Stabilization and improvement of the convergence of hybrid-Trefftz stress elements for plate bending analysis

The polynomial boundary basis usually applied in the implementation of hybrid-Trefftz stress elements for plate bending is extended to render its rate of convergence insensitive to the shear-to-bending stiffness ratio of the plate. The boundary basis is also extended to improve the accuracy of the element in the modelling of boundary layer effects and of singular stress fields caused by wedge effects. Numerical testing problems are selected to illustrate and validate the effect of the proposed extensions on the stabilization and improvement of finite element solutions. The solutions modelling boundary layer effects in Mindlin-Reissner plates are used to recover the equivalent shear and corner force concepts of the Kirchhoff plate bending model. • Hybrid-Trefftz stress element for both Mindlin-Reissner and Kirchhoff plate bending. • Enhancement of the boundary displacement basis to attain optimal rates of convergence. • Full insensitivity of the rate of convergence to the shear stiffness of the plate. • Fast convergence of solutions for thin and thick plates with edge and wedge boundary layer effects. • Mindlin-Reissner recovery of Kirchhoff's equivalent shear and corner forces.