Actuator Placement in Smart Structures by Discrete-Continuous Optimization

Abstract

Abstract Multi-functional smart materials, which can be used as conventional load bearing structural elements as well as actuators and sensors — e.g. as part of a multi-layered composite — in conjunction with suitable control systems are the basis of the development of adaptive structural systems for shape control, vibration damping etc. The effectiveness of an adaptive structural system depends decisively on the placement of the actuators and sensors. In the present paper a general mathematical method for the determination of an optimal actuator placement is given, which takes advantage of additional mechanical information about the structural behavior, i.e. the sensitivity of the system with respect to the design variables. Following concepts of geometry and topology optimization in the present paper an optimization strategy is presented for the simultaneous determination of the discrete positions of the actuators as well as the continuous parameters of the control law. For the verification of the optimization strategy a complete variant test of the ten-bar-truss problem is analyzed. The results of the optimization strategy match the results of the variant test.