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

Abstract

AbstractThe existence of optimal stress sampling points in finite elements was first 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 different for the cubic bar element. Prathap proposed the best‐fit approach to predict the optimal sampling points, and showed that the best‐fit 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‐fit approach for predicting the optimal sampling points is extended to the linear and quadratic plane triangular elements, and the effectiveness of Barlow points, Gaussian points and best‐fit 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‐fit points are better candidates for patch recovery. Copyright © 2003 John Wiley & Sons, Ltd.