A general method for recovering equilibrating element tractions Original Research Article

A new geometrical presentation of a general method for recovering equilibrating element tractions is developed for 2D finite element models of problems in structural mechanics. The data for the method consists of the prescribed loading and the stress fields resulting from a conventional linear elastic finite element analysis. The geometrical presentation utilises the physical concepts of nodal forces and Maxwell force diagrams based on nodal equilibrium. Only small problems have to be solved for each node. This presentation complements the original algebraic approach of Ladeveze, and extends the method to cover the use of hierarchical p-elements in regular meshes, and general higher-order elements in 1-irregular meshes as encountered in h-p mesh refinement. The same presentation is considered for the recovery of residual tractions as required in the solution of the local residual problem. Comparison is made with related methods for obtaining residual tractions, in particular those proposed by Bank and Weiser and Ainsworth et al. Detailed examples are included to illustrate the presentation. This paper considers only the fundamental aspects of recovering equilibrating tractions. The knowledge gained may be used in various applications such as error analysis, limit analysis, and structural design.