Finite element shakedown analysis of two-dimensional structures

In the present paper, the formulation proposed by Casciaro and Garcea (Comput. Meth. Appl. Mech. Eng., 2002; 191:5761–5792) and applied to the shakedown analysis of plane frames, is extended to the analysis of two-dimensional flat structures in both the cases of plane-stress and plane-strain. The discrete formulation is obtained using a mixed finite element in which both stress and displacement fields are interpolated. The material is assumed to be elasto-plastic and a linearization of the elastic domain is performed. The result is a versatile iterative scheme well suited to implementation in general purpose FEM codes. An extensive series of numerical tests is presented showing the reliability of the proposed formulation