ANNOUNCEMENTS

ANNOUNCEMENT FOR 2019
Advanced Courses on Mathematical Models of Piezoelectric Solids and Related Problems Date: 23  26 September, 2019 Location: Tbilisi International Centre of Mathematics and Informatics at I. Vekua Institute of Applied Mathematics of I. Javakhishvili Tbilisi State University (Tbilisi, Georgia)
Lecturers: Ayech Benjeddou (Institut Supérieur de Mécanique de Paris (SUPMECA) & Université de Technologie de Compiègne (UTC)/Centre National de la Recherche Scientifique (CNRS) FRE 2012 ROBERVAL, France) Piezoelectric Material, Effective and Structural Behaviours Abstract:
Piezoelectric materials are popularly used for sensing, actuation and
transduction in the framework of smart structures applications such as for
structural noise, vibration, shape, control and health monitoring or energy
harvesting for autonomous and wireless smart, internet of things or
communication devices. Therefore, mastering the behaviours of such smart
materials is the key issue for the correct mathematical modelling of
piezoelectric solids and related problems. Piezoelectric materials exist in
monolithic and composite forms for which the main representatives of the former
are piezoelectric ceramics (or piezoceramics) and polymers (or piezopolymers),
while those of the latter are piezoelectric fibre composites. The latter use
particles and short or long fibres as reinforcements of polymertype (usually
epoxy) matrices. Besides, the long fibres can have micro circular or macro
rectangular cross sections leading, respectively, to the socalled active fibre
composites or macrofibre composites (MFC).
Bernadette Miara (Université ParisEst Marne la Vallée, France) Homogenization and Control of a Piezoelectric Body
Abstract: In
this lecture, focused on the modelling of piezoelectric materials we present two
examples in the general framework of linearized threedimensional evolution
equations.
Wolfgang H. Müller, Wilhelm Rickert, Felix A. Reich (Institut für Mechanik, Kontinuumsmechanik und Materialtheorie, Technische Universität Berlin, Germany) An Examination of Elastic Deformation Predictions of Polarizable Media due to Various Electromagnetic Force Models Abstract: This study investigates the implications for the deformation of electrets due to various electromagnetic force models. This deformation of dielectric materials due to electromagnetic forces is called electrostriction. Analytical solutions for the electrostriction problem of spherical electrets are derived in five different situations. First, an affine linear dielectric sphere with surface charges in an external field is considered. The electric field is computed analytically in a stationary situation. From this solution several model simplifications yield the electric fields of: a linear dielectric in an external field without surfaces charges, a realcharge electret without polarization, an orienteddipole electret and a realcharge electret with linear dielectric material. With the electric field solutions the electromagnetic forces can be computed for selected force models. Expanding the forces conveniently in terms of Legendre polynomials, the method of Hiramatsu and Oka is applied to obtain the elastic deformation of the spheres.
Gia Avalishvili^{*}, Mariam Avalishvili^{**} (^{*}Faculty of Exact and Natural Sciences, I. Javakhishvili Tbilisi State University, ^{**}School of Science and Technology, University of Georgia, Tbilisi, Georgia) On Variational Methods of Investigation of Mathematical Problems for Thermoelastic Piezoelectric Solids
Abstract: In
this lecture, we present the results of investigation of boundary and
initialboundary value problems corresponding to mathematical models of
thermoelastic piezoelectric solids with regards to magnetic field. We consider
threedimensional static and dynamical models of multidomain general
inhomogeneous anisotropic thermoelastic piezoelectric solids with mixed boundary
conditions, when on certain parts of the boundary density of surface force, and
normal components of electric displacement, magnetic induction and heat flux are
given, and on the remaining parts of the boundary mechanical displacement,
temperature, electric and magnetic potentials vanish. We obtain variational
formulations of the boundary and initialboundary value problems in suitable
function spaces and present existence, uniqueness and continuous dependence
results. Moreover, we construct and investigate hierarchical models of
thermoelastic piezoelectric thin structures applying extensions and
generalizations of dimensional reduction method, which was suggested by I. Vekua
in the classical theory of elasticity for plates with variable thickness.
George Jaiani (I. Vekua Institute of Applied Mathematics & Faculty of Exact and Natural Sciences of I. Javakhishvili Tbilisi State University, Tbilisi, Georgia) Piezoelectric Cusped Prismatic Shells
Abstract: The
present lecture course is devoted to construction of differential hierarchical
models for piezoelectric nonhomogeneous porous elastic and viscoelastic
KelvinVoigt prismatic shells on the basis of linear theories. Using I. Vekua's
dimension reduction method, governing systems are derived and in the Nth
approximation of hierarchical models boundary value problems (BVPs) and initial
boundary value problems (IBVPs) are set. In the N=0 approximation,
considering, e.g., elastic, plates of a constant thickness, governing systems
mathematically coincide with the governing systems of the plane strain
corresponding to the basic threedimensional (3D) linear theory up to a
separate equation for the out of plane component of the displacement vector. The
ways of investigation of BVPs and IBVPs, including the case of cusped prismatic
shells, are indicated and some preliminary results are presented. Antiplane
deformation of piezoelectric nonhomogeneous materials in the threedimensional
formulation and in N=0 approximation is analyzed. Wellposedness of
Dirichlet and Keldysh type problems (BVP) are studied in the N=0 order
approximation of hierarchical models for cusped prismatic shells. Some BVPs are
solved in explicit forms in concrete cases.
David Natroshvili (Georgian Technical University & I. Vekua Institute of Applied Mathematics of I. Javakhishvili Tbilisi State University , Tbilisi, Georgia) Dynamical Problems of Generalized ThermoElectroMagnetoElasticity theory
Abstract:
The lecture course is dedicated to the theoretical investigation of basic,
mixed and crack type threedimensional initialboundary value problems of the
generalized thermoelectromagnetoelasticity theory associated with
GreenLindsay's model. The essential feature of the generalized model under
consideration is that heat propagation has a finite speed. We analyse dynamical
initialboundary value problems and the corresponding boundary value problems of
pseudooscillations, which are obtained from the dynamical problems by the
Laplace transform.
Coordinators: Gia Avalishvili, Mariam Avalishvili Sponsor: The Advanced Courses on Mathematical Models of Piezoelectric Solids and Related Problems will be supported by Shota Rustaveli National Science Foundation of Georgia (SRNSF) [217596, Construction and investigation of hierarchical models for thermoelastic piezoelectric structures]. Deadline for registration: August 10, 2019.
Further information: Address: Tbilisi International Centre of Mathematics and Informatics, I. Vekua Institute of Applied Mathematics of Tbilisi State University, University Str.2, Tbilisi 0143, Georgia Website: http://www.viam.science.tsu.ge/ticmi/ Emails: gavalish@yahoo.com, gia.avalishvili@tsu.ge (Gia Avalishvili) m.avalishvili@ug.edu.ge (Mariam Avalishvili) The Advanced Courses can be followed by junior (Masters, PhDs, or PostDocs) and senior (Assistant, Associate, or Full Professors) academics, as well as researchers and engineers from industry. Only basic mathematics and mechanics are required to follow adequately and fruitfully the Advanced Courses. The participants will also have an opportunity to give 20minute talks on their own work at the International Conference on Applications of Mathematics and Informatics in Natural Sciences and Engineering (AMINSE 2019), which will be held during the Advanced Courses. Abstracts of the talks will be published and distributed among the lecturers and participants before the Advanced Courses. The registration fee for participants is 650 EUR which includes all local expenses during the Advanced Courses. The detailed information about AMINSE 2019 can be found on the website: For information about history, culture and sights of Tbilisi and Georgia please visit the website: 