Optimal voltage design for static shape control of smart structures with Nonlinear piezoelectric actuators

In this paper, static shape control of structures with nonlinear piezoelectric actuators is investigated. Firstly, an adhesive element is developed to model smart plates with nonlinear piezoelectric actuator patches. The adhesive element combines a pair of collocated four-node quadrilateral elements for the upper and lower adherents and a pseudo-adhesive layer element with constant shear and peel strains along its thickness. Secondly, after establishing the equilibrium equations with nonlinear actuating forces, an explicit iterative algorithm for finding the optimal control voltage distribution on the nonlinear piezoelectric actuators is formulated, and the converging speed of this iterative algorithm is also estimated. Finally, a simulation example is given to illustrate that the present algorithm is effective in finding the optimal control voltage distribution for shape control of nonlinearly actuated structures. Significant effect of the nonlinear piezoelectric constitutive relationship on the optimal control voltage is also observed.