Mixed plate theories based on the Generalized Unified Formulation. Part IV: Zig-zag theories

Abstract

Abstract The generalized unified formulation was introduced in Part I for the case of plate theories based upon Reissner’s mixed variational theorem. Part II analyzed the case of layerwise theories and Part III studied advanced mixed higher order shear deformation theories. In this work the generalized unified formulation is applied, for the first time in the literature, to the case of advanced mixed higher order zig-zag theories. The so called zig-zag form of the displacements is enforced a priori by the adoption of Murakami’s zig-zag function. An equivalent single layer description of the displacements u x , u y and u z is adopted. The out-of-plane stresses σ zx , σ zy and 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. ∞ 6 mixed higher order zig-zag theories are therefore presented. The kernels have the same formal expressions as the ones used in the layerwise theories analyzed in Part II and in the higher order shear deformation theories presented in Part III.