Stress recovery and error estimation for shell structures

The Penalized Discrete Least-Squares (PDLS) stress recovery (smoothing) technique developed for two- dimensional linear elliptic problems [1{3] is adapted here to three-dimensional shell structures. The surfaces are restricted to those which have a 2-D parametric representation, or which can be built-up of such sur- faces. The proposed strategy involves mapping the nite element results to the 2-D parametric space which describes the geometry, and smoothing is carried out in the parametric space using the PDLS-based Smooth- ing Element Analysis (SEA). Numerical results for two well-known shell problems are presented to illustrate the performance of SEA=PDLS for these problems. The recovered stresses are used in the Zienkiewicz{Zhu a posteriori error estimator. The estimated errors are used to demonstrate the performance of SEA-recovered stresses in automated adaptive mesh re nement of shell structures. The numerical results are encouraging. Further testing involving more complex, practical structures is necessary