Wein F (2011)
Publication Language: English
Publication Type: Thesis
Publication year: 2011
Numerical topology optimization based on the ersatz material model is very attractive in the research community and industry. Large scale nonlinear problems can be solved efficiently through the availability of appropriate optimizers, often resulting in non-intuitive solutions. However, topology optimization has not yet been established in the design of practical sensors and actuators. To this end we perform a thorough analysis and discussion of two exemplary piezoelectric devices, a single-frequency loudspeaker and a cantilevered energy harvester.
With respect to the loudspeaker a broad range of objective functions is compared and discussed, culminating in a fully coupled piezoelectric-mechanical-acoustic near field topology optimization problem. Piezoelectric strain cancellation and acoustic short circuits need to be balanced with structural resonance in order to obtain close to resonance performance for almost arbitrary target frequencies. Providing appropriate initial designs proved to be essential for robust optimization.
Cantilevered piezoelectric energy harvesters have been subject to various optimization approaches. However these have generally been based on reduced model assumptions. We present topology optimization of a realistic cantilevered energy harvester model. It proved to be necessary to use advanced topology optimization techniques, stress constraints to enforce practically feasible designs and Heaviside filtering for void features size control and for obtaining a black and white design pattern. To the best of our knowledge, this is the first time that dynamic piezoelectric stress constraints have been formulated for topology optimization. The obtained result is mechanism-based and interpretable to manufacture. This appears to be a novel finding in the field of cantilevered piezoelectric energy harvesting design.
Performing numerical experiments, we were surprised to observe pronounced piezoelectric self-penalization, which means optimal black and white solutions without penalizing design interpolation and additional constraints beside box constraints on the design variable. This phenomenon is only rarely and briefly described in the literature. Within this thesis we perform initial heuristic steps in the analysis of the self-penalization phenomenon, which indeed appears in many different topology optimization problems. Once self-penalization is rigorously understood, our vision is to find methods supporting the self-penalizing effect and to obtain solutions potentially closer to the original problem than constrained and penalized ersatz problems. To this end we present oscillation constraints, a feature size control with independent solid and void feature size without enforcing intermediate pseudo material.
APA:
Wein, F. (2011). Topology optimization of smart piezoelectric transducers (Dissertation).
MLA:
Wein, Fabian. Topology optimization of smart piezoelectric transducers. Dissertation, 2011.
BibTeX: Download