New findings on limit state analysis with unstructured triangular finite elements

Abstract

SUMMARY The emergence of high performance unstructured mesh generators enables the use of low‐order triangles and tetrahedras for a wide variety of problems, where no structured quadrangular mesh can be easily constructed. Some of the results acknowledged by the community of computational mechanics therefore need to be carefully looked at under the light of these recent advances in unstructured and adaptive meshing. In particular, we question evidence of locking during plastic flow, as it has been presented by several authors in the past. We claim that locking can also manifest through stress oscillations. Overshoot of limit loads or displacement locking can be explained by other causes: Insufficient mesh refinement or comparison with analytical solutions that are based on assumptions that are inconsistent with the finite element model. We present a stabilized Galerkin mixed method that allows accurate and converging limit loads to be computed for any elastic‐plastic problem using standard equal‐order interpolation for both displacements and mean stress for low‐order linear triangular elements. The method is attractive for simulations where the cost of meshing is more important than the added computational cost of an additional nodal unknown required by the mixed formulation. Copyright © 2013 John Wiley & Sons, Ltd.

Quadratic velocity-linear stress interpolations in limit analysis

“…However, because of certain favorable features of low‐order triangles, considerable effort has been dedicated to obtaining effective linear interpolations that are free from the locking phenomenon. For instance, a thorough theoretical and numerical study on stabilized finite elements that allow equal‐order interpolations (for displacements and mean stress in plasticity) in linear triangles can be found in . In contrast, in this paper, we focus on quadratic velocity interpolations and offer no further remarks on the relative merits of linear and quadratic representations of displacements.…”