On using degenerated solid shell elements in adaptive refinement analysis

Three di!erent degenerated shell elements are studied in an adaptive re"nement procedure for the solution of shell problems. The stress recovery procedure expressed in a convective patch co-ordinate system is used for the construction of continuous smoothed stress "elds for the a posteriori error estimation. The performance of the stress recovery procedure, the error estimator and the adaptive re"nement strategy are tested by solving three benchmark shell problems. It is found that when adaptive re"nement is used, the adverse e!ects of boundary layers and stress singularities are eliminated and all the elements tested are able to achieve their optimal convergence rates. It is also found that the accuracy of the shell elements increases with the number of polynomial terms included in the stress and strain approximations. In addition, if complete Lagrangian polynomial terms are used, the element will be less sensitive to shape distortion than the one in which only complete polynomial terms are employed