Hybrid equilibrium plate elements of high degree

Abstract

This paper concerns the modelling of plate bending problems governed by Reissner-Mindlin theory when hybrid equilibrium elements of high polynomial degree are used. The fields of statically admissible stress-resultants are categorised into three types according to the nature of their incompatibilities, i.e. pure Trefftz or strongly compatible, weakly compatible, and hyperstatic or strongly incompatible. The effects of this categorisation are reflected in the element formulation. Incompatibilities are quantified in terms of local discontinuities which also account for transverse twist terms. The construction of bases for the three corresponding subspaces of stress-resultants by numerical and/ or algebraic means is reviewed. The potential use of a reformulated element is considered in the context of glass plate structures where residual or hyperstatic stresses play an important role.