T. Buchukuri, O. Chkadua, D. Natroshvili, A.-M. Sändig
abstract:
We investigate linear three-dimensional boundary transmission problems related
to the interaction of metallic and piezoelectric ceramic media with regard to
thermal stresses. Such type of physical problems arise, e.g., in the theory of
piezoelectric stack actuators. We use the Voigt's model and give a mathematical
formulation of the physical problem when the metallic electrodes and the
piezoelectric ceramic matrix are bonded along some proper parts of their
boundaries. The mathematical model involves different dimensional physical
fields in different sub-domains, occupied by the metallic and piezoceramic parts
of the composite. These fields are coupled by systems of partial differential
equations and appropriate mixed boundary transmission conditions. We investigate
the corresponding mixed boundary transmission problems by variational and
potential methods. Existence and uniqueness results in appropriate Sobolev
spaces are proved. We present also some numerical results showing the influence
of thermal stresses.
Mathematics Subject Classification: 74F05, 74F15, 74B05
Key words and phrases: Thermoelasticity, thermopiezoelasticity, boundary transmission problems, variational methods, potential method