Optimal stress sampling points of plane triangular elements for patch recovery of nodal stresses

The existence of optimal stress sampling points in nite elements was rst observed by Barlow. Knowledge of optimal stress sampling points is important in stress-recovery methods such as the superconvergent patch recovery (SPR). Recently, MacNeal observed that Barlow points and Gaussian quadrature points are the same for the linear and quadratic bar elements, and di erent for the cubic bar element. Prathap proposed the best- t approach to predict the optimal sampling points, and showed that the best- t points coincide with Gaussian quadrature points not only for the linear and quadratic bar elements but also for the cubic bar element. In this paper, the best- t approach for predicting the optimal sampling points is extended to the linear and quadratic plane triangular elements, and the e ectiveness of Barlow points, Gaussian points and best- t points as candidates of sampling points for the patch recovery of nodal stresses with these triangular elements is investigated for typical problems. The numerical results suggest that Barlow points do not exist for all strain=stress components, and Gaussian quadrature points which are the same as or close to the best- t points are better candidates for patch recovery