Thesis supervisor: Balázs Tóth
Location of studies (in Hungarian): Institute of Applied Mechanics Abbreviation of location of studies: MMI
Description of the research topic:
The strongly coupled fundamental differential equations suitable for describing time-dependent nonequilibrium termodynamic processes of linearly elastic solids can be analytically or semi-analytically solved only for a few particular initial-boundary value problems of the thermoelastic bodies with characteristic geometry, specific initial- and boundary conditions. However, the variational form of these equations makes it possible to construct approximate solutions for the wide range of much more complex, heat conductivity problems for instance with the use of the finite element method [4]. The mentioned variational approach serves as an useful and promising mathematical basis for the construction of the related finite element models.
Besides, the mixed hyperbolic-parabolic characteristic of the fully coupled heat conductivity equations based on the classical Fourier’s law leads to an infinite speed of thermal wave propagation, which is not consistent with the real physical phenomena, when the elastic body is exposed to a thermal shock. Namely the related (standard) mathematical model does not provide satisfactory results for such time-dependent thermoelasticity problems, see, for example, [1].
In order to overcome the latter-mentioned contradictions the standard fully coupled thermoelasticity theory has to be modified with the various improvements of the mathematical models, see a comrepehensive overview in [2, 3]. These are called nonstandard or nonclassical theories which have a great significance especially when the continua is subjected to a thermal shock load and/or very high heat fluxes. Such physical phenomena can be experienced for example in nuclear reactors and particle accelerators.
In accordance with the aforementioned experiences and problems the aim of the research work is to apply multi-field dual-mixed variational formulation to the development of such hp-version finite element models that provide reliable and efficient results for the thermal stresses and strains, as well as, the heat and entropy flux of the linearly elastic body exposed to a thermal shock load acting in a very short time interval and/or very high heat flux.
Main steps in the realization of the research are:
• a comprehensive and thorough study of the associated scientific literature and the recent research directions and the related theoretical background,
• the consistent and systematic derivation of the applied mathematical/mechanical model, using the mathematical packages and tools of Maple and/or Maxima for the symbolic calculations,
• development of new hp-finite elements, algorithms and subroutines in the programming language C/C++ and/or the environment GNU Octave/Python/Mathlab/Scilab,
• testing the finite element code through some benchmark problems and comparing the obtained results to the computed ones by other models appearing in the scientific literature,
• publishing the scientific results in highly-ranked international journals and presenting the elaborated theoretical and numerical models in internationally high-qualified conferences and/or in seminars.
Supervisor: Balázs Tóth, PhD
associate professor
Institute of Applied Mechanics
University of Miskolc
References:
1. C. C. Ackermann, B. Bertman, H. A. Fairbank and R. A. Guyer: Second sound in solid Helium, Physical Review Letters, 16 (1966) 789-791.
2. A. Berezovski and P. Ván: Internal Variables in Thermoelasticity, volume 243 of Solid Mechanics and Its Applications, Springer, 2017.
3. M. R. Eslami., R. B. Hetnarski, J. Ignaczak, N. Noda, N. Sumi, and Y. Tanigawa: Theory of Elasticity and Thermal Stresses. Solid Mechanics and its Applications. Netherland: Springer, 2013.
4. B. Tóth: Dual and mixed nonsymmetric stress-based variational formulations for coupled thermoelastodynamics with second sound effect, Continuum Mechanics and Thermodynamics, 30 (2018) 319-345.
Number of students who can be accepted: 1
Deadline for application: 2024-12-31
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
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