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Том 223, № 2 (2017)
- Год: 2017
- Статей: 7
- URL: https://bakhtiniada.ru/1072-3374/issue/view/14826
Article
Stress-Strain State of a Piecewise Homogeneous Thermally Sensitive Cylinder in the Presence of Heat Removal by Liquid Boiling
Аннотация
By analyzing an example of a finite cylinder three-component in its axial coordinate, we illustrate the formulation of a mathematical model and a method aimed at the determination and investigation of the steady-state distributions of temperature and stresses in the presence of heat removal through one of the plane boundaries by liquid boiling. In this case, we use the mathematical model of thermally sensitive body. It is assumed that the second layer of the cylinder contains heat sources distributed according to the parabolic law, a heat flux is directed toward one of the plane boundaries, and the heat removal by liquid boiling takes place trough the other boundary. We determine the stresses and study the effect of temperature dependences of the thermomechanical characteristics of materials of components of the cylinder and the intensity of boiling on the character and level of the distributions of temperature and stresses.
103-116
Quasistatic Thermoelastic State of a Heat-Sensitive Three-Component Layer Under the Conditions of Convective-Radiative Heat Exchange
Аннотация
We present an analytic-numerical approach to the determination of the thermoelastic state of a three-component heat-sensitive layer interacting with an ambient medium by means of the convective-radiative heat exchange and subjected to the action of heat sources. The proposed approach is based on the use of the Kirchhoff transformation, generalized functions, Green function of the linear nonstationary problem of heat conduction for the three-component space, and linear splines. The influence of thermal sensitivity and the values of the parameters of heat exchange on the distributions of temperature and stresses is investigated.
117-131
Integral Equation for the Radial Stresses in a Radially Inhomogeneous Heat-Sensitive Hollow Sphere
Аннотация
We determine the thermal stressed state of a heat-sensitive radially inhomogeneous hollow sphere for given constant loads acting on its surfaces and a known temperature field inside the sphere. The corresponding problem of thermoelasticity in stresses is reduced to the solution of the Fredholm integral equation of the second kind for the radial component of the stress tensor. The influence of temperature dependences of the characteristics of radially inhomogeneous material on the stresses and displacements is investigated.
132-144
Quasistatic Plane Problem of Thermoelasticity for the Half Space with Coating Under Mixed Conditions of Heating
Аннотация
The Laguerre and Fourier integral transformations are used to construct the solution of a plane quasistatic problem of thermoelasticity for the half space with coating. The surface of the coating is heated by a heat flux symmetrically distributed in a strip of certain width and is cooled according to the Newton law outside this strip. The results of numerical analysis of the thermal stressed states of the half space and the coating as functions of the intensity of cooling and the relative thickness of the coating are presented.
145-158
Stresses in an Anisotropic Half Plane with Notches
Аннотация
We develop an algorithm for the determination of stresses in an anisotropic half plane with notches based on the method of boundary integral equations. Integral equations are solved numerically by the method of mechanical quadratures. The investigation of stresses near notches of different shapes is performed. We establish the characteristic features of the stress distributions depending on the shapes and sizes of notches and the mechanical characteristics of the material of the plates. The asymptotic relations are proposed for the determination of the stress concentration factors for narrowed notches of elliptic shapes.
159-172
Optimization of Nonstationary Thermal Displacements in a Given Cross Section of a Half Space in the Plane Strain State
Аннотация
We construct the solution of the problem of optimal control over the distribution of nonstationary vertical thermal displacements of a half space in the plane strain state. The power of internal heat sources concentrated in a plane parallel to the boundary is chosen as the control function. Under the assumption of existence of the control function guaranteeing the attainment of the greatest lower bound of the uniform deviation of the controlled distribution of vertical displacements from the given distribution, we reduce the problem of optimization to the inverse problem of thermoelasticity. The solution of the obtained inverse problem is constructed and analyzed.
173-183
Heat Conduction in Plates with Thin Two-Sided Multilayer Coatings Under the Conditions of Nonstationary Heating
Аннотация
On the basis of the analytic solution of a one-dimensional problem of heat conduction for a plate with two-sided thin multilayer coating obtained with the help of generalized boundary conditions, we perform the investigation and establish the regularities of development of the thermal processes in the body with coating under the conditions of heating by an ambient medium with variable temperature.
184-197