steady-state thermal and mechanical stresses in two-dimensional functionally graded piezoelectric materials (2d-fgpms) for a hollow infinite cylinder

In this paper, the general analysis of two-dimensional steady-state thermal and mechanical stresses for a hollow thick cylinder made of functionally graded piezoelectric materials (2d-fgpms) is developed.the general form of thermal ,mechanical and electrical boundary conditions is considered on the inside and outside surfaces. a direct method is used to solve the heat conduction equation and the non-homogenous system of partial differential navier equations, using the complex fourier series and the power law functions method.the material properties are assumed to depend on the radial and circumferential variables and are expressed as power law functions along the radial and circumferential direction.