Publications Details

An exploration of accuracy and convergence of the degenerate uniform strain hexahedral element (a solution to the unmeshed void in an all-hexahedral mesh)

Shelton, Timothy S.; Crane, Nathan K.; Cox, James C.

The uniform strain hexahedral element mesh has long been a work horse for getting accurate and convergent answers in high deformation solid mechanics analyses. Obtaining an allhexahedral mesh can be a difficult and time consuming process thus limiting the element's use in design phase computations. Unconstrained paving and plastering offers a technique to get an all-hexahedral mesh automatically but still can leave un-meshable voids [1] . While degenerated forms of the uniform strain hexahedral element such as the wedge have been used sparingly, they have garnered limited general acceptance. We present a more exhaustive numerical exploration of the degenerated hexes with the hope of encouraging their use to resolve the un-meshable voids. The results of patch tests are used to numerically demonstrate linear completeness of the degenerate elements. A manufactured solution analysis is then used to show optimal convergence rates for meshes containing degenerate elements. Additionally, applications to a torsion rod and high velocity impact are used to highlight the accuracy and applicability of degenerates for solving more complex problems. Copyright © 2013 by ASME.