Comparison of the temperature stresses in a free and in a constrained cylinder

The conditions under which the radial and peripheral stresses in a free and in a constrained cylinder coincide at the ends of the cylinder when the temperature distribution is axially symmetrical are considered.P. I. Baranov Central Institute for Aircraft Engine Construction, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 163–165, January–February, 1972.     

Control of thermal stresses and displacements in thermoelastic bodies

By developing the method of the inverse thermoelastic and thermal conductivity problem we study problems of optimal control of thermal stresses and displacements in the case of one- and two-dimensional temperature fields. The solution of the optimization problems reduces to solving integral equations of first or second kind for determining the internal heat sources.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 18–23.     

Thermo-magneto-dynamic stresses and perturbation of magnetic field vector in a non-homogeneous hollow cylinder

An analytical method is presented to investigate thermo-magneto-elastic stresses and perturbation of the magnetic field vector in a conducting non-homogeneous hollow cylinder under thermal shock. The interaction between the deformation and the magnetic field vector in a non-homogeneous hollow cylinder is considered by adding a Lorentz’s electro-magneto-force into the equation of thermo-elastic motion of the non-homogeneous hollow cylinder in an axial magnetic field. The exact solution for magneto-thermo-dynamic stresses and perturbation responses of an axial magnetic field vector in a conducting non-homogeneous hollow cylinder was obtained by using finite integral transforms. From numerical calculations, the dynamic characteristics on both thermo-magneto-stresses and perturbation of the axial magnetic field vector in the conducting non-homogeneous hollow cylinder is revealed and discussed.     

Diffraction of the field of a point source by a circular cone (nonaxisymmetric case)

The problem of the diffraction of the wave field of a point source by an ideally reflecting circular cone is considered; the source is located off the axis of the cone but at a distance from it such that the space outside the cone is completely illuminated by waves from the source. Equations are obtained describing the behavior of the diffraction field in various regions of variation of the angular coordinates and which are convenient for numerical computations; integrals corresponding to the field of the incident and reflected waves are aso distinguished.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 42, pp. 212–227, 1974.     

A study of the thermoelastic behavior of a cylinder of low electrical conductivity in a uniform steady external electromagnetic field

We determine and study the temperature fields and stresses in a cylinder of low electrical conductivity resulting from force and thermal actions on it by a uniform external electromagnetic field. We study resonance phenomena and the behavior of the unknown fields in the vicinity of the resonance frequencies of the electromagnetic field. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 80–86.     

The temperature field of a multilayer cylinder in asymptotic thermal mode

We propose a method of determining one-dimensional temperature fields in a multilayer cylinder corresponding to asymptotic thermal mode. We give the temperature distribution when the temperature of the surrounding medium varies polynomially and harmonically with time and with a heat source density concentrated on one of the interfaces of adjacent layers.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 162–169.     

Thermoelastic stresses in a nonuniform orthotropic cylinder

The stress distribution in a cylinder with cooling nonuniform with respect to the circumferential coordinate is investigated. The nonuniformity of the mechanical properties of the material in this direction is taken into account. Numerical results obtained at values of the parameters characteristic of wound glass-reinforced products are discussed.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 3, pp. 560–563, May–June, 1975.     

The uncoupled problem of thermoelastic vibrations of a cylinder

Using the theory of functions of a complex variable, we construct an approximate solution of the problem of steady thermoelastic vibrations of a cylinder with curvilinear cavities, not taking account of the interaction of the strain and temperature fields. The results of numerical computations are given in the case of radially symmetric vibrations of a cylinder with a cavity. Two figures. Bibliography: 5 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 107–112.     

Axially symmetric temperature stresses in an elastic isotropic cylinder of finite length

We consider an axially symmetric problem of the thermostressed state of a solid cylinder of finite length with a load-free surface. Using the method of superposition, we have constructed the complete analytical solution of this problem, which is reduced to the solution of a system of linear algebraic equations. We have proposed a method for determining the asymptotic behavior of coefficients in these systems, which enables us to develop an efficient algorithm for the calculation of stresses in the cylinder, including regions near its end-face circles. Typical examples are considered.     

Viscoelastic cylinder reinforced with thin elastic casing in a heterogeneous temperature field

The problem of a viscoelastic cylinder reinforced with a thin elastic casing with consideration given to a heterogeneous temperature field is presented. The method of numerical solution of the problem is discussed. The results of computation are presented in the form of curves.     

Influence of the mechanical properties of a cylinder on the temperature stresses with allowance for the edge effect

The volume state of stress of a hollow homogeneous cylinder with temperature varying along the radius is analyzed for various values of Poisson's ratio, which in polymers may fluctuate over a wide range. The stresses in a cylinder of polymeric material, calculated with and without allowance for the temperature dependence of the modulus of elasticity for the same loading conditions, are subjected to a comparative analysis. Numerical results are obtained on the basis of a solution of the axisymmetric three-dimensional problem of thermoelasticity for an inhomogeneous cylinder using a collocation method.Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1083–1086, November–December, 1969.     

The coupled problem of thermoelastic vibrations of a cylinder with cavities

Using a method based on the machinery of analytic functions of complex variables, we construct the solution of the problem of steady planar strain of an isotropic cylinder with curvilinear cavities caused by uneven heating of the surfaces of the cylinder and the cavities. It is an exact solution of the equations and an approximate solution of the boundary conditions. The results of numerical studies are given for a hollow cylinder undergoing thermoelastic radially symmetric vibrations. Two figures. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 82–86.     

Nonstationary nonaxisymmetric temperature fields of multilayer orthotropic cylinders

A solution of the three-dimensional nonstationary nonaxisymmetric problem of heat conduction for a preliminarily heated multilayer infinite orthotropic cylinder under the action of heat sources and in the presence of convective heat exchange is obtained. In this case, a Green function of the corresponding problem of heat conduction is used. As an example, we consider the heating of the cylinder by a mobile normally distributed heat flow. The temperature field in a two-layer cylinder caused by a heat flow that moves along the generator and a helical curve is investigated.     

Optimal nonaxisymmetric temperature fields produced in a shell of revolution by local heating

A two-criterion extremal problem of determining the stress-optimized nonaxisymmetric temperature fields produced in shells of revolution by local heating is formulated. A method is proposed for solving this problem numerically on the basis of the method af finite elements. Computational results are presented for specific problems.Translated from Matematicheskie Melody i Fiziko-mekhanicheskie Polya, No. 26, pp. 50–54, 1987.     

On the accuracy of a difference scheme for solving the nonstationary coupled thermoelastic problem in stresses

For numerical solution of the coupled one-dimensional problem of dynamic thermoelasticity in stresses (strains) we construct a second-order approximating difference scheme. We study its stability and obtain an a priori estimate. We prove that the solution of the scheme converges to a generalized solution of the original problem in the Sobolev class W ₂ ² (Q_T).Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 34, 1991, pp. 95–99.