The four-node C0 Mindlin plate bending element reformulated, Part II. Verification

Abstract

The modified formulation proposed in Part I of this work for the four-node C 0 Mindlin/Reissner plate bending element allows for the internal moment redistribution mechanism, present with the classical formulation under reduced integration, to be retained, yet with the shear locking mechanism rejected. The performance of the reformulated four-node C 0 plate bending element, tested numerically with classical plate bending problems, is found to be excellent in (a) completely removing all shear locking problems developing with the classical formulation under full integration, (b) avoiding the zero energy modes usually developing with the classical formulation under reduced integration schemes, (c) allowing for the potential activation of the internal moment redistribution mechanism, as needed. Activation of the internal moment redistribution mechanism eliminates the problematic behaviour of the original version of the present formulation manifested in the form of flexible elastic finite element models in some cases of plate element applications. The revised, under the present formulation, C 0 four-node plate bending element yields displacements and stress resultants in close agreement with the analytical solutions exhibiting excellent convergence characteristics.