Formulation of elastostatic hybrid-Trefftz stress elements Original Research Article

The hybrid-Trefftz stress (HTS) element is derived from the fundamental conditions of linear elastostatics. The stress and boundary displacement fields are directly approximated. Consistent finite element variables are so defined as to obtain boundary integral expressions for the finite element equilibrium and compatibility conditions, encoded by dual transformations independent of the constitutive relations. Reciprocity is preserved in the finite element elasticity relations, which are also found to be described by boundary integral arrays when the Trefftz constraint is enforced. Consequent upon duality and reciprocity, the resulting boundary integral solving system is symmetric and sparse. The energy statements associated with the hybrid-Trefftz stress element are established and the conditions for the existence, uniqueness, multiplicity and static and kinematic admissibility of the finite element solutions are presented. The HTS clement is compared with the displacement frame based hybrid-Trefftz (HT-D) element of Jirousek. It is shown that the HT-D element is in fact an hybrid stress element. The numerical tests performed to assess the relative performances of the HTS and HT-D elements show that better accuracy levels are obtained using discontinuous boundary approximation bases.