Vol. 14, No. 1, 2019

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Some general theorems for local gradient theory of electrothermoelastic dielectrics

Olha Hrytsyna and Halyna Moroz

Vol. 14 (2019), No. 1, 25–41
Abstract

Using the basic equations of local gradient theory of electrothermoelastic nonferromagnetic polarized solids, which accounts for the local mass displacement and its effect on mechanical, thermal and electromagnetic fields, the governing set of equations is obtained for a linear approximation. On this basis, the coupled initial-boundary-value problems corresponding to this gradient-type theory are formulated. The reciprocity and uniqueness theorems for non-stationary problems of the local gradient electrothermoelasticity are proved.

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Keywords
Local gradient theory, nonferromagnetic dielectrics, electrothermoelasticity, local mass displacement, initial-boundary-value problems, uniqueness and reciprocity theorems
Milestones
Received: 6 February 2018
Revised: 12 July 2018
Accepted: 25 November 2018
Published: 7 April 2019
Authors
Olha Hrytsyna
Center of Mathematical Modeling of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics
National Academy of Sciences of Ukraine
Lviv
Ukraine
Institute of Construction and Architecture
Slovak Academy of Sciences
Bratislava
Slovak Republic
Halyna Moroz
Center of Mathematical Modeling of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics
National Academy of Sciences of Ukraine
Lviv
Ukraine