Hybrid Trefftz finite element method for axisymmetric elasticity problems under torsion

An eight-node axisymmetric element AX88T is proposed for predicting the torsional response of axisymmetric elasticity based on the hybrid fundamental solution based finite element method (HFS-FEM). In this approach, two displacement fields are independently assumed in the domain and on the boundary of the element, respectively. The intra-element displacement field is expressed in terms of fundamental solutions satisfying the governing equation of the problem while a conforming frame displacement field is related to the nodal degrees of freedom by standard one-dimensional interpolation functions. By applying the Gauss divergence theorem to the hybrid functional, the resultant finite element formulation completely avoids the need for domain integration, which renders the AX88T element insensitive to distortion. The accuracy and efficiency of HFS-FEM are demonstrated through three numerical examples which includes thick-walled cylinder, flange-shaped cylinder and stepped cylindrical shaft.