Quadrilateral and triangular plane elements with rotational degrees of freedom based on the hybrid Trefftz method

In this paper, we suggest flexible, accurate, and robust linear elastic plane elements. We introduce drilling degrees of freedom to the hybrid Trefftz plane element by using Allman's quadratic displacement instead of conventional finite element approximation for the boundary displacement. Added drilling degrees increase the accuracy and robustness to mesh quality though they keep the advantages of the hybrid Trefftz method such as efficiency and freedom of the shape of the element. In addition, due to the hybrid Trefftz formulation, Poisson's locking, which may come from Allman's quadratic displacement, disappears.