Thermoelastic Equilibrium of A Rectangular Parallelepiped with Nonhomogeneous Symmetry and Antisymmetry Conditions on its Faces

2000 ◽  
Vol 7 (4) ◽  
pp. 701-722 ◽  
Author(s):  
N. Khomasuridze
Keyword(s):  
Exact Solution ◽  
Thermal Field ◽  
Displacement Vector ◽  
Separation Of Variables ◽  
Normal Component ◽  
Rectangular Parallelepiped ◽  
Thermoelastic Equilibrium ◽  
Tangential Stresses ◽  
In Series ◽  
Surface Disturbances

Abstract An exact solution of the boundary value problems of thermoelastic equilibrium of a homogeneous isotropic rectangular parallelepiped is constructed. The parallelepiped is affected by a stationary thermal field and surface disturbances, in particular, on each side of the rectangular parallelepiped the following parameters are defined: a normal component of the displacement vector and tangential stresses (nonhomogeneous symmetry conditions) or normal stress and tangential stresses (nonhomogeneous antisymmetry conditions). The solution of the problems is constructed in series using the method of separation of variables.

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.

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.

Exact solution of some exterior boundary value problems of elasticity in parabolic coordinates

2017 ◽  
Vol 23 (6) ◽  
pp. 929-943 ◽  
Author(s):  
Natela Zirakashvili
Keyword(s):  
Exact Solution ◽  
Boundary Value Problems ◽  
Separation Of Variables ◽  
Boundary Value ◽  
Elastic Equilibrium ◽  
Isotropic Body ◽  
External Boundary ◽  
Matlab Software ◽  
Exterior Boundary ◽  
Tangential Stresses

The present work, by using the method of the separation of variables, states and analytically (exactly) solves the external boundary value problems of elastic equilibrium of the homogeneous isotropic body bounded by the parabola, when normal or tangential stresses are given on a parabolic border. Using MATLAB software, the numerical results and constructed graphs of the mentioned boundary value problems are obtained.

scholarly journals Atom-atom entanglement in a not-resonant two-photon Tavis-Cummings model

2019 ◽  
Vol 220 ◽  
pp. 03018
Author(s):  
Marya O. Guslyannikova ◽  
Eugene K. Bashkirov
Keyword(s):  
Exact Solution ◽  
Density Matrix ◽  
Thermal Field ◽  
Time Dependent ◽  
Two Photon ◽  
Atomic States ◽  
Dependent Density

The entanglement between two two-level atoms (qubits) interacting not-resonantly with a one mode of thermal field in a lossless cavity via effective degenerate two-photon transitions is investigated. Based on the exact solution for the time-dependent density matrix of the system under consideration, negativity is calculated as a measure of the entanglement of atoms. The influence of a detuning on the dynamics of entanglement of atoms for separable and entangled initial atomic states and thermal cavity state is investigated.

Conductance through two dots coupled in series: application of the exact solution

Microscopy ◽  
2005 ◽  
Vol 54 (suppl_1) ◽  
pp. i57-i60 ◽  
Author(s):  
Rui Sakano ◽  
Norio Kawakami
Keyword(s):  
Exact Solution ◽  
In Series

scholarly journals An exact solution of linearized flow of an emitting, absorbing and scattering grey gas

1971 ◽  
Vol 45 (4) ◽  
pp. 673-699 ◽  
Author(s):  
Ping Cheng ◽  
A. Leonard
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Transport Theory ◽  
Neutron Transport ◽  
Separation Of Variables ◽  
Closed Form Solution ◽  
Strong Shock ◽  
Form Solution ◽  
Isotropic Scattering ◽  
Differential Approximation

The governing equations for the problem of linearized flow through a normal shock wave in an emitting, absorbing, and scattering grey gas are reduced to two linear coupled integro-differential equations. By separation of variables, these equations are further reduced to an integral equation similar to that which arises in neutron-transport theory. It is shown that this integral equation admits both regular (associated with discrete eigenfunctions) and singular (associated with continuum eigenfunctions) solutions to form a complete set. The exact closed-form solution is obtained by superposition of these eigen-functions. If the gas downstream of a strong shock is absorption–emission dominated, the discrete mode of the solution disappears downstream. The effects of isotropic scattering are discussed. Quantitative comparison between the numerical results based on the exact solution and on the differential approximation are presented.

Axisymmetric Potential Flow Over Two Spheres in Contact

1975 ◽  
Vol 42 (4) ◽  
pp. 763-765 ◽  
Author(s):  
R. D. Small ◽  
D. Weihs
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Coordinate System ◽  
Laplace Equation ◽  
Potential Flow ◽  
Separation Of Variables ◽  
Added Mass ◽  
Tangent Sphere

An exact solution for the axisymmetric incompressible potential flow over two touching spheres is presented. A tangent-sphere coordinate system is used to simplify the boundary conditions. The Laplace equation is solved by means of separation of variables and the expression for the added mass obtained.

scholarly journals Solving Systems of Volterra Integral and Integrodifferential Equations with Proportional Delays by Differential Transformation Method

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Şuayip Yüzbaşı ◽  
Nurbol Ismailov
Keyword(s):  
Exact Solution ◽  
Nonlinear Equations ◽  
Taylor Series ◽  
Transformation Method ◽  
Integrodifferential Equations ◽  
Differential Transformation Method ◽  
Differential Transformation ◽  
Proportional Delays ◽  
In Series ◽  
Linear And Nonlinear

In this paper, the differential transformation method is applied to the system of Volterra integral and integrodifferential equations with proportional delays. The method is useful for both linear and nonlinear equations. By using this method, the solutions are obtained in series forms. If the solutions of the problem can be expanded to Taylor series, then the method gives opportunity to determine the coefficients of Taylor series. Hence, the exact solution can be obtained in Taylor series form. In illustrative examples, the method is applied to a few types of systems.

Asymmetric Contact Problem Including Wear for Nonhomogeneous Half Space

1982 ◽  
Vol 49 (1) ◽  
pp. 43-46 ◽  
Author(s):  
T. S. Sankar ◽  
V. Fabrikant
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Elastic Modulus ◽  
Contact Problem ◽  
Half Space ◽  
Tangential Stresses ◽  
Method Of Solution ◽  
Work Done ◽  
General Method ◽  
Asymmetric Contact

Contact problem with wear for asymmetric rigid die acting on a half space whose elastic modulus is a power function of depth is considered for the case when the die is rotating according to an arbitrary law. Zone of contact is taken to be a circle, and the wear is proportional to the work done by the tangential stresses obeying Coloumb’s law. Integral equation of the problem is derived and an exact solution of the equation is obtained in closed form. The case of inclined flat die is discussed as an illustrative example of the general method of solution that is proposed.

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