Mixed plate theories based on the Generalized Unified Formulation. Part III: Advanced mixed high order shear deformation theories

Abstract

Abstract The Generalized Unified Formulation was introduced in Part I in the case of plate theories based upon Reissner’s Mixed Variational Theorem. Part II analyzed the case of layerwise theories. In this work ( Part III ) the Generalized Unified Formulation is applied, for the first time in the literature, to the case of mixed higher order shear deformation theories. The displacements u x , u y , u z have an equivalent single layer description, whereas the stresses σ zx , σ zy , σ zz have a layerwise description. The compatibility of the displacements and the equilibrium of the transverse stresses between two adjacent layers are enforced a priori . If the out-of-plane stresses are eliminated using the Static Condensation Technique the resulting theories are formally identical to the displacement-based “classical” higher order shear deformation theories. If the static condensation is not applied then a quasi-layerwise higher order theory is obtained. ∞ 6 Mixed higher order shear deformation theories are therefore presented. All ∞ 6 theories are generated by expanding thirteen 1 × 1 invariant matrices (the kernels of the Generalized Unified Formulation). The kernels have the same formal expressions as the ones used for the layerwise theories analyzed in Part II . This makes the generation of the present mixed higher order shear deformation theories particularly effective and easy to implement in a computer code.