New improved hourglass control for bilinear and trilinear elements in anisotropic linear elasticity

Abstract

One-point reduced integration method is studied for 4-node quadrilateral and 8-node brick elements together wih correction terms of the numerical integration rule for selective and directional reduced integration schemes for anisotropic linear elasticity. These correction terms were previously called hourglass control to the reduced integration method by Belytschko and others. In the present work the idea of existing hourglass control is carefully examined for its convergence and accuracy, and is extended to include both selective and directional reduced integration methods.

Hourglass stabilization and the virtual element method

“…On the other hand, for a hexahedral element the mean-gradient and the gradient obtained via the one-point Gauss rule do not coincide, and employing (14) does not lead to a linearly consistent scheme, which was recognized in…”

“…In the literature, following Reference [8], many other initial contributions related to hourglass stabilization have also appeared [12][13][14]; for a historical perspective and an exhaustive list of references on this topic, the interested reader can see References [10,15].…”

A practical large-strain solid finite element for sheet forming

“…Also, in the SRI scheme, RI on shear terms could activate 'torsional' hourglassing in torsion-dominant problems where only shear strain exists [4]. Koh and Kikuchi proposed directional RI (DRI) where RI is applied on certain directions based on element geometry [4]. Though DRI works well on two-dimensional problems, in three dimensions it still suffers hourglassing in certain cases.…”

“…SRI does not improve computational efficiency because FI and RI have to be applied to different terms in ESM. Also, in the SRI scheme, RI on shear terms could activate 'torsional' hourglassing in torsion-dominant problems where only shear strain exists [4]. Koh and Kikuchi proposed directional RI (DRI) where RI is applied on certain directions based on element geometry [4].…”

Contribuição para teoria de placas: análises estruturais de compósitos laminados e estruturas sanduíches via formulações unificadas

“…The methods to achieve such control are known as hour-glass control due to the most common shape of the spurious energy modes (Figure 25). For details see Belytschko et al (1984), Schulz (1987), Koh and Kikuchi (1987) and Zienkiewicz and Taylor (2000a). Locally, the shell elements only have five out of six physical DOFs, because the drilling rotational stiffness is null.…”