Analytic solution of effect of electric field on elasto-plastic response of a functionally graded piezoelectric hollow cylinder

An analytical technique is developed to obtain the effect of electric potential on mechanical and electrical response of a functionally graded piezoelectric (FGP) hollow cylinder under action of internal and external pressure and temperature gradient. It is assumed that properties of FGP material are changed through thickness according to power law function. The exact solution is done in two elastic and plastic sections and stresses, strains and displacements are obtained. It is shown in two examples that for a pressure vessel under interior pressure and thermal loads in electric potential field, yielding may commence from the outside, or from inside and outside simultaneously, depending on material inhomogeneity and combination of loads and the plastic area is extended towards inside with the increase of electric potential.