Static analysis of a functionally graded cylindrical shell with piezoelectric layers as sensor and actuator

In this paper, an analytical approach to the static behavior of functionally graded material (FGM) cylindrical shells with simply supported edges is developed. The Poisson's ratios of the FGM shell are assumed to be constant, but it is the modulus of elasticity which varies continuously through the radial direction according to the exponential function. The shell has finite length and embedded piezoelectric layers. The partial differential equilibrium equations as well as the stress–displacement relations are reduced to the ordinary one with constant coefficient by using the Fourier series expansion. Finally, the problem is solved by using the state space method. Numerical results are given to demonstrate the accuracy of the presented method. The influences of the gradient index, applied voltage and radius to thickness ratios on the static behavior of FGM shells are also studied