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Vol 226, No 1 (2017)
- Year: 2017
- Articles: 7
- URL: https://journals.rcsi.science/1072-3374/issue/view/14857
Article
Modeling and Analysis of the Thermoelastic State of a Thermosensitive Cylinder Layered Along the Axis Under the Conditions of Heat Removal by the Evaporation of Liquid
Abstract
By using an example of a cylinder with three layers along the axis, we illustrate the formulation of the mathematical model and procedure of determination of the steady-state thermal and thermoelastic states of a thermosensitive cylinder in the presence of a heat flux directed toward one bounding surface of the cylinder and the heat removal by the evaporation of liquid through the other bounding surface. Moreover, it is assumed that the second layer of the cylinder contains heat sources distributed according to the parabolic law and the conditions of perfect thermal contact between the layers are satisfied. We study the influence of the thermomechanical characteristics of the materials of layers regarded as functions of temperature and the intensity of evaporation on the character and level of the distributions of temperature and stresses.
1-10
Well-Posedness of the Green–Lindsay Variational Problem of Dynamic Thermoelasticity
Abstract
On the basis of the Green–Lindsay initial-boundary-value problem of thermoelasticity, we formulate the corresponding variational problem in terms of displacements and temperature. Sufficient conditions of regularity of the initial data of the problem and the uniqueness of its solution are established from the energy equation of the variational problem. To prove the existence of the generalized solution (and simultaneously, as the first step to a well-justified procedure for finding its approximation), we use the method of Galerkin semidiscretization with respect to the spatial variables and show that the limit of the sequence of its approximations is the solution of the Green–Lindsay variational problem.
11-27
Thermoelasticity of a Cylindrical Shell with Low Shear Stiffness in a Local Temperature Field
Abstract
On the basis of the shear model of deformation of thin-walled structural elements, we solve the quasistatic problem of thermoelasticity for a long cylindrical shell with annular distribution of heat sources and heat transfer from the surface. For different values of the ratio of Young’s modulus to the shear modulus of the material of the shell, we study the thermoelastic state of the shell in the asymptotic mode of heating for which the computed quantities attain their maximum values. The numerical analysis is performed. We indicate the possibility of generalizing the results of investigation to the case of finitely many heating rings for various values of their widths and the power of heat sources.
28-40
Numerical-Analytic Technique for the Solution of Nonstationary Problems of Heat Conduction in Locally Inhomogeneous Media
Abstract
We propose a procedure of simultaneous application of the splitting method, boundary-element method, step-by-step time scheme, and iterative FD (Finite-Discrete) procedure for the construction of the integral representation of the solution of a nonstationary problem of heat conduction for a closed domain with Dirichlet condition given on its boundary containing a locally inhomogeneous subdomain whose physical characteristics depend on the coordinates. We perform a comprehensive numerical analysis of this approach with regard for the fact that the heat field is affected by the dependences of the heatconduction coefficient and specific heat capacity of the material on the coordinates.
41-51
Equations of Thin Anisotropic Elastic Shells of Revolution in the {m, n}-Approximation Method
Abstract
We construct a system of differential equations aimed at the description of elastic deformations of thin anisotropic shells of revolution and solved with respect to the first-order partial derivatives with respect to the meridional coordinate. These equations are obtained by the {m,n}-approximation method. The approximations of unknown functions are in good agreement with force boundary conditions imposed on the front faces.
52-68
Investigation of the Acoustic Interaction of Shells with Liquid
Abstract
We propose a mathematical model of acoustic interaction of the shells of revolution with liquid under axisymmetric loads. The model is based on the linear relations of Timoshenko–Mindlin shells and the acoustic approximation for the liquid. We formulate the initial boundary-value problem and the corresponding variational problem of interaction between two media. For the solution of the variational problem of acoustic interaction between the shell of revolution and the liquid, we develop a projectionmesh scheme, where the Galerkin semidiscretization is used together with approximations of the finiteelement method in the space variables and the one-step recurrence scheme of integration with respect to time. The stress-strain state of the shell subjected to the action of normal hydrostatic pressure is analyzed. The results of numerical analysis of deflections obtained by using the proposed method are compared with the available analytic solutions.
69-78
Stress State of a Partially Fixed Spherical Shell Filled with Liquid and Subjected to Impulsive Excitation
Abstract
We study the stress-strain state of a closed elastic spherical shell filled with ideal compressible liquid. The energy introduced in the form of pulses in the gas cavity in the central part of the system serves as the source of its excitation. The hypotheses used for the investigations by the finite-difference method are presented and a correct mathematical statement of the problem is formulated. We obtain the data on the behavior of stresses as function of time in the cases of free shell and of the partial rigid fixing of its surface. The effect of rigid fixing on the stress-strain state of the shell is analyzed.
79-87