Variational Integrators for Piezoelectricity
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Variational integrators have been used to study the transient response of a number of dynamic problems, while displaying superior conservation characteristics. The purpose of this thesis is to develop variational integrators for piezoelectric problems. A two-field piezoelectric functional is first discretized in space and time and then the coupled discrete Euler-Lagrange equations for displacement and electrical potential are consequently derived. Afterwards, to validate this new formulation, the numerical results for two initial/boundary value problems involving a piezoelectric plate are compared to the corresponding analytical and Abaqus FE results. The excellent correlation of these solutions clearly indicates the capability of variational integrators in modeling transient piezoelectric behavior.