Analytical Methods for the Plane Problem in Piezoelectric Plate Containing a Polygonal Hole

Bayati Chaleshtari, M. H.; Safarabadi Farahani, M.; Abdolalian, H.

doi:10.22084/jrstan.2023.27303.1232

Analytical Methods for the Plane Problem in Piezoelectric Plate Containing a Polygonal Hole

Document Type : Original Research Paper

Authors

M. H. Bayati Chaleshtari ¹

M. Safarabadi Farahani ¹

H. Abdolalian ²

¹ Advanced Composites & Nanocomposites Research (ACNR) Lab, School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

² School of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

10.22084/jrstan.2023.27303.1232

Abstract

In the engineering design of perforated piezoelectric plates, understanding the effect of geometrical and significant parameters on stress concentration is of vital importance. In this paper, the effect of the hole shape on the stresses induced in perforated piezoelectric plates under mechanical loading was studied. The stress concentration was investigated using an analytical method based on the two-dimensional elastic theory, the Lekhnitskii method and conformal mapping by PZT-4 material and the load angle, the bluntness, and the rotation angle of the 3- to 6-sided polygonal holes. It was found out that the desirable hole angular position for which the minimum stress concentration was obtained was dependent on the order of the polygonal hole. To validate the precision of the reported solution, its results were evaluated by numerical methods achieved from finite element method (FEM) in ABAQUS software. The analytical results were in a reasonable correlation with the finite element (FE) results.

Keywords

Stress concentration factor

Complex variable method

Non-circular hole

Piezoelectric plate

Uniaxial loading