Keywords: error estimator, finite element, moving least-squares, statically admissible, stress recovery.

This paper gives first an overview of the stress recovery techniques, with special attention to those proposed since 2000. Then a statically admissible stress recovery (SAR) method is detailed. It uses basis functions, which meet the equilibrium condition within the domain and the local traction conditions on the exterior boundaries, and moving least-squares (MLS) to fit the stresses at sampling points (e.g., quadrature points) obtained by the finite element method (FEM). A widely used benchmark problem, a circular hole in an infinite plate subjected to remote uniaxial tension, is used to demonstrate the advantages of the method, especially its potential for accurate boundary stress extraction.

SAR recovers highly accurate stresses adjacent to holes and close to a crack tip. These results suggest that exact enforcement of local traction conditions on the boundary is essential for accurate boundary stress extraction, while satisfaction of interior equilibrium seems to be of secondary importance.

In principle, SAR can be used with traditional FEs as well as the recently introduced meshless methods and extended FEM. It seems most suitable when using the extended FEM in situations when the actual local fields are not available, and enrichment functions can only be chosen to meet local displacement conditions.

The superconvergent points, if they exist, can of course be used as sampling points in the recovery process. However, SAR is not limited to linear problems, if quadrature points are chosen as sampling points.

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