A composite mixed finite element model for plane structural problems

Abstract

The paper proposes a mixed finite element model and experiments its capability in the analysis of elastic and plastic collapse plane problems. The model is easy to formulate and implement because it is based on simple assumptions for the unknown fields. A composite triangular mesh is assumed over the domain. Within each triangular element the displacement field is described by a quadratic interpolation, while the stress field is represented by a piece-wise constant description by introducing a subdivision of the element into three triangular regions. The elastic solution is constructed through the stationarity condition of the mixed Hellinger–Reissner functional. The plastic collapse analysis is formulated as a mathematical programming problem and is accomplished by an Interior Point algorithm which furnishes both the collapse multiplier and the collapse mechanism. A series of numerical experiments shows that the proposed model performs well in elastic problems and achieves the favorite context in plastic analysis, where it takes advantage of the absence of volumetric locking and the piecewise constant interpolation of the stress field within the element.