On the structure of the stresses inside an ellipsoidal irregularity in thermoelastic problems

We study the structure of the stresses inside an ellipsoidal irregularity. We obtain a result that generalizes the theorem on polynomial conservation for thermoelastic problems under homogeneous and linear external stress and temperature fields when there is perfect thermal and mechanical contact on the phase interface. We show by a specific example how significantly the stress structure inside the irregularity changes when the form of interaction on the boundary surface changes.Translated fromVychislitel'naya i Prikladnaya Matematika, Issue 71, 1990, pp. 70–77.     

Rational regimes for induction heating of cylindrical articles for graphitation

We develop a method of computing regimes for induction heating of cylindrical carbon devices during graphitation. We study the electromagnetic, temperature, and mechanical fields as functions of the parameters of the heating regime.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 27–31.     

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.     

Cellulose-Based Composite Films

The mechanical and optical properties of cellulose-based composite films are investigated.It is shown that the use of toluene diisocyanate as a coupling agent and Avicel fibers as reinforcing elements give films with the highest mechanical characteristics. Using differential scanning calorimetry, it is also found that the glass transition temperature T _g of all the materials studied is below the room temperature and that the T _g increased with cross-linking and introduction of Avicel.     

The thermoelastoplastic computation of the stressed state of shells of rotation under nonaxisymmetric heating taking account of secondary plastic deformations

The problem is solved in a geometrically linear formulation in the context of the Kirchhoff-Love hypothesis taking account of the temperature dependence of the mechanical characteristics of the material. We use the linearized relations of the theory of small curvature processes. Using a numerical example we study the influence of the loading history and the effect of secondary plastic deformations on the stressed state of a shell of revolution whose meridian has a complicated shape.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 77–80.     

Application of the method of generalized coupling problems in the thermoelasticity of piecewise-homogeneous bodies under nonideal contact

We analyze the specifics of applying the method of generalized coupling problems to determine and study the temperature fields and the stresses they cause in piecewise-homogeneous bodies under nonideal thermomechanical contact at the interfaces. Translated fromMatematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 1, 1998, pp. 108–116.     

Stress state of thermosensitive thick cylinders made of anisotropic composites

The class of problems on the axially symmetric stress state of thick cylinders made of anisotropic materials is considered. The problems are solved numerically. The temperature and mechanical fields in the composite cylinders are investigated taking into account the temperature dependence of the matrix and reinforcement characteristics, as well as the variability of density and angle of reinforcement across the thickness.Institute of Mechanics, Ukrainian National Academy of Sciences, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 367–374, May–June, 1999.     

Thermodynamic foundations of locally gradient generalized thermomechanics

We consider the thermodynamic foundation of locally gradient generalized thermomechanics. In describing the local situation we take account of the gradient of the temperature field and the chemical potential field, as well as the inertial effects of mechanical, thermal, and self-diffusive forms of motion.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 20–24.     

Stability conditions for singularly perturbed delay differential equations

Singular perturbation problems containing a small positive parameter ε occur in many areas, including biochemical kinetics, genetics, plasma physics, and mechanical and electrical systems. A uniformly valid, reliable interpretable approximation of such problems is required. This paper provides sufficient conditions to ensure the exponential stability of the analytical and numerical solutions of the singularly perturbed delay differential equations with a bounded time-lag for suf.ciently small ε > 0. The Halanay inequality is used to prove the main results of the paper. A numerical example is provided to illustrate the methodology and clarify the need for a stiff solver for numerical solutions of these problems.     

Global weak solution of planetary geostrophic equations with inviscid geostrophic balance

A reformulation of the planetary geostrophic equations (PGEs) with the inviscid balance equation is proposed and the existence of global weak solutions is established, provided that the mechanical force satisfies an integral constraint. There is only one prognostic equation for the temperature field, and the velocity field is statically determined by the planetary geostrophic balance combined with the incompressibility condition. Furthermore, the velocity profile can be accurately represented as a function of the temperature gradient. In particular, the vertical velocity depends only on the first-order derivative of the temperature. As a result, the bound for the L∞ (0, t ₁ ; L ²) ∩ L ² (0, t ₁ ; H ¹) norm of the temperature field is sufficient to show the existence of the weak solution.     

The thermally stressed state of a thickwalled hollow composite cylinder

We propose an approach to the determination of the temperature, stress, and displacement, fields in laminated hollow composite cylinders. The cylinders are studied in three-dimensional formulation; the material of each lamina has the properties of thermal and elastic orthotropy. We study the influence of the heat flow passing through the end surfaces and nonuniform heating of the cylinder to its thermally stressed state. We exhibit peculiarities in the stress and displacement distributions caused both by anisotropy of the mechanical and thermophysical properties and by the nature of the thermal actions applied. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 14–18     

The axisymmetric thermoelastoplastic state of a circular two-layer hollow cylinder taking account of frictional heating

We state and solve the axisymmetric thermoelastoplastic problem for a circular two-layer hollow cylinder taking account of frictional heating under the condition that the mechanical and thermophysical characteristics of the materials are independent of temperature. Translated fromMatermatichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 100–106.     

Sui potenziali elettromagnetici per alcuni modelli di isteresi magnetica

Summary In this paper we study electromagnetic potentials (free energy and enthalpy) for some simple models of ferromagnetic materials exhibiting hysteresis loops and obeying constitutive equations of rate type (1), (34).For the sake of simplicity, mechanical and electric effects are ignored and isothermal conditions are assumed. Involving thermodynamic arguments of Coleman and Owen [1]we show the existence of a convex set of lower-potentials whose minimum, and maximum elements are explicitly constructed as functions of state. Finally, some problems on state-space representation and convexity of various lower-potentials are discussed.

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Lavoro eseguito nell'ambito delle attività del G.N.F.M. del C.N.R. e dei progetti di ricerca ministeriali 40% e 60%.     

Automatic solution of regular and singular vector Sturm-Liouville problems

This paper describes the algorithms and theory behind a new code for vector Sturm-Liouville problems. A new spectral function is defined for vector Sturm-Liouville problems; this is an integer valued function of the eigenparameter which has discontinuities precisely at the eigenvalues. We describe numerical algorithms which may be used to compute the new spectral function, and its use as amiss-distance function in a new code which solves automatically a large class of regular and singular vector Sturm-Liouville problems. Vector Sturm-Liouville problems arise naturally in quantum mechanical applications. Usually they are singular. The advantages of the author's code lie in its ability to solve singular problems automatically, and in the fact that the user may specify the required eigenvalue by its index.     

Three-dimensional mixed problems of thermoelasticity for isotropic plates

We obtain the homogeneous thermal solutions due to a temperature field for the three-dimensional thermoelastic problem for isotropic plates on whose plane faces homogeneous thermal and mixed mechanical conditions of flat face and diaphragm type are prescribed. This makes it possible to reduce the thermoelastic boundary-value problem to the corresponding elasticity problem. Translated fromTeoreticheskaya i Prikladnaya Mekhanika. No. 25, 1995, pp. 3–8.     

Optimization of the heating of a heat-sensitive layer under constraints on the stresses in the plastic region of deformation of the material

We study the problem of optimal control for rapidity of the heating of a heat-sensitive layer under constraints on the control (the temperature of the heating medium or the heat flux) and maximal values of the stress intensity in the plastic region of deformation of the material. We propose an algorithm for solving the problem that presumes it has been reduced to the inverse problem of thermoplasticity. For the case of one-sided heating we give a numerical analysis of the direct and inverse problems of thermoplasticity. Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.     

Solution of a class of three-dimensional boundary value problems of the theory of heat conduction

We consider a class of connected three-dimensional boundary-value problems for the quasi-linear heat equation that model the temperature fields in molds under a continuous cyclic molding of flat castings. We propose a method of approximate solution. The results of the computations are shown as the dependence of the dimensionless temperature on the time throughout ten cycles.Translated fromVychislitel'naya i Prikladnaya Matematika, Issue 71, 1990, pp. 84–90.     

The axisymmetric problem of thermoelasticity of a multilayer thermosensitive tube

We propose a method of solving stationary heat-conduction problems of contacting bodies with coefficient of thermal conductivity that are linear functions of the temperature and the corresponding problems of thermoelasticity based on the method of perturbations. We give a numerical analysis of the thermal stresses in a two-layer tube. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 97–103.     

On one contact problem of plane elasticity theory with partially unknown boundary

Applications of elastic plates weakened with full-strength holes are of great interest in several mechanical constructions (building practice, in mechanical engineering, shipbuilding, aircraft construction, etc). It's proven that in case of infinite domains the minimum of tangential normal stresses (tangential normal moments) maximal values will be obtained on such contours, where these values maintain constant(the full strength holes). The solvability of these problems allow to control stress optimal distribution at the hole boundary via appropriate hole shape selection. The paper addresses a problem of plane elasticity theory for a doubly connected domain S on the plane z = x + iy, which external boundary is an isosceles trapezoid boundary; the internal boundary is required full-strength hole including the origin of coordinates. In the provided work the unknown full-strength contour and stressed state of the body were determined. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Existence and uniqueness results for minimization problems with nonconvex functionals

In some physical problems (mechanical problems, optimal control problems, phase transition problems, etc.), we have to minimize a functionalJ over a topological spaceU for whichJ is not sequentially lower semicontinuous. In this article, we prove new existence results for general one-dimensional vector problems of calculus of variations without any convexity condition on the integrand of the problem. In particular, we do not suppose that the integrand is split in two parts, one part depending on the gradient variable and the other part depending on the state variable, as is often supposed in recent results. In the case where the integrand is the sum of two functions, the first one depending on the gradient variable and the second one depending on the state variable, we also prove a uniqueness result without any convexity assumption with respect to the gradient variable.A preliminary version of some results given in this article was presented at the Workshop on Calculus of Variations and Nonlinear Elasticity organized at Cortona, Italy, 27–31 May 1991 by B. Dacorogna, P. Marcellini, and C. Sbordone. The author would like to thank the organizers of this workshop for their invitation.