An asymptotically correct classical model for smart beams

An asymptotically correct classical beam model has been developed for smart slender structures using the variational asymptotic method. Taking advantage of the slenderness of the structure, we asymptotically split the original three-dimensional electromechanical problem into a two-dimensional electromechanical cross-sectional analysis and a one-dimensional beam analysis. The one-dimensional beam analysis could be geometrically nonlinear or linear depending whether the original three-dimensional analysis is geometrically nonlinear or linear. The cross-sectional analysis, implemented using the finite element method, provides an asymptotically correct, one-dimensional constitutive model for smart slender structures without a priori assumptions regarding the geometry of the cross section, the distribution of the electric field, and the location of smart materials, such as embedded or surface mounted. Several examples are used to validate the accuracy of the present theory with available results in the literature and three-dimensional commercial finite element packages.

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