On analytical and finite element modelling of piezoelectric extension and shear bimorphs

A number of well-established analytical and numerical modelling techniques of classical extension bimorphs are assessed and evaluated using general purpose finite element codes. This allows the clarification of several confusing common validation practices, using well-known experimental data and analytical formulas. New analytical formulas are presented and evaluated for the relatively new shear bimorph concept and a more general extension–shear one, resulting from the combination of the extension- and shear-piezoelectric modes via an off-axes polarisation. The corresponding new simple analytical formulas accurately reproduced the three-dimensional piezoelectric finite element results, confirming their usefulness for preliminary designs.