Abstract
A partial mixed finite element (FE)–state space method (SSM) semi-analytical approach is presented for the static analysis of piezoelectric smart laminate composite and functionally graded material (FGM) plates. Hence, using the Hamiltonian formalism, the three-dimensional piezoelectricity equations are first worked so that a partial mixed variational formulation, which retains the translational displacements, electric potential, transverse stresses, and transverse electric displacement as primary variables, is obtained; this allows, in particular, straightforward fulfillment of the electromechanical continuity constraints at the laminate interfaces. After an in-plane FE discretization only, the problem is first reduced, for a single layer, to a Hamiltonian eigenvalue problem that is solved using the symplectic approach; then, the multilayer solution is reached via the SSM propagator matrix. The proposed methodology is finally applied to the static analysis of piezoelectric-cross-ply hybrid laminated composite and FGM plates. In a comparison with open literature, available tabulated results show good agreements, thus validating the proposed approach.
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Dedicated to Professor Hans Irschik on the occasion of his 60th birthday.
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Andrianarison, O., Benjeddou, A. Hamiltonian partial mixed finite element-state space symplectic semi-analytical approach for the piezoelectric smart composites and FGM analysis. Acta Mech 223, 1597–1610 (2012). https://doi.org/10.1007/s00707-012-0646-8
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DOI: https://doi.org/10.1007/s00707-012-0646-8