A UNIFIED APPROACH TO MIXED FINITE-ELEMENT METHODS - APPLICATION TO INPLANE PROBLEMS

A general method to treat internal constraints within the context of mixed finite element methods has been presented in previous work. The underlying idea is to constrain the assumed stress and strain fields to satisfy the homogeneous equilibrium equations in a weak sense and thus satisfy a priori the internal constraints. This method is now applied to generate four-node plane stress/strain elements. For these elements, it is proved that locking at the nearly incompressible limit (plane strain) is avoided at the element level. The proposed elements are shown to yield excellent results on a set of standard problems. Furthermore, excellent stresses are obtained at the element level.