Plane hybrid stress elements for 3D analysis of moderately thick solids subjected to loading symmetric to midsurface

Plane semi-analytical hybrid stress elements are formulated from the 3D Hellinger–Reissner principle for modelling moderately thick structural components with and without hollows subjected to loadings symmetric to the midsurface. These components possess symmetry in the thickness direction but could not be idealised as either plane stress or plane strain problems. 3D displacement and stress fields conforming to the exact plane stress solution are assumed and normal stresses on the surfaces parallel to the thickness direction are nullified. These 2D elements possess good convergence characteristics and simulate the 3D behaviour of solids whose stress free surfaces exhibit negligible out-of-plane distortion with good level of accuracy comparable to 3D analyses by ABAQUS.