Finite element modelling of structures including piezoelectric active devices

Finite element modelling is used to study the response of plate structures on which piezoelectric active devices are mounted. Such devices are typically small in relation to the size of the structure which can be modelled as a plate or shell structure. In modelling the response of such devices, it is necessary to use a detailed model of the device but to do the same for the whole structure is computationally expensive and unnecessary. Full three-dimensional elements are used to model the piezoelectric devices because such devices are anisotropic, couple electric and elastic fields and satisfy boundary conditions independently on the two fields. Shell elements, approximated by many flat-shell elements are used in modelling the structure. Transition elements have been derived to connect the three-dimensional solid elements in the piezoelectric region to the flat-shell elements used for the plate. This approach has merits in terms of accuracy in modelling the piezoelectric device and computational economy for the plate structure. The use of shell elements is preferred for the structure since brick elements lead to unnatural stiffening of the plate and artificially high natural frequencies. The aspect ratio of the transition elements are first optimized through a numerical study and the sensor and actuator performance of the devices is then verified.