3D Analytical Solutions of Mechatronic Coupling for Functionally Graded Piezoelectric Material Plates With a Circular Hole

ZHANG Youyuan; FAN Huiduo; SHEN Lulu; YANG Bo

doi:10.21656/1000-0887.460016

Volume 46 Issue 11

Nov. 2025

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ZHANG Youyuan, FAN Huiduo, SHEN Lulu, YANG Bo. 3D Analytical Solutions of Mechatronic Coupling for Functionally Graded Piezoelectric Material Plates With a Circular Hole[J]. Applied Mathematics and Mechanics, 2025, 46(11): 1416-1428. doi: 10.21656/1000-0887.460016

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3D Analytical Solutions of Mechatronic Coupling for Functionally Graded Piezoelectric Material Plates With a Circular Hole

doi: 10.21656/1000-0887.460016

1. School of Civil Engineering and Architecture, Zhejiang SciTech University, Hangzhou 310018, P.R.China;
2. Construction Engineering School, Zhejiang College of Construction, Hangzhou 311231, P.R.China

Funds:

The National Science Foundation of China(11872336)

Received Date: 2025-01-24
Rev Recd Date: 2025-03-24

Available Online: 2025-12-05

Abstract

Abstract

Based on the extended England-Spencer functionally graded plate theory, the functionally graded elastic material (FGM) was extended to functionally graded piezoelectric material (FGPM) and the responses of the transversely isotropic FGPM plate containing a circular hole were investigated. By virtue of this theory, a 3D boundary value problem can be transformed into a 2D one. The 3D analytical solution was obtained from 4 analytical functions based on the complex variable function method. For a FGPM plate with a circular hole and subjected to mechanical loads, the specific expressions of the 4 analytical functions were determined according to the boundary conditions. Numerical examples were presented to discuss the effects of boundary conditions and relevant parameters on the 3D stresses along the circular hole edge with the material parameters varying exponentially along the plate thickness. The analytical method provides an effective tool for accurate analysis of 3D hole-related issues in functionally graded piezoelectric plates.
- functionally graded piezoelectric material,
- circular hole,
- mechatronic coupling,
- complex function,
- analytic solution

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References(21)

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