Boundary value problems of stationary oscillation of thermoelasticity of microstretch materials with microtemperatures

2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Levan Giorgashvili ◽  
Aslan Jaghmaidze ◽  
Giorgi Karseladze ◽  
Guram Sadunishvili
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Representation Formula ◽  
Convergent Series ◽  
Homogeneous System ◽  
Stationary Oscillation ◽  
Neumann Type ◽  
Uniformly Convergent ◽  
Type Boundary ◽  
Linear Thermoelasticity

AbstractWe consider the stationary oscillation case of the theory of linear thermoelasticity with microtemperatures of microstretch materials. A representation formula of a general solution of a homogeneous system of differential equations is written in terms of eight metaharmonic functions. Such formulas are very convenient and useful in many specific problems of concrete geometry. We demonstrate an application of these formulas to Dirichlet and Neumann type boundary value problems in a ball. Explicit solutions in the form of absolutely and uniformly convergent series are constructed.

scholarly journals Explicit Solutions of the Basic Boundary Value Problems of Statics of the Elastic Mixture Theory for an Annulus

2004 ◽  
Vol 11 (1) ◽  
pp. 49-58
Author(s):  
M. Basheleishvili
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Mixture Theory ◽  
Convergent Series ◽  
Explicit Solutions ◽  
Neumann Type ◽  
Uniformly Convergent ◽  
Type Boundary ◽  
Solutions Of Equations ◽  
Basic Boundary

Abstract Using the complex representation formulae of regular solutions of equations of statics of the theory of elastic mixtures, we construct the explicit solutions of the Dirichlet and Neumann type boundary value problems for an annulus in the form of absolutely and uniformly convergent series.

scholarly journals Explicit Solutions of the Boundary Value Problems for an Ellipse with Double Porosity

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Lamara Bitsadze ◽  
Natela Zirakashvili
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Convergent Series ◽  
Double Porosity ◽  
Theory Of Elasticity ◽  
Classical Elasticity ◽  
Dimensional Boundary ◽  
Uniformly Convergent ◽  
Isotropic Bodies ◽  
Fully Coupled

The basic two-dimensional boundary value problems of the fully coupled linear equilibrium theory of elasticity for solids with double porosity structure are reduced to the solvability of two types of a problem. The first one is the BVPs for the equations of classical elasticity of isotropic bodies, and the other is the BVPs for the equations of pore and fissure fluid pressures. The solutions of these equations are presented by means of elementary (harmonic, metaharmonic, and biharmonic) functions. On the basis of the gained results, we constructed an explicit solution of some basic BVPs for an ellipse in the form of absolutely uniformly convergent series.

scholarly journals Problem of Statics of the Linear Thermoelasticity of the Microstretch Materials with Microtemperatures for a Half-space

2021 ◽  
pp. 202-219
Author(s):  
Maia Kharashvili ◽  
◽  
Ketevan Skhvitaridze
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Half Space ◽  
Boundary Value ◽  
Representation Formula ◽  
Subject Classification ◽  
Uniqueness Theorems ◽  
Type Boundary ◽  
Linear Thermoelasticity

We consider the statics case of the theory of linear thermoelasticity with microtemperatures and microstrech materials. The representation formula of differential equations obtained in the paper is expressed by the means of four harmonic and four metaharmonic functions. These formulas are very convenient and useful in many particular problems for domains with concrete geometry. Here we demonstrate an application of these formulas to the III type boundary value problem for a half-space. Uniqueness theorems are proved. Solutions are obtained in quadratures. 2010 Mathematics Subject Classification. 74A15, 74B10, 74F20.

scholarly journals Polyanalytic boundary value problems for planar domains with harmonic Green function

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Heinrich Begehr ◽  
Bibinur Shupeyeva
Keyword(s):  
Green Function ◽  
Boundary Value Problems ◽  
Arbitrary Order ◽  
Boundary Value ◽  
Planar Domains ◽  
Schwarz Problem ◽  
Bianalytic Functions ◽  
Neumann Type ◽  
The Neumann Problem ◽  
Well Posed

AbstractThere are three basic boundary value problems for the inhomogeneous polyanalytic equation in planar domains, the well-posed iterated Schwarz problem, and further two over-determined iterated problems of Dirichlet and Neumann type. These problems are investigated in planar domains having a harmonic Green function. For the Schwarz problem, treated earlier [Ü. Aksoy, H. Begehr, A.O. Çelebi, AV Bitsadze’s observation on bianalytic functions and the Schwarz problem. Complex Var Elliptic Equ 64(8): 1257–1274 (2019)], just a modification is mentioned. While the Dirichlet problem is completely discussed for arbitrary order, the Neumann problem is just handled for order up to three. But a generalization to arbitrary order is likely.

Direct integration of the third-order two point and multipoint Robin type boundary value problems

2021 ◽  
Vol 182 ◽  
pp. 411-427
Author(s):  
Nadirah Mohd Nasir ◽  
Zanariah Abdul Majid ◽  
Fudziah Ismail ◽  
Norfifah Bachok
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Direct Integration ◽  
Third Order ◽  
The Third ◽  
Type Boundary
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