A Semi-Analytical Finite Layer Method for Analyzing the 3D Coupled Electro-Mechanical Behavior of Exponentially Graded Piezoelectric Circular Hollow Microscale Cylinders

Within the framework of consistent couple-stress theory (CCST), we develop a semi-analytical finite layer method (FLM) to investigate the three-dimensional (3D) coupled electro-mechanical behavior of an exponentially graded (EG) piezoelectric circular hollow microscale cylinder under simply supported boundary conditions. The microscale cylinder is subjected to mechanical loads and electric voltages and is placed under closed-circuit surface conditions on its outer and inner surfaces. Using the principle of stationary potential energy, we first derive a 3D Galerkin weak formulation for this study. We divide the microscale cylinder into nl layers and select each layer’s elastic displacements and electric potential as the primary variables. We then incorporate a layer-wise generalized displacement model into the weak formulation to develop the semi-analytical FLM. The novelty of our method lies in its ability to accurately determine the electric and elastic field variables induced in the microscale cylinder. This feature has not been explored in previous research. We rigorously validate our method’s accuracy by comparing its solutions for EG piezoelectric circular hollow macroscale cylinders with the corresponding 3D solutions reported in the literature, with the material length-scale parameter set to zero. We also examine the impact of several key factors on the coupled electro-mechanical behavior of the microscale cylinder, including the radius-to-thickness ratio, inhomogeneity index, piezoelectricity, and material length-scale parameter, which appear to be significant.