Revisiting the electroelastic solution for an FGPM thick-walled cylinder subjected to mechanical and electric loadings

Abstract

Theoretical analysis for an empty thick-walled FGPM cylinder exposed to electric and mechanical loadings are investigated. The cylinder is a composite material composed of PZT4 and PVDF and the volume fraction of PZT4 is given by the power law with three controllable parameters which can cover more complex circumstances. The hypergeometric equation of the radial displacement is acquired by utilizing the Voigt method, and the solutions of the stresses and the electric potential are obtained after solving the radial displacement. The method in this paper is appropriate for real functionally graded piezoelectric materials and can avoid assumptions about unknown overall material parameters appeared in previous references. Finally, the impacts of the parameter n in volume fraction of FGPM cylinder on mechanical and electric behaviors are examined. Furthermore, the distinction between the hoop stress and radial stress is discussed to decrease the pressure concentration in FGPM cylinder. Nomenclature a, b inner and outer radii r radial coordinate c(r) volume fraction of material A c 0 , k, n material parameters in the volume fraction c(r) p a , p b internal and external pressures j a , j b internal and external electric potentials C ijkl i (i=1, 2) elastic modulus of the component e mij i (i=1, 2) piezoelectric tensor modulus of the component k mk i (i=1, 2) dielectric modulus of the component u radial displacement j electric potential e , r i ( ) e q i ( ) radial and hoop strains of the component e , r e q average radial and hoop strains of the cylinder s , r i ( ) s q , i ( ) s z i ( ) radial, hoop, and axial stresses of the component s , r s q , s z average radial, hoop, and axial stresses of the cylinder E , r i ( ) D r i ( ) radial electric field and electric displacement of the component E , r D r average radial electric field and electric displacement of the cylinder a(r), b(r), d(r), g(r), f (r), h(r), k(r) functions related to the volume fraction c(r)