Homogenization of a fully coupled thermoelasticity problem for a highly heterogeneous medium witha prioriknown phase transformations

This paper deals with a fully-coupled thermoelastic problem, in a heterogeneous medium, arising from the metallurgical industry. The aim is to prove regularity properties of the solution with respect to space and time. Regularity in space is obtained by means of regularity properties for elliptic operators. In order to prove regularity in time, a mathematical induction technique, together with an existence and uniqueness result for this type of problems, is applied.

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AVERAGED CONTROLLABILITY OF THERMOELASTICITY EQUATIONS. AVERAGE STATE OF A RECTANGULAR PLATE

Proceedings of the YSU A: Physical and Mathematical Sciences ◽

10.46991/pysu:a/2021.55.2.123 ◽

2021 ◽

Vol 55 (2 (255)) ◽

pp. 123-130

Author(s):

Samvel H. Jilavyan ◽

Asatur Zh. Khurshudyan

Keyword(s):

Rectangular Plate ◽

Approximate Controllability ◽

Theoretical Background ◽

Coupled Systems ◽

Function Approach ◽

Usual Sense ◽

Coupled Thermoelasticity ◽

Controllability Of Systems ◽

Fully Coupled ◽

Average State

The concept of averaged controllability has been introduced relatively recently aiming to analyse the controllability of systems or processes containing some important parameters that may affect the controllability in usual sense. The averaged controllability of various specific and abstract equations has been studied so far. Relatively little attention has been paid to averaged controllability of coupled systems. The averaged state of a thermoelastic rectangular plate is studied in this paper using the well-known Green's function approach. The aim of the paper is to provide a theoretical background for further exact and approximate controllability analysis of fully coupled thermoelasticity equations which will appear elsewhere.

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Mixed Convolved Action for Thermoelasticity

International Journal of Applied Mechanics ◽

10.1142/s1758825118500023 ◽

2018 ◽

Vol 10 (01) ◽

pp. 1850002 ◽

Cited By ~ 1

Author(s):

Jinkyu Kim ◽

Jinwon Shin

Keyword(s):

Finite Element ◽

Variational Formulation ◽

Space Time ◽

Lagrange Equations ◽

Coupled Thermoelasticity ◽

Finite Element Approach ◽

Theoretical Significance ◽

Element Approach ◽

Thermoelastic Problems ◽

Fully Coupled

In the present work, a variational formulation for fully coupled thermoelasticity is developed in the context of the mixed convolved action. This weak variational formulation recovers all the governing differential equations along with proper initial and boundary conditions as its Euler–Lagrange equations. Thus, it encapsulates the entire description of thermoelastic problems. In addition to theoretical significance, it provides sound basis for the development of novel computational methods involving unified space-time finite element approach. The simplest unified space-time finite element method is also developed here with representative examples for its viability.

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