Comparative study of p-extensions based on conventional assumed displacement and Hybrid-Trefftz fe models

Abstract

The p-extension of the conventional conforming assumed displacement model has become a highly efficient and well-established tool. Theory and numerical experience have also clearly shown the advantages of such higher order elements. More recently an alternative p-method formulation has been presented based on the so-called Hybrid-Trefftz (HT) FE model whereby the interelement continuity is enforced on a non-conforming internal displacement field chosen so as to a priori satisfy the governing differential equations of the problem (Trefftz field). The paper addresses some theoretical and practical aspects of the two models (accuracy, convergence rates, handling of geometry or load dependent singularities and stress concentrations, error estimation, adaptivity, computational efficiency, etc.) and compares their advantages and drawbacks.