Reverse adjustment to patch test and two 8-node hexahedral elements

Abstract

Several treatments can make non-conforming elements pass the strong patch test but at the cost of the degradation in anti-distortion performance. Recently, two planar elements rQm6 and rNQ6 showed that a reverse adjustment (RA) method is very effective for remedying and even improving an element after passing patch test. This paper analyzes the mechanism of RA, introduces a numerical method to determine the optimal adjustment factor, and generalizes the RA method to the 3D non-conforming elements Hm11 and NH11. Accordingly, two 8-node hexahedral elements rHm11 and rNH11 are obtained. The element rHm11 adjusts the adjoint matrix of Jacobian matrix as [J∗r]=(1–r)[J∗]+r[J∗0]; The element rNH11 adjusts the additional linear items introduced by NH11 as Pi' = Pi+c(ωiξ+φiη+δiζ). Since the bending performance of Hm11(r = 1) or NH11(c = 1) is lower than that of H11(r = 0 or c = 0), it is necessary that c < 0, which means RA. Numerical examples show that the RA is very effective, just as in the 2D case. The optimal adjustment factor is −2, the corresponding elements perform much better than their original ones, and the overall performance and accuracy are comparable to the best of various 8-node hexahedral solid elements cited.