On constructing accurate recovered stress fields for the finite element solution of Reissner-Mindlin plate bending problems

Abstract

The effectiveness and reliability of three local least squares fit procedures for the construction of smoothed moments and shear forces for the solution of the Reissner-Mindlin (RM) thick plate model are reviewed. The three procedures considered are, namely, the superconvergent patch recovery technique (SPR), the recovery by equilibrium in patches (REP) and the recovery procedure suggested by Lee, Park and Lee (LP). Numerical studies are carried out by applying these three recovery procedures for the construction of smoothed stress fields for various RM plate bending problems. The results obtained indicate that if the order of polynomial used in the stress recovery is the same as that for the finite element analysis, all three procedures produce recovered stress fields with very similar accuracy and convergence rate. However, when the order of polynomial is raised, if the exact solution is smooth without any strong boundary layers or singularities, both the REP and LP procedures can produce more accurate stress fields than the SPR. In case that singularities or boundary layers are present, the LP procedure often outperforms the REP procedure and results in more stable recovery matrices and more accurate recovered stress fields.