Asymptotic Distribution of Eigenelements of the Basic Two-Dimensional Boundary-Contact Problems of Oscillation in Classical and Couple-Stress Theories of Elasticity

2000 ◽  
Vol 7 (1) ◽  
pp. 11-32
Author(s):  
T. Burchuladze ◽  
R. Rukhadze
Keyword(s):  
Couple Stress ◽  
Correlation Method ◽  
Contact Problems ◽  
Asymptotic Formulas ◽  
Two Dimensional ◽  
Closed Curves ◽  
Dimensional Boundary ◽  
Isotropic Elastic Medium ◽  
Boundary Contact ◽  
Basic Boundary

Abstract The basic boundary-contact problems of oscillation are considered for a two-dimensional piecewise-homogeneous isotropic elastic medium bounded by several closed curves. Asymptotic formulas for the distribution of eigenfunctions and eigenvalues of the considered problems are derived using the correlation method.

Asymptotic Distribution of Eigenfunctions and Eigenvalues of the Basic Boundary-Contact Oscillation Problems of the Classical Theory of Elasticity

1999 ◽  
Vol 6 (2) ◽  
pp. 107-126
Author(s):  
T. Burchuladze ◽  
R. Rukhadze
Keyword(s):  
Elastic Medium ◽  
Asymptotic Distribution ◽  
Classical Theory ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Asymptotic Formulas ◽  
Closed Surfaces ◽  
Isotropic Elastic Medium ◽  
Boundary Contact ◽  
Basic Boundary

Abstract The basic boundary-contact oscillation problems are considered for a three-dimensional piecewise-homogeneous isotropic elastic medium bounded by several closed surfaces. Using Carleman's method, the asymptotic formulas for the distribution of eigenfunctions and eigenvalues are obtained.

Solvability and Asymptotics of Solutions of Crack-Type Boundary-Contact Problems of the Couple-Stress Elasticity

2003 ◽  
Vol 10 (3) ◽  
pp. 427-465
Author(s):  
O. Chkadua
Keyword(s):  
Couple Stress ◽  
Contact Problems ◽  
Crack Edge ◽  
Open Crack ◽  
Asymptotics Of Solutions ◽  
Couple Stress Elasticity ◽  
Transversally Isotropic ◽  
Type Boundary ◽  
Boundary Contact ◽  
Asymptotic Expansion Of Solutions

Abstract Spatial boundary value problems of statics of couple-stress elasticity for anisotropic homogeneous media (with contact on a part of the boundary) with an open crack are studied supposing that one medium has a smooth boundary and the other one has an open crack. Using the method of the potential theory and the theory of pseudodifferential equations on manifolds with boundary, the existence and uniqueness theorems are proved in Besov and Bessel-potential spaces. The smoothness and a complete asymptotics of solutions near the contact boundaries and near crack edge are studied. Properties of exponents of the first terms of the asymptotic expansion of solutions are established. Classes of isotropic, transversally-isotropic and anisotropic bodies are found, where oscillation vanishes.

Numerical Approximation of Basic Boundary-Contact Problems

2017 ◽  
Author(s):  
Manana Chumburidze ◽  
David Lekveishvili
Keyword(s):  
Numerical Approximation ◽  
Singular Integral Equations ◽  
Contact Problems ◽  
Potential Method ◽  
Static System ◽  
Elastic Materials ◽  
Generalized Fourier Series ◽  
Boundary Contact ◽  
Basic Boundary ◽  
Fourier Series Analysis

This paper is devoted to the development of approximation method for numerical solution of basic boundary-contact problems of coupled thermo-elasticity in the Green-Lindsay formulation. In particular, we consider a static system of partial differential equations for two-dimensional isotropic inhomogeneous elastic materials in assumptions that surfaces are sufficiently smooth. The tools applied in this development are based on singular integral equations, the potential method and the generalized Fourier series analysis.

On the solution to a two-dimensional boundary value problem of heat conduction in a degenerating domain

2020 ◽  
Vol 98 (2) ◽  
pp. 100-109
Author(s):  
Minzilya T. Kosmakova ◽  
◽  
Valery G. Romanovski ◽  
Dana M. Akhmanova ◽  
Zhanar M. Tuleutaeva ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Two Dimensional ◽  
Dimensional Boundary

Size effects in two-dimensional layered materials modeled by couple stress elasticity

2021 ◽  
Author(s):  
Wipavee Wongviboonsin ◽  
Panos A. Gourgiotis ◽  
Chung Nguyen Van ◽  
Suchart Limkatanyu ◽  
Jaroon Rungamornrat
Keyword(s):  
Size Effects ◽  
Couple Stress ◽  
Layered Materials ◽  
Two Dimensional ◽  
Couple Stress Elasticity
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