Analytical solution for functionally graded piezoelectric cantilever beam subjected to thermal and transverse loading

This paper considers the bending problem of functionally graded piezoelectric cantilever beam subjected to thermal and transverse loading. The material properties can be arbitrary functions of the height coordinate. The heat conduction problem is treated as a 1D problem in the thickness direction. Based on the elementary formulations for plane stress problem, the stress function and electric displacement function are assumed to be linear form of the longitudinal coordinate variable, from which the stresses and electric displacements can be derived. The stress function and electric displacement functions are then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.