Asymmetric Thermal Stresses of Hollow FGM Cylinders with Piezoelectric Internal and External Layers

In this paper ,the general solution of steady-state one dimensional asymmetric thermal stresses and electrical and mechanical displacements of a hollow cylinder made of functionally graded material and piezoelectric layers is developed .the material properties ,except the poisson's ration, are assumed to depend on the variable radius and they are expressed as power functions of radius. the temperature distribution is assumed to be a function of radius with general thermal and mechanical boundary conditions on the inside and outside surfaces. by using the separation of variables method and complex fourier series, the navier equations in term of displacements are derived and solved.