Combined techniques for 3D stresses smoothing

In this work it is presented the combined application of improved SPR-R and REP-R techniques, individually implemented in [1], for smoothing the tensions on hexahedrons for three-dimensional domain problems. This allows obtaining more exact results when using the finite elements method. In order to analyze the combination behavior of these techniques, an hadaptive procedure is made, using the Zienkiewicz-Zhu estimator (Z²) [2] for estimating the error that involves the smoothing stress range. In this way, the effectiveness indices and the error convergence for problems with smooth solution are analyzed and a case where the solution is singular is presented. The convergence results and effectiveness index show that both techniques separately are computationally analogous when the meshes have elevated degrees of freedom as appears in [3]. The most suitable composition for the sphere global solution is: SPR-R to REP-R, whereas for the crack is the REP-R to SPR-R composition. In both cases, these combinations display that greater convergence speed and effectiveness index threshold can be obtained with smaller amount of refinements.