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

Abstract

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.

Highlights

1. A CCST-based Hermitian C² finite layer method (FLM) is developed for analyzing functionally graded (FG) piezoelectric microplates.

2. The current FLM can be reduced to that for analyzing FG elastic microplates by ignoring the piezoelectric and flexoelectric effects.

3. The current FLM can be reduced to that for analyzing FG piezoelectric macroplates by setting the material length scale parameter at zero.

4. Implementing the current FLM reveals that its solutions converge rapidly and are in excellent agreement with those obtained using the exact 3D models.

5. The effects of piezoelectricity, flexoelectricity, and the material length scale parameter on the static bending behavior of FG piezoelectric microplates are significant.

Keywords:

• Consistent couple stress theory
• finite layer methods
• Hermitian C² polynomials
• microplates
• piezoelectricity
• static bending

Disclosure statement

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Data availability

The processed data required to reproduce these findings are available to download from [https://drive.google.com/file/d/1GYwo3WIwL8kkW1hlNllW_5LdUJTDwKpv/view?usp=share_link].

Additional information

Funding

This work was supported by the Ministry of Science and Technology of the Republic of China through Grant MOST 109-2221-E-006-015-MY3.