The Nonclassical Boundary-contact Problems of Elasticity for Homogeneous Anisotropic Media

1995 ◽  
Vol 172 (1) ◽  
pp. 49-64 ◽  
Author(s):  
O. O. Chkadua
Keyword(s):  
Anisotropic Media ◽  
Contact Problems ◽  
Boundary Contact

scholarly journals Some Problems of Thermoelastic Equilibrium of a Rectangular Parallelepiped in Terms of Asymmetric Elasticity

2001 ◽  
Vol 8 (4) ◽  
pp. 767-784
Author(s):  
N. Khomasuridze
Keyword(s):  
Thermal Field ◽  
Separation Of Variables ◽  
Contact Problems ◽  
Rectangular Parallelepiped ◽  
Effective Solution ◽  
Contact Conditions ◽  
Thermoelastic Equilibrium ◽  
Boundary Contact ◽  
Asymmetric Elasticity ◽  
Surface Disturbances

Abstract An effective solution of a number of boundary value and boundary contact problems of thermoelastic equilibrium is constructed for a homogeneous isotropic rectangular parallelepiped in terms of asymmetric and pseudo-asymmetric elasticity (Cosserat's continuum and pseudo- continuum). Two opposite faces of a parallelepiped are affected by arbitrary surface disturbances and a stationary thermal field, while for the four remaining faces symmetry or anti-symmetry conditions (for a multilayer rectangular parallelepiped nonhomogeneous contact conditions are also defined) are given. The solutions are constructed in trigonometric series using the method of separation of variables.

scholarly journals Boundary-contact problems for domains with conical singularities

2005 ◽  
Vol 217 (2) ◽  
pp. 456-500 ◽  
Author(s):  
David Kapanadze ◽  
B.-Wolfgang Schulze
Keyword(s):  
Contact Problems ◽  
Conical Singularities ◽  
Boundary Contact

scholarly journals Unilateral Contact of Elastic Bodies (Moment Theory)

2001 ◽  
Vol 8 (4) ◽  
pp. 753-766
Author(s):  
R. Gachechiladze
Keyword(s):  
Contact Zone ◽  
Couple Stress Theory ◽  
Contact Problems ◽  
Theory Of Elasticity ◽  
Unilateral Contact ◽  
Stress Theory ◽  
Nonhomogeneous Media ◽  
Elastic Bodies ◽  
The Moment ◽  
Boundary Contact

Abstract Boundary contact problems of statics of the moment (couple-stress) theory of elasticity are studied in the case of a unilateral contact of two elastic anisotropic nonhomogeneous media. A problem, in which during deformation the contact zone lies within the boundaries of some domain, and a problem, in which the contact zone can extend, are given a separate treatment. Concrete problems suitable for numerical realizations are considered.

scholarly journals Boundary-contact problems for domains with edge singularities

2007 ◽  
Vol 234 (1) ◽  
pp. 26-53 ◽  
Author(s):  
David Kapanadze ◽  
B.-Wolfgang Schulze
Keyword(s):  
Contact Problems ◽  
Edge Singularities ◽  
Boundary Contact

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.

The Boundary-Contact Problem of Elasticity for Homogeneous Anisotropic Media with a Contact on Some Part of the Boundaries

1995 ◽  
Vol 2 (2) ◽  
pp. 111-123
Author(s):  
O. Chkadua
Keyword(s):  
Contact Problem ◽  
Potential Theory ◽  
Existence And Uniqueness ◽  
Anisotropic Media ◽  
Bessel Potential ◽  
Manifolds With Boundary ◽  
Uniqueness Of Solutions ◽  
Pseudodifferential Equations ◽  
Boundary Contact

Abstract The existence and uniqueness of solutions of the boundary-contact problem of elasticity for homogeneous anisotropic media with a contact on some part of their boundaries are investigated in the Besov and Bessel potential classes using the methods of the potential theory and the theory of pseudodifferential equations on manifolds with boundary. The smoothness of the solutions obtained is studied.

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