Some remarks on the applicability of rectangular elements to plane strain boundary value problems - Jarzębowski, Andrzej; Maciejewski, Jan (Computer Assisted Methods in Engineering and Science; Vol 5 No 3 (1998), 2023)
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.