Invariant Finite Element Model for Composite Structures: The Generalized Unified Formulation

Abstract

The generalized unified formulation presented here is a modern approach for the finite element analysis of sandwich plates and in general multilayered structures. A large variety of types of theories with any combination of orders of expansion for the different displacement variables can be obtained from the expansion of six 1 x 1 arrays (the kernels or fundamental nuclei of the generalized unified formulation). Each of the displacement variables is independently treated and different orders of expansions for the different unknowns can be chosen. Because infinite combinations can be freely chosen for the displacements, the generalized unified formulation allows the user to write ∞ 3 higher-order shear deformation theories, ∞ 3 zig-zag theories, and ∞ 3 layerwise theories with a single invariant formulation implemented in a single finite element method code. The six independent fundamental nuclei are formally invariant with respect to the order used for the expansion or with respect to the type of theory. The generalized unified formulation can be also adopted for mixed variational statements. In such cases the number of independent kernels would be different but their size would still be 1 x 1 arrays. This paper assesses bending of sandwich structures. Analytical and elasticity solution are compared. The effect of the zig-zag form of the displacement is discussed.