An asymptotic approach for the analysis of piezoelectric fiber composite beams

초록

An asymptotic-expansion-method-based approach is developed to analyze piezoelectric fiber composite beams by employing the virtual work principle. Starting from the three-dimensional linear piezoelectricity, a microscopic two-dimensional model and a macroscopic one-dimensional model are systematically derived by taking advantage of the slenderness of the beam. This enables us to derive a sophisticated yet efficient tool for the modeling and analysis of piezoelectric fiber-based composites, which can provide us with good physical insights on the behavior of slender adaptive structures in terms of actuation and sensing. The non-classical boundary conditions of the beam are obtained by applying the orthogonality of asymptotic displacements to the beam fundamental solutions. The accuracy and efficiency of the proposed approach are demonstrated by comparing its analytical/numerical predictions with the experimental results, three-dimensional finite element solutions, and one-dimensional beam solutions obtained by the classical rule of mixture.

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