Mixed plate theories based on the Generalized Unified Formulation. Part V: Results

Abstract

Parts I, II, III and IV presented the Generalized Unified Formulation in the framework of Reissner’s Mixed Variational Theorem. Layerwise theories, mixed higher order shear deformation theories and zig-zag models were introduced. In all these types of theories the displacement variables and out-of-plane stresses are independently treated and different orders of expansion for the different unknowns can be chosen. All the possible ∞6 theories are generated by expanding 13 invariant fundamental nuclei. The relative orders used for the expansion of the stresses and displacements are important and can be the source of numerical instabilities. How the instabilities are eliminated is discussed. In the case of layerwise theories and the examined problems, it is shown that there is no numerical instability if the order of displacement uz is the same as the order of stress σzz. New light is also shed on the mixed equivalent single layer theories. It is shown that the poor representation of the a priori calculated transverse stresses is due to the above mentioned numerical instabilities and not only to the insufficient representation of the effects of σzz. Finally, for the mixed case, it is demonstrated that the addition of Murakami’z zig-zag function (MZZF) is convenient but this is not a general property, as was believed in the literature before this work. The convenience of the addition of MZZF is linked to the relative orders of the starting theory that is being improved with the zig-zag term. Several new layerwise and equivalent single layer theories are introduced for the first time in the literature and an assessment is given with new cases compared against the elasticity solution.