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.     

Temperature stresses in an inhomogeneous cylinder of finite length

An analytic method of determining the temperature stresses in circular cylinders is described. In the solution of the problem, based on a collocation method, together with the finite length of the cylinder its arbitrary inhomogeneity is also taken into account. In a particular case this may be caused by the effect of temperature on the mechanical constants of the material, which is especially typical of polymers at negative temperatures. The results of a calculation of the stresses in a hollow cylinder of finite length with a variable modulus of elasticity are presented as an example.Dzherzhinskii Military Engineering Academy. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 710–715, July–August, 1968.     

Steady-state thermal stresses in an elastic cone

Zusammenfassung Diese Arbeit befasst sich mit der Bestimmung der stationären Wärmespannungen, die in einem elastischen Kreiskegel durch eine unstetige Verteilung der Oberflächentemperatur hervorgerufen werden. Die Temperatur der Mantelfläche wird oberhalb und unterhalb einer festen Entfernung von der Kegelspitze konstant angenommen. Das zugehörige Wärmeleitungsproblem wurde in einer früheren Veröffentlichung unabhängig gelöst. In der vorliegenden Arbeit wird eine strenge Lösung für die gesuchten Wärmespannungen mit Hilfe der Mellin-Transformation hergeleitet. Das hier benutzte Verfahren ist auch anwendbar auf das gewöhnliche Randwertproblem für einen elastischen Kegel, der durch eine entsprechende unstetige Oberflächenbelastung beansprucht wird.

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The results communicated in this paper were obtained in the course of an investigation conducted under Contracts Nonr 562(20) and Nonr 562(25) of Brown University with the Office of Naval Research in Washington, D. C.     

Residual stresses caused by linear incompatibility of strains in an orthotropic cylindrical shell

We analyze a healed crack in an orthotropic cylindrical nonshallow shell using a continuously distributed dislocation model. The field of residual stresses on the faces of the shell is investigated for different cases of transverse dislocations of normal opening.     

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.     

Numerical solution of the propagation problem of longitudinal elastic waves in an orthotropic hollow cylinder

Wave processes in an orthotropic cylinder are analyzed. Harmonic oscillations are considered for which the original problem is reduced to a system of ordinary differential equations. This system is solved by the numerically stable discrete-orthogonalization method. Discrete curves for specific problems are given.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 75–78, 1985.     

Retrieving the time-dependent thermal conductivity of an orthotropic rectangular conductor

The aim of this paper is to determine the thermal properties of an orthotropic planar structure characterized by the thermal conductivity tensor in the coordinate system of the main directions (Oxy) being diagonal. In particular, we consider retrieving the time-dependent thermal conductivity components of an orthotropic rectangular conductor from nonlocal overspecified heat flux conditions. Since only boundary measurements are considered, this inverse formulation belongs to the desirable approach of non-destructive testing of materials. The unique solvability of this inverse coefficient problem is proved based on the Schauder fixed point theorem and the theory of Volterra integral equations of the second kind. Furthermore, the numerical reconstruction based on a nonlinear least-squares minimization is performed using the MATLAB optimization toolbox routine lsqnonlin. Numerical results are presented and discussed in order to illustrate the performance of the inversion for orthotropic parameter identification.     

Steady-state thermal stresses in an infinite elastic medium containing an annular crack

An axisymmetric steady-state thermoelastic problem of an infinite isotropic medium containing an annular crack is considered. The faces of the crack are exposed to prescribed temperature distribution. The normal components of stress and displacement on the crack plane and the stress-intensity factors at the boundaries of the crack are expressed in power series in terms of the ratio between the radii of the inner and outer boundaries. These are illustrated graphically.     

Optimal rigidity of a thin-walled orthotropic cylinder in combined tension and torsion

The problem of optimizing the reinforcement of an orthotropic cylinder in combined torsion and tension is considered in relation to the condition of minimum displacement. A numerical example is given. It is shown that the stiffness depends on the ratio of the normal and shear stresses, the elastic moduli, and the parameters.Moscow Aviation Technological Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1121–1123, November–December, 1973.     

Steady state thermal stresses in an elastic solid bounded by two cones

Zusammenfassung Es wird für das Problem der Wärmespannungen in einem kegelförmig begrenzten elastischen Körper eine Ähnlichkeitstransformation entwickelt. Ist die Temperatur an der freien Oberfläche als Potenz des Abstandes von der Spitze vorgeschrieben, so lässt sich ein Satz von Ähnlichkeitsvariablen angeben, welcher die thermoelastischen Beziehungen auf Legendre-Gleichungen reduziert und damit der Lösung leicht zugänglich macht. Die Rechnung ist für den Sonderfall konstant gehaltener Oberflächentemperatur im einzelnen durchgeführt.

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This work has been done at the Mathematics Research Center, University of Wisconsin, under the U.S. Army Contract DA-11-022-ORD-2059.     

Critical compressive stresses in cylindrical shells composed of orthotropic layers with different orientations

The laws of variation of the strains and critical stresses for smooth thin circular cylindrical glass-reinforced plastic shells based on ÉDT-10P resin have been experimentally investigated at different orientations of the fabric reinforcement. The results of the tests are compared with the theoretical data obtained from the relations of the theory of elasticity of an orthotropic body and orthotropic shells.N. E. Zhukovskii Central Aerohydrodynamic Institute of Production Technology and Organization, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 684–690, July–August, 1973.     

Determination of the stresses in an orthotropic plate with fillets bent by forces normal to the plane of the plate

Methods based on Verkhovskii's hypothesis of nonplanar sections are used to derive equations for the stresses in an orthotropic plate with fillets bent by forces or moments whose plane of action is normal to the plane of the plate. In deriving these equations the depth of the fillets is taken into account.Gor'kii Zhdanov Polytechnic Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1112–1115, November–December, 1969.     

Effect of the rotation on a non-homogeneous infinite cylinder of orthotropic material

The present investigation is concerned with a study effect of non-homogeneous on the elastic stresses in rotating orthotropic infinite circular cylinder subjected to certain boundary conditions. Closed form stress solutions are obtained for rotating orthotropic cylinder with constant thickness for three cases: (1) a solid cylinder; (2) cylinder mounted on a circular rigid shaft; and (3) cylinder with a circular hole at the center. Analytical expressions for the components of the displacement and the stress in different cases are obtained. The effect of the rotation and non-homogeneity on the displacement and stress are studied. Numerical results are given and illustrated graphically for each case is considered. The effects rotating and non-homogeneity are discussed. Comparisons are made with the results predicted in the presence and absence of rotation.     

Calculation of contact stresses in axisymmetric underwater explosions

The problem of an underwater electrical explosion in a long layered elastoplastic cylinder is solved. The solution is obtained numerically with use of artificial viscosity. The law for energy produced by the explosion is determined experimentally and residual stresses are determined by the establishment method. Contact stress is presented as a function of explosion energy for various cylinders.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 20, pp. 106–109, 1989.     

Helical flow of an Oldroyd-B fluid due to a circular cylinder subject to time-dependent shear stresses

Exact solutions corresponding to the unsteady helical flow of an Oldroyd-B fluid due to an infinite circular cylinder subject to torsional and longitudinal time-dependent shear stresses are established using Hankel transforms. These solutions, presented under series form in terms of Bessel functions J ₀(·), J ₁(·) and J ₂(·), can be easily specialized to give the similar solutions for Maxwell, Second grade and Newtonian fluids performing the same motion. Some characteristics of the motion, as well as the influence of pertinent parameters on the velocity profiles, are underlined by graphical illustrations.     

Helical flow of an Oldroyd-B fluid due to a circular cylinder subject to time-dependent shear stresses

Exact solutions corresponding to the unsteady helical flow of an Oldroyd-B fluid due to an infinite circular cylinder subject to torsional and longitudinal time-dependent shear stresses are established using Hankel transforms. These solutions, presented under series form in terms of Bessel functions J ₀(·), J ₁(·) and J ₂(·), can be easily specialized to give the similar solutions for Maxwell, Second grade and Newtonian fluids performing the same motion. Some characteristics of the motion, as well as the influence of pertinent parameters on the velocity profiles, are underlined by graphical illustrations.     

Compression of an orthotropic prism

The formulation and mathematically correct solution of a three-dimensional boundary value problem are given. A numerical calculation is presented for a prism of Canadian spruce and the displacement and stress fields are determined.Presented at a scientific seminar on polymer mechanics held in the Mechanics-Mathematics Department of Moscow State University, February 7, 1968.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 810–815, September–October, 1968.