A new scheme for designing the penalty factor in 3-D penalty-equilibrating mixed elements

In this paper, a new scheme for designing the penalty factor in 3-D penalty-equilibrating mixed elements based on the Hu-Washizu three-field variational functional is proposed to improve the performance of the elements when applied to beam, plate and shell structures. In order to construct this new scheme, the role played by the penalty factor is first discussed in detail by comparing it with the selective reduced factor designed by Sze for overcoming the so-called 'trapezoid locking'. The reason of the poor performance of the penalty-equilibrating element for the distorted elemental geometry is investigated thoroughly. Furthermore, the penalty factor is designed to alleviate the influence of false strain/stress in elements by considering the geometrical characteristics of beam, plate and shell structures. The new scheme is applied to the penalty-equilibrating 3-D mixed element proposed by the present authors previously. Some challenging numerical examples are selected to demonstrate the effectiveness of the present approach.