Smart structures, which are equipped with piezoelectric actuators and sensors, and which involve automatic control, represent an important branch of Mechatronics. This paper gives a review over own research on smart structures, which has been performed during the last decade based on the principles of analogy and interdisciplinarity. The latter principles form a research strategy, which seems to be perfectly suited in order to answer the innovation request in Mechatronics, namely to decrease the time-lag between consecutive steps in the scientific development, and to keep fundamental and applied research in close co-operation. We start our report with a short excursion into the history of engineering sciences, in order to demonstrate this time-lag, where we use the history of elastic and piezoelastic plates as an example, and we discuss the notions of analogy and interdisciplinarity as means to systematically decrease the timelag. In our own work, we particularly have used an eigenstrain analogy as guideline. In the light of this analogy, various own works in the following fields are reviewed: Accurate electromechanically modeling; dynamic shape control by piezoelectric actuation and sensing; extension of dynamic shape control to closed loop control and active noise cancellation.