Equilibrium and displacement elements for the design of plates and shells

This paper reconsiders the finite-element modelling of the linear elastic behaviour of plates and shells as governed by the Reissner–Mindlin first-order shear deformation theory. Particular attention is given to the problems associated with the locking of thin forms of structure when modelled with isoparametric conforming elements. As a means of ameliorating or removing these problems, three recent alternative types of elements are studied. Two are displacement elements which include different approaches to the definition of assumed strains, and the third is based on a hybrid equilibrium formulation of a flat shell element. The purpose of the paper is to compare and explain their performances and outputs in the context of two benchmark problems: a trapezoidal plate and the Scordelis−Lo cylindrical shell. Numerical examples are used to illustrate the convergence of stress-resultant contours as well as global quantities such as strain energy. The main conclusion is that while all three alternative types of element overcome locking with regard to displacements, the hybrid models are generally more efficient at providing good quality stress resultants. This is particularly so for those which contribute little to the total strain energy but yet may be significant in design.