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3D static bending analysis of functionally graded piezoelectric microplates resting on an elastic medium subjected to electro-mechanical loads using a size-dependent Hermitian C2 finite layer method based on the consistent couple stress theory

    1. [1] National Cheng Kung University

      National Cheng Kung University

      Taiwán

  • Localización: Mechanics based design of structures and machines, ISSN 1539-7734, Vol. 52, Nº. 7, 2024, págs. 3799-3841
  • Idioma: inglés
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  • Resumen
    • Based on the consistent couple stress theory (CCST), we develop a size-dependent Hermitian C2 finite layer method (FLM) for carrying out the three-dimensional (3D) static bending analysis of a simply-supported, functionally graded (FG) piezoelectric microplate which is placed under closed-circuit surface conditions. The microplate of interest is assumed to be resting on a Winkler-Pasternak foundation and subjected to either sinusoidal or uniformly distributed electro-mechanical loads. By setting the material length scale parameter at zero and ignoring the piezoelectric and flexoelectric effects, we reduce the formulation of the Hermitian C2 FLM for analyzing FG piezoelectric microplates to that for analyzing FG piezoelectric macroplates and FG elastic microplates, respectively. The accuracy and the convergence rate of the Hermitian C2 FLM are assessed by comparing the solutions it produces with the exact and approximate 3D solutions of FG piezoelectric macroplates and FG elastic microplates reported in the literature. Because the Hermitian C2 FLM requires that the first-order and second-order derivatives of the primary variables must be continuous at each nodal plane, which in turn leads to their solutions converging rapidly and being able to obtain the accurate results of the electric and elastic variables induced in the microplates, especially for the transverse shear and normal stresses and the electric displacements. The effects of piezoelectricity, flexoelectricity, and the material length scale parameter on the deformations and stresses induced in the FG piezoelectric microplates are significant.


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