Eight-node hexahedral elements configured for reducing shear locking in the finite element method

摘要

Improved 8-node hexahedral elements configured for reducing shear locking in finite element method are disclosed. According to one aspect, aspect-ratio based scale factors are introduced to modify partial derivatives of the isoparametric shape function of the hexahedral element with respect to isoparametric dimensions, respectively. The modified derivatives are used for calculating the Jacobian matrix thereby the rate-of-strain. The scale factor is configured such that no changes for a perfect cubic solid element (i.e., element having aspect ratio of 1 (one) in all three spatial dimensions), while significant changes for element having poor aspect ratio. In other words, elements with poor aspect ratio are mapped to a perfect cubic element using the aspect-ratio based scale factors. According to anther aspect, off-diagonal components in the local Jacobian matrix are directly modified by cancelling terms related to spurious shear deformation modes. This measure completely alleviates the shear locking effect even for perfectly shaped elements.