| In order to realize the full compatibility of advanced composite and sandwich structures an internally consistent and accurate modeling process is needed. Hansen and de Almeida developed a unified hierarchical theory for layered beams which has the ability to accurately predict through-the-thickness stress and strain distributions, as well as displacement moments of all combinations of symmetric laminates and sandwich structures. This theory asserts that these predictions can be developed as a superposition of sets of well chosen fundamental states, where a hierarchical sequence of bending states occurs. Fundamental states are described as numerical experiments performed on an infinitesimal segment of the physical beam. Here, piezoelectric actuation effects are considered and a new fundamental state is developed modeling the actuation within the composite or sandwich structure through the application of a uniform electric field. The capabilities of this fundamental state are shown within the confines of the hierarchical beam theory by solving three problems: a purely actuated system, a system subjected to both electrical and mechanical loads and a system of piezoelectric patches that are embedded within a composite structure. The calculated through-the-thickness stress and strain distributions and the displacement moments yield comparable results to 2-D ANSYS finite element predictions. |
