Modelling of Kirchhoff and Mindlin–Reissner Plate Bending With Hybrid‐Trefftz Stress Elements

ABSTRACT The polynomial bases usually applied in the implementation of hybrid‐Trefftz stress elements for plate bending are extended to include the formal solutions necessary to model high‐gradient stress fields associated with boundary layer and singular wedge effects. To this end, the approximation of the stress‐resultant field includes the (Trefftz) solutions of the harmonic, biharmonic, and Helmholtz governing systems of differential equations. Numerical testing problems are selected to show that the element can be used to solve the Kirchhoff model and to adequately simulate both boundary layer and singular wedge effects in thin and moderately thick Mindlin–Reissner plates.