An isogeometric extension of Trefftz method for elastostatics in two dimensions

In this paper, an approach to blend the Hybrid-Trefftz Finite Element Method (HTFEM) and the Isogeometric Analysis (IGA) called the Isogeometric Trefftz (IGAT) method is presented. The structure of the isogeometric extension of the Trefftz method is formally the same as for its conventional counterpart, except the approximation of the boundary displacements and geometry that are carried out using the Non-Uniform Rational B-Splines (NURBS) instead of polynomials. In other words, only the element boundaries are approximated using NURBS basis while the Trefftz approximation is used in the interior of the elements. For that reason, IGAT can be ranked alongside recently developed Isogeometric Boundary Element Method (IGABEM), the NURBS-Enhanced Finite Element Method (NEFEM), the Isogeometric Local Maximum Entropy (IGA-LME) method, and the Isogeometrically enhanced Scaled-Boundary element method (SBFEM), which all use NURBS approximation at the domain boundary only. Theoretical conjectures made in this paper are accompanied by three examples that show that IGAT leads to excellent results using only a few elements.