A hierarchical theory for layered beams with piezoelectric actuation

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.