Some remarks on the applicability of rectangular elements to plane strain boundary value problems

Abstract

The aim of this paper is the discussion on the applicability of some rectangular elements to plane strain boundary value problems. Four different elements were considered: 4-node, 5-node, Serendipity 8-node and Lagrangian 9-node. Two cases: the material layer loaded by a concentrated vertical force and the same layer loaded by a symmetrical rigid punch were discussed. An elastic material was used to avoid the influence of the constitutive model on solutions. To model interface behaviour on the contact surface a Coulomb friction condition was applied. The use of the 4- and 5-node elements resulted in the predictionf the "island" pattern of stress and strain tensors distributions and their non-applicability was proved independently fTom the boundary condition. The 8-node element predicted erroneous distributions of nodal forces and should be avoided in the case of contact problems. Among the discussed group of elements only the 9-node element turned out to be applicable for boundary value problems under plane strain condition.