Three dimensional hourglass stabilization for one point quadrature finite elements

To achieve more efficient three dimensional finite element formulations, single point quadrature methods are used. The spurious hourglass deformation modes that may occur with such elements must be controlled if useful results are to be obtained. Successful hourglass stabilization can be realized with simplified approximations to an otherwise rigorous, but more computational intensive theory. The simplified methods provide improved efficiency, but performance could suffer for distorted or high aspect ratio elements. Therefore, use of the complete theory is desirable, if it can remain computationally competitive. Here, a revised approach to the complete hourglass control theory results in a three dimensional element of comparable efficiency to approximate formulations. Implementation and application of the new element demonstrate its performance.