We propose a new three-dimensional formulation based on the mixed Tangential-Displacement Normal-Normal-Stress (TDNNS) method for elasticity. In elastic TDNNS elements, the tangential component of the displacement field and the normal component of the stress vector are degrees of freedom and continuous across inter-element interfaces. TDNNS finite elements have been shown to be locking-free with respect to shear locking in thin elements, which makes them suitable for the discretization of laminates or macro-fibre composites. In the current paper, we extend the formulation to piezoelectric materials by adding the electric potential as degree of freedom.

翻译：本文提出一种基于混合切向位移-法向应力（TDNNS）方法的新型三维弹性公式。在弹性TDNNS单元中，位移场的切向分量与应力矢量的法向分量作为自由度，并在单元界面间保持连续。已有研究表明，TDNNS有限元在薄层单元中能有效避免剪切锁闭现象，因而适用于层合板或宏纤维复合材料的离散化。本文通过引入电势作为自由度，将该方法扩展至压电材料领域。