Adaptive methods for hybrid equilibrium finite element models Original Research Article

This paper presents initial results of work directed at the development of practical adaptive methods for equilibrium finite element models of elastostatic problems in solid mechanics. The formulation of hybrid elements is reviewed, with particular emphasis on recent developments for equilibrium elements. Compatibility defaults for 3D and 2D models are proposed, together with an explicit expression for an error indicator based on such defaults. Two further error indicators are defined which are based on the availability of dual conforming displacement solutions. These solutions are derived from two forms of dual analysis. The one may be considered as being in parallel, the other as being sequential with conforming displacements recovered locally from an equilibrium solution. The two latter error indicators provide upper bounds to the global error. A self-adaptive strategy is proposed to exploit any of these error indicators and estimators, and numerical results are presented and compared for a simple plane stress problem.