Evaluation of higher-order theories of piezoelectric plates in bending and in stretching

Many models for the flexural and membranal behaviour of piezoelectric plates are available in the literature. They are based on different assumptions concerning the strain, stress, electric and electric-displacement fields inside the plate. A critical comparison among such models is presented here in a completely analytic way, in order to assess the accuracy of the results they provide and determine their range of applicability. The comparison is made by using a class of case-study problems, whose analytical solutions in the framework of the linear theory of piezoelectricity are available, as benchmarks for the solutions supplied by the plate models. The evaluated models are also here rationally derived from the three-dimensional theory of piezoelectricity, and a consistent treatment of the stress and electric-displacement relaxation conditions is proposed.

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