An edge-based smoothed three-node mindlin plate element (ES-MIN3) for static and free vibration analyses of plates

Abstract

The edge-based strain smoothing technique is combined with the three-node Mindlin plate element (MIN3) to give a so-called the edge-based smoothed three-node Mindlin plate element (ES-MIN3) for static and free vibration analyses of plates. In the formulation of the ES-MIN3, the MIN3 together with a shear stabilized technique is used to compute the strains and to avoid the shear locking. Then the strain smoothing technique on the smoothing domains associated with edges of elements is used to smooth the strains on the adjacent elements. This strain smoothing technique can provide proper softening effect, which will effectively relieve the stiff behavior of the MIN3 and thus improve significantly the accuracy of solutions. The numerical examples demonstrated that the ESMIN3 is free of shear locking, passes the patch test and shows three superior properties such as: (1) be a strong competitor to others existing plate elements in the static analysis; (2) can give high accurate solutions in free vibration analysis; (3) can provide accurately the values of high frequencies of plates by using only coarse meshes.