Optimal sizing of piezo-actuators for minimum-deflection design of frames under uncertain loads

Optimal piezo-actuator sizes and locations for a frame structure under bending load uncertainty are determined with the objective of minimizing the deflection under worst case of loading. The bending moments generated by the piezo-actuators are used for deflection control, i.e., to minimize the maximum deflection. The frame is subjected to a tip load which lies in an uncertainty domain with regard to its magnitude and direction. The specific uncertain loading studied in the present paper involves a load of given magnitude but of unknown direction, which should be determined to produce the highest deflection. The worst case of loading depends on the size and location of the actuators leading to a nested problem of optimization (design) and anti-optimization (uncertainty problem). Results are given for deterministic and uncertain loading conditions.