A regularized dual mixed element for plane elasticity implementation and performance of the BDM element Original Research Article

In the present work we consider aspects of the formulation and numerical implementation of the BDM element [1, 2]. This element is based on an extended dual Hellinger-Reissner principle which leads to optimal convergence rates for the stresses and displacements. The element is characterized by a non-symmetric approximation of the stress field [3], which implies an approximation of the work-conjugate rotation field, by adding the couple equilibrium with a Lagrangian multiplier. In order to get a generalized displacement method, the displacement and rotation fields approximation have to be discontinuous, and only the interelement tractions have to be continuous. Conditions for stability checks and optimal convergence of this element have been pointed out by Stein and Rolfes [4]. Within this paper we discuss in detail, algorithmic aspects of the implementation and give comparisons with respect to the approximation behaviour of the Q1, Pian-Sumihara and the recently developed Q1E5 element.