Dynamics of thermoelastic half-plane by action of periodic loads and heat flows at its boundary

2021 ◽  
pp. 108128652199388
Author(s):  
Lyudmila Alexeyevna Alexeyeva ◽  
Bakhyt Alipova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Differential Algebra ◽  
Operator Method ◽  
Surface Forces ◽  
Generalized Function ◽  
Periodic Surface ◽  
Heat Flows ◽  
Generalized Function Theory ◽  
Thermal Sources

The problem of the dynamics of a thermoelastic half-space under periodic surface forces and heat flows is solved using the model of coupled thermoelasticity. The Green’s tensor for one boundary value problem is constructed utilizing Fourier transformation. Analytical solutions for arbitrary surface forces and heat flow using the theory of generalized functions are constructed. To solve this boundary value problem, generalized function theory, tensor and differential algebra, the operator method, and integral transformations were used. The solutions obtained make it possible to investigate the thermal stress–strain state of an array with natural and artificial thermal sources and mass power forces acting at its surface.

scholarly journals The first boundary value problem of the dynamics of an anisotropic elastic half-space under the action of subsonic transport loads

2020 ◽  
Vol 4 (78) ◽  
pp. 45-52
Author(s):  
G. K. ZAKIR’YANOVA ◽  
◽  
L. A. ALEXEYEVA ◽  
Keyword(s):  
Rock Mass ◽  
Boundary Value Problem ◽  
Half Space ◽  
Wide Class ◽  
Boundary Value ◽  
Operator Method ◽  
Elastic Half Space ◽  
Theory Of Elasticity ◽  
Wide Range ◽  
Anisotropic Elastic

The first boundary value problem of the theory of elasticity for an anisotropic elastic half-space is solved when a transport load moves along its surface. The subsonic Raleigh case is considered, when the velocity of motion is less than the velocity of propagation of bulk and surface elastic waves. The Green’s tensor of the transport boundary value problem is constructed and on its basis the solution of boundary value problems for a wide class of distributed traffic loads is given. To solve the problem, the methods of tensor and linear algebra, integral Fourier transform, and operator method for solving systems of differential equations were used. The obtained solution makes it possible to investigate the dynamics of the rock mass for a wide class of transport loads, in a wide range of velocities, both low velocities and high velocities, and to evaluate the strength properties of the rock mass under the influence of road transport. In particular, determine the permissible velocities of its movement and carrying capacity. In addition, a investigation on its basis of the movement of the day surface along the route will make it possible to establish criteria for the seismic resistance of ground structures and the permissible distances of their location from the route.

scholarly journals Mathematical Model of a Surface Radiance Factor

2019 ◽  
Author(s):  
Александр Басов ◽  
Alexander Basov ◽  
Владимир Будак ◽  
Vladimir Budak
Keyword(s):  
Mathematical Model ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Lower Boundary ◽  
Operator Method ◽  
Angular Spectrum ◽  
Discrete Ordinates ◽  
Optical Parameters ◽  
Anisotropic Part ◽  
Radiance Factor

The article is devoted to the creation of a surface radiance factor mathematical model. The basis of the model is the solution of the boundary value problem of the radiative transfer equation (RTE). The surface is considered as a structure consisting of several turbid layers, each of which is characterized by its optical parameters. The top of the structure is randomly rough, uncorrelated, Fresnel. The lower boundary reflects perfectly diffusely. The complexity of solving the RTE boundary value problem for real layers is due to the fact that the suspended particles in each layer are always much longer than the wavelength. This leads to a strong anisotropy of the radiance angular distribution according to Mie theory. The solution comes down to a system of equations by the discrete ordinates method that consists of several hundred of differential equations. Subtraction of the anisotropic part from the solution based on an approximate analytical solution of the RTE allows avoiding this problem. The approximation is based on a slight decrease in the anisotropic part of the angular spectrum. The matrix-operator method determines the general solution for a complex multilayer structure. The calculation speed can be increased without compromising the accuracy of the solution with the help of the synthetic iterations method. The method consists of two stages: the first one repeats the described one with a small number of ordinates; on the second one the iteration of it is performed. The model is realised in the Matlab software.

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