Semi-analytical analysis for piezoelectric plate using the scaled boundary finite-element method

• We develop a 3D-consistent technique to analyse piezoelectric plates.
• Representing the through-thickness solutions of piezoelectric plates analytically.
• The technique can be flexibly tailored for different piezoelectric applications.
• Analysing the plates as 3D structures without sacrificing computational efficiency.
• Modelling curved boundaries effectively with high order spectral elements.

This paper presents an accurate semi-analytical technique to analyse piezoelectric plates. The proposed technique is built upon the scaled boundary finite-element method. No kinematic and electrostatic assumptions are introduced in the derivation process. The in-plane dimensions are divided into 2D elements and the 3D geometry is obtained by translating the mesh in thickness direction. The through-thickness solutions are expressed analytically with a matrix exponential function. The 3D-onistent nature allows the proposed technique to describe the through-thickness behaviour of piezoelectric plates accurately. Numerical shear locking does not arise. Four numerical examples are presented to highlight the performance of the proposed technique.