainless modes which are intrinsic to Allman's interpolation are stabilized by using a penalty method. The penalty also enforces the equality of the nodal rotation and the continuum-defined rotation. To enhance computational efficiency, 39 stress modes are initially assumed, three constraints on the stress field are then imposed. The flexibility matrix is simplified, such that only four symmetric 3 × 3 matrices are required to be inverted. Numerical test results are presented, showing good accuracy. © 1993 Springer-Verlag.