Coupled thermoelasticity with non-zero thermal boundary conditions

We consider one-dimensional wave propagation in a thermoelastically coupled half space. The boundary conditions involve an application of a non-zero temperature or temperature gradient. The strain, temperature, stress and particle velocity are obtained and compared when both time and distance are large. The ratios of the temperature to the strain, the stress to the strain, and the particle velocity to the strain are found to be the same for all the six cases considered.     

To the solution of the thermoelasticity problem for conical shells

We consider the stress-strain state of thin conical shells in the case of arbitary distribution of the temperature field over the shell. We obtain equations of the general theory based on the classical Kirchhoff-Love hypotheses alone. But since these equations are very complicated, attempts to construct exact solutions by analytic methods encounter considerable or insurmountable difficulties. Therefore, the present paper deals with boundary value problems posed for simplified differential equations. The total stress-strain state is constructed by “gluing” together the solutions of these equations. Such an approach (the asymptotic synthesis method) turns out to be efficient in studying not only shells of positive and zero curvature [1, 2] and cylindrical shells [3] but also conical shells [4, 5]. Here we illustrate it by an example of an arbitrary temperature field, and the problem is reduced to solving differential equations with polynomial coefficients and with right-hand side containing the Heaviside function, the delta function, and their derivatives.     

Two-dimensional problem of anisotropic elastic body with a hyperbolic boundary

The general and simplified formula for anisotropic medium with a hyperbolic boundary subjected to pure bending M_o is provided in this paper. The stress and strain fields in medium are obtained. Based upon the above results, we analyse the hoop stress along the hyperbolic curve and the stress distributions on the planex₂=0 for aluminium (cubic crystal). When the boundary curve degenerates into an external crack three kinds of stress intensity factors (k₁, k₂, k₃) are obtained, and it is easily found that the first stress intensity factor k₁ is independent of the material constants.     

A particle transport problem with a quadratic nonlinearity and general boundary conditions: The stationary solution

Summary We study a stationary, nonlinear, particle transport problem in slab geometry with general boundary conditions. The existence and uniqueness of the solution is proved by means of fixed point techniques, provided that the source term is sufficiently small.

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Sommario Si studia un problema stazionario nonlineare di particelle in geometria piana con condizioni al contorno generali. L'esistenza e unicitá della soluzione è dimostrata con tecniche di punto fisso purchè il termine di sorgente sia sufficientemente piccolo.

     

Asymptotic approximation for the solution of a boundary-value problem with varying type of boundary conditions in a thick two-level junction

We consider a mixed boundary-value problem for a Poisson equation in a plane two-level junction Ω_ε that is the union of a domain Ω₀ and a large number 3N of thin rods with thickness of order . The thin rods are divided into two levels depending on their length. In addition, the thin rods from each level are ε-periodically alternated. The homogeneous Dirichlet conditions and inhomogeneous Neumann conditions are given on the sides of the thin rods from the first level and the second level, respectively. Using the method of matched asymptotic expansions and special junction-layer solutions, we construct an asymptotic approximation for the solution and prove the corresponding estimates in the Sobolev space H ¹(Ω_ε) as ε → 0 (N → +∞). Published in Neliniini Kolyvannya, Vol. 9, No. 3, pp. 336–355, July–September, 2006.     

Numerical solution of moving boundary problem in a finite domain

The temperature distribution in two regions and the location of moving interface during freezing in a finite domain is studied numerically. The differential equations governing the process of heat transfer in two regions are converted to initial value problem of vector matrix form. The solution of this initial value problem is utilized iteratively in the interface heat flux equation to determine interface location as well as the temperature distribution in two regions. The whole analysis is presented in a nondimensional form and the results thus obtained are discussed in detail. Received on 4 March 1998     

A moving boundary hyperbolic problem for a stress impact in a bar of rate-type material

In this paper we present some results obtained by studying the mathematical model describing a moving boundary hyperbolic problem related to a time dependent stress impact in a bar of Maxwell-like material. Due to the impact a shock front propagates with a finite speed. Here our interest is to underline the influence of the dissipative term on the propagation of the shock front.

In the framework of the similarity analysis we are able to reduce the moving boundary hyperbolic problem to a free boundary value problem for an ordinary differential system. It is then possible, by applying two numerical transformation methods, to solve the free boundary value problem numerically. The influence of the dissipative term is evident: the free boundary (that defines the shock front propagation) is an increasing function of the dissipative coefficient.     

Continuation of the solution of a free boundary problem in cylindrical symmetry

Summary We perform an a priori analysis of the behavior of the solution to a Stefan type free boundary problem in cylindrical symmetry, in arbitrarily large time intervals; a nonlinear flux condition is prescribed on the fixed boundary, for t>0.Next we find some relations between the occurrence of each possible case and the behavior of the initial datum, assuming that the flux is null on the fixed boundary for t>0.

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Sommario Si esegue un'analisi a priori del comportamento, in intervalli di tempo arbitrariamente grandi, della soluzione di un problema a frontiera libera del tipo di Stefan in simmetria cilindrica; sulla frontiera fissa, per t>0, è stabilita una condizione di flusso non lineare.Si trovano quindi relazioni tra i vari casi possibili e il comportamento del dato iniziale, sotto l'ulteriore ipotesi che il flusso sulla frontiera fissa, per t>0, sia nullo.

     

Theoretical solution of the boundary problem of subsonic aerodynamics

A general theoretical solution of the boundary problem of aerodynamics of high subsonic velocities is presented. The solution of the partial differential equation for the velocity potential is carried out in the physical plane in streamline co-ordinates. The principle of the solution is the representation flow of a compressible fluid around a given profile to a hypothetical flow of an incompressible fluid around a different associated profile. In other words, the problem of compressible flow is transformed to the problem of incompressible flow, which can easily be solved. The results of this solution show very good agreement with solutions of other authors and with experiments.     

On the solution of nonlinear two-point boundary value problem

In this paper, a non-variational version of a max-min principle is proposed, andan existence and uniqueness result is obtained for the nonlinear two-point boundaryvalue problenl u"+g(t.u)=f(t),u(0)=u(2π)=0