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.

Thermoelastic Equilibrium of Bodies in Generalized Cylindrical Coordinates

1998 ◽  
Vol 5 (6) ◽  
pp. 521-544
Author(s):  
N. Khomasuridze
Keyword(s):  
Separation Of Variables ◽  
Contact Problems ◽  
The Body ◽  
Cylindrical Coordinates ◽  
Thermoelastic Equilibrium ◽  
Transversally Isotropic ◽  
Boundary Contact ◽  
Plane Of Isotropy ◽  
Surface Disturbances ◽  
Orthogonal Coordinates

Abstract Using the method of separation of variables, an exact solution is constructed for some boundary value and boundary-contact problems of thermoelastic equilibrium of one- and multilayer bodies bounded by the coordinate surfaces of generalized cylindrical coordinates ρ, α, 𝑧. ρ, α are the orthogonal coordinates on the plane and 𝑧 is the linear coordinate. The body, occupying the domain Ω = {ρ 0 < ρ < ρ 1, α 0 < α < α 1, 0 < 𝑧 < 𝑧1}, is subjected to the action of a stationary thermal field and surface disturbances (such as stresses, displacements, or their combinations) for 𝑧 = 0 and 𝑧 = 𝑧1. Special type homogeneous conditions are given on the remainder of the surface. The elastic body is assumed to be transversally isotropic with the plane of isotropy 𝑧 = const and nonhomogeneous along 𝑧. The same assumption is made for the layers of the multilayer body which contact along 𝑧 = const.

scholarly journals Some basic contact problems in couple stress elasticity

2014 ◽  
Vol 51 (11-12) ◽  
pp. 2084-2095 ◽  
Author(s):  
Th. Zisis ◽  
P.A. Gourgiotis ◽  
K.P. Baxevanakis ◽  
H.G. Georgiadis
Keyword(s):  
Couple Stress ◽  
Contact Problems ◽  
Couple Stress Elasticity

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.

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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