Characterisation of Anisotropic, Non-Homogeneous Beam Sections with Embedded Piezo-Electric Materials

The paper discusses the problem of the characterisation of untwisted, untapered, anisotropic and non-homogeneous straight beams with embedded piezo-electric devices. The determination of the section properties, i.e. the generalised electro-elastic sti ness and compliance matrices, is performed through an in-plane discretisation in a nite element way, in which the axial dependence of the unknown is handled in analytical form. This leads to a semianalytical formulation that allows the solution of both the \central" and the \extremity" problems, namely the inde nite and the boundary solutions. The piezo-electric generalisation implies the modelling of the electro-static potential eld. The peculiar bound for piezo-electric devices, the conductive laminae that allow sensing and actuation, implies a distributed non-holonomic constraint to the related electric variables. The section nite element discretisation allows detailed stress and electric displacement recovery, thus giving the designer a powerful analysis tool. A Finite Volumes formulation is used in order to simplify the determination of the three dimensional beam properties. This technique leads to punctual sti ness matrix evaluation, skipping numerical integration, and is intrinsically locking free. A complete set of numerical simulations and comparisons with three dimensional models demonstrate the e ectiveness and soundness of the proposed formulation.