Development of quadratic enhanced assumed strain elements for three-dimensional linear elasticity

Enhanced assumed strain (EAS) elements are widely used in the literature to address the issue of locking associated with conventional elements. However, existing literature in the context of three-dimensional (3D) elasticity problems is predominantly restricted to the eight-node linear EAS elements. Thus, existing 3D EAS elements do not exploit the superior performance offered by quadratic elements over linear elements. In the current work, we propose a novel twenty-seven node quadratic EAS element, which, to the best of our knowledge, is the first such attempt in the literature. Additionally, the manuscript also presents a six-node wedge and an eighteen-node wedge EAS element. The proposed elements are derived methodically by investigating the interrelation between the two-field Hellinger-Reissner (HR) and three-field Veubeke-Hu-Washizu (VHW) variational formulations. The robustness and performance of the proposed EAS elements is demonstrated through numerous examples.

Automated summary

The study introduces a novel twenty-seven node quadratic EAS element, addressing the underutilization of quadratic elements in existing 3D EAS elements. Additionally, a six-node wedge and an eighteen-node wedge EAS element are presented in the manuscript.