Competing anticlastic and piezoelectric deformation at large deflections

In bending of a purely elastic beam or plate, it is well established that the cross-sectional shape changes character with decreasing bending radius-of-curvature and that the transition can be characterized by the Searle parameter. In a piezoelectric structure, the cross-sectional deformation is affected by the opposite anticlastic and electromechanical bending curvatures. The behavior is consequently more complicated and it is an open question how the cross-sectional shape develops with increasing bending. In this paper, analytical solutions are used to study the cross-sectional deformation of piezoelectric cantilever-actuators taking both anticlastic and electromechanical bending effects into account. We consider unimorph and bimorph actuators. In the case of electrical actuation, as for the purely mechanical case, we find that the Searle parameter is an important parameter characterizing the shape of the cross-section. A load scaling rule gives a criterion for fixed cross-section-deflection for different actuator widths. Using this scaling rule, the Searle parameter is kept unchanged. The analytical results are verified by non-linear finite element analysis using electric potential and mechanical moment as applied loads.

Automated summary

This study investigates the cross-sectional deformation of piezoelectric cantilever-actuators considering both anticlastic and electromechanical bending effects. The Searle parameter is found to play a key role in characterizing the shape of the cross-section. A load scaling rule provides a criterion for fixed cross-section deflection for different actuator widths, maintaining the Searle parameter unchanged.