Finite element modelling and static shape control of a functionally graded piezoelectric beam

A finite element model is developed for discretization and analysis of the functionally graded piezoelectric material (FGPM) beam based on the Timoshenko beam theory and assuming linear constitutive relation for the corresponding piezoelectric material behavior. Results obtained using the developed finite element code are compared with the available experimental and numerical results for smart structures with and without graded properties. Static shape control of the beam is conducted using the Buildup Voltage Distribution (BVD) algorithm by implementing this method in the finite element routine. Numerical simulations have been performed to study the performance of the shape control algorithm by optimizing the distribution of the applied voltages. Furthermore, the effect of the number of iterations on the result accuracy as well as the variation of the control voltage distribution with the number of discretized regions and the volume fractions of the constituent material is studied. A fast numerical convergence with good accuracy is observed for the shape control of FGPM beams using the developed method. The proposed technique is a good candidate for the modeling, analysis, and control of smart structures with graded properties.