Accurate solution of traction free boundaries using hybrid stress membrane elements with drilling degrees of freedom

Methodologies for the accurate solution of traction free sides using hybrid stress membrane elements with drilling degrees of freedom are presented. Firstly, a method based on direct enforcement of the traction free condition through manipulation of the elemental assumed stress field is presented. Secondly, a penalty-equilibrated approach, in which stress equilibrium is enforced in individual elements, is presented. In the second approach, weak enforcement of equilibrium is proposed, in which the stress derivatives are modified as to alleviate locking-like behavior.