Development of semianalytical axisymmetric shell models with embedded sensors and actuators

Abstract

This paper presents the development of two semianalytical axisymmetric shell finite element models, which have the possibility of having embedded and/or surface-bonded piezoelectric ring actuators and/or sensors. A mixed finite element approach is used, which combines the equivalent single-layer higher-order shear deformation theory, to represent the mechanical behavior with a layerwise discretization in the thickness direction to represent the distribution of the electrical potential of each piezoelectric layer of the frusta conical finite element. The electrical potential function is represented through a layerwise discretization in the thickness direction and can be assumed linear or quadratic with two or six electrical potential ring nodes per piezoelectric layer. The displacement field and the electrical potential are expanded by Fourier series in the circumferential direction, considering symmetric and anti-symmetric terms. Several examples are presented and discussed to illustrate the accuracy and capabilities of both models.