Analysis of hybrid methods of mixed-shear-projected triangular and quadrilateral elements for Reissner-Mindlin plates
For computational mechanics researchers, this provides theoretical justification for the observed robustness of two existing plate elements.
The paper proves that the MiSP3 and MiSP4 hybrid finite elements for Reissner-Mindlin plates are uniformly stable with respect to plate thickness and free from shear-locking, confirming their robustness in numerical tests.
It is known that the 3-node hybrid triangular element MiSP3 and 4-node hybrid quadrilateral element MiSP4 presented by Ayad, Dhatt and Batoz (Int. J. Numer. Meth. Engng 1998, 42: 1149-1179) for Reissner-Mindlin plates behave robustly in numerical benchmark tests. These two elements are based on Hellinger-Reissner variational principle, where continuous piecewise linear/isoparametric bilinear interpolations, as well as the mixed shear interpolation/projection technique of MITC family, are used for the approximations of displacements, and piecewise-independent equilibrium modes are used for the approximation of bending moments/shear stresses. We show that the MiSP3 and MiSP4 elements are uniformly stable with respect to the plate thickness and thus free from shear-locking.