A four-node hybrid-Trefftz annular element for analysis of axisymmetric potential problems
For the axisymmetric potential problems, a new four-node annular element has been developed based on the hybrid-Trefftz approach. This element makes use of two independent potential fields: (i) A non-conforming internal field, whose trial functions satisfy a priori the governing differential equations of the problem under analysis, approximates the intra-element potential distribution and, (ii) An auxiliary conforming frame field, which has the same form as in conventional finite element method, enforces the potential continuity between elements. Following the modified variational functional in three dimensional domain, an axisymmetric version is constructed for derivation of the hybrid-Trefftz finite element formulation. Numerical examples show that the proposed element exhibits a marked insensitivity to mesh distortion, as well as good accuracy and robustness.
annular element axisymmetric potential problem hybrid-trefftz approach variational functional quasi-harmonic polynomial