Adaptivity in hybrid-trefftz finite element formulation

With the advent of computer aided design (CAD), the development of fully or semi-automated procedures by which a solution warranting the specified accuracy can most efficiently be reached has become a necessity. It is now of utmost interest to investigate finite element (FE) formulations offering a simple form of adaptivity, easy to implement. The present study (which is a sequel to an earlier paper1 on error estimation by the authors) identifies as a particularly promising approach of attaining this goal the p-method associated with the so-called hybrid-Trefftz FE model.2 Based on a simple stress error estimator1 and prior knowledge of the convergence rate, the solution warranting specified stress accuracy may be reached in a single trial by suitably respecifying just one parameter in the input data. The reported approach has successfully been implemented into the general purpose FE program SAFE3 and its high efficiency is illustrated in the paper through practical applications involving corner singularities and stress concentrations.