Electro-thermo-elastic formulation for the analysis of smart structures

Abstract

Coupled electro-thermo-elastic equations applicable for the analysis of smart structureswith piezoelectric patches/layers have been derived from the fundamental principles ofmass, linear momentum, angular momentum, energy and charge conservation. The relevantconstitutive equations have been obtained by using the second law of thermodynamics. Theinteraction of the electric field and polarization introduces distributed non-linear body forcein the piezo material, and in addition renders the stress tensor non-symmetric due todistributed couple. Using the linear equations, and applying a layer-by-layer finite elementmodel, the induced electric potential and mechanical deformations in the piezoand non-piezo core material have been obtained for various cases of actuationand sensing of a smart beam under external mechanical, electrical and thermalloadings. The mathematical formulation and the solution technique have beenvalidated by comparing the results of the present study with those available in theliterature. It is also shown that piezo patches can be effectively used for shapecontrol.