On the stability of hybrid equilibrium and Trefftz finite element models for plate bending problems

This paper is concerned with hybrid stress elements in the context of modelling the behaviour of plates subject to out of plane loading and based on Reissner-Mindlin assumptions. These elements are considered as equilibrium elements with statically admissible stress fields of which Trefftz fields form a special case. The existence of spurious kinematic modes in star patches of triangular elements is reviewed when boundary displacement fields are defined independently for each side. It is shown that for elements of moment degree > 1, the spurious modes for stars only exist at specific locations and/or for certain configurations. The kinematic properties of these modes are used to define sufficient conditions for the stability of a complete mesh of triangular elements. A method is proposed to check mesh stability, and introduce local modifications to ensure overall stability.