The effects of dynamical treatment of thermal stresses on a circular region due to continuous point heat source

The investigation referring to the effects of inertia term on the plane transient thermal stress problems are treated for a solid circular cylinder under a continuous point heat source.     

Thermal deformation in a thin circular plate due to a partially distributed heat supply

In this paper, we develop an integral transform to determine temperature distribution in a thin circular plate, subjected to a partially distributed and axisymmetric heat supply on the curved surface, and study the thermal deformation. The results, obtained in series form in terms of Bessel’s functions, are illustrated numerically.     

Thermal stresses in a viscoelastic trimaterial with a combination of a point heat source and a point heat sink

A general solution for a thermoviscoelastic trimaterial combined with a point heat source and a point heat sink is presented in this work. Based on the method of analytic continuation associated with the alternation technique, the solutions to the heat-conduction and thermoelastic problems for three dissimilar, sandwiched media are derived. A rapidly convergent series solution for both the temperature and stress field, expressed in terms of an explicit general term of the corresponding homogeneous potential, is obtained in an elegant form. The hereditary integral in conjunction with the Kelvin–Maxwell model is applied to simulate the thermoviscoelastic properties, while a thermorheologically simple material is considered. Based on the correspondence principle, the Laplace transformed thermoviscoelastic solution is directly determined from the corresponding thermoelastic one. The real-time solution can then be solved numerically by taking the inverse Laplace transform. A typical example concerning the interfacial stresses generated from a combined arrangement of a heat source and sink are discussed in detail. The corresponding thin-film problem is also discussed.     

The temperature field in a body bounded by conical surfaces due to an instantaneous annular heat source

The authors investigate the influence of the internal cavity and apex angle of a cone on the temperature field due to an instantaneous annular source.     

Thermal stresses in a shrink fit due to an inhomogeneous temperature distribution

Summary Based on Tresca's yield condition and its associated flow rule, a semianalytical method is presented for the calculation of thermal stresses due to steady-state thermal loading in an assembled shrink fit. The calculation is evaluated assuming plane stress conditions, linear elastic-perfectly plastic materials, and linearly temperature dependent yield stresses. Depending on the temperature gradient, different combinations of pure elastic and plastic zones arise in the shaft and in the hub.     

Temperature stresses due to a heat source located on one side of a straight wedge

A heat source acts on one side of a straight wedge with adiabatic boundaries. The temperature stresses are determined in terms of the displacement potential and Airy stress function.     

Temperature stresses in a circular plate with a central crack induced by a heat source

L'viv Polytechnic Institute, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No. 2, pp. 125–127, March–April, 1994.     

Interaction between a point heat source and a nonuniformly coated circular inclusion

This paper investigates the interaction between a point heat source and a nonuniformly coated circular inclusion under plane deformation. Based on the complex variable theory and conformal mapping in conjunction with the analytical continuation method, the general expressions of the temperature, displacements, and stresses for three dissimilar media are derived explicitly in a series form. Numerical results are provided for some particular examples to investigate the effect of material combinations on the interfacial stresses. The derived analytical solution can also be used as a fundamental solution for the boundary element method as well as for other physical models, including welding and cutting.     

Plane strain deformation in an orthotropic micropolar thermoelastic solid with a heat source

The problem of plane strain deformation in an orthotropic micropolar generalized thermoelastic half-space subjected to an arbitrary point heat source is solved. Closed-form solutions for spatial distributions of displacements, stresses, and temperature are derived by using the Fourier transform. A numerical inversion technique has been applied to obtain the solution in the physical domain. Numerical results are obtained and presented graphically along with a comparison of the ones for concentrated and distributed, as well as mechanical and thermal, sources.     

Transient thermal stresses in a transversely isotropic finite circular cylinder due to an arbitrary internal heat-generation

The transient thermal stresses in a transversely isotropic, finite, solid, circular cylinder resulting from a unsteady-state, axisymmetrical temperature field are examined. A general method of solution based upon a set of stress functions is presented for the case of an arbitrary internal heat-generation. The temperature field is exactly determined by combined use of finite Fourier-cosine and finite Hankel transforms. Numerical calculations are carried out for various cases of the thermal and elastic anisotropies of the materials.     

Local heating of an anisotropic body by a circular heat source

The solution and analysis of the two-dimensional nonstationary heat-conduction problem are presented for an anisotropic (orthotropic) body heated by a circular heat source.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 828-835, May, 1988.     

Analytical solution for the singular stress distribution due to V-notch in an orthotropic plate material

On the basis of general solutions of two-dimensional linear elasticity, displacement and singular stress fields near the singular point in orthotropic materials are derived in closed form expressions. According to the presented expressions, analysis formulas of displacement and singular stress fields near the tip of a V-notch under the symmetric and the anti-symmetric modes are obtained subsequently. The open literatures devoted to developing stress singularity near the tip of the V-notch in anisotropic or orthotropic materials. In this study, however, not only direct eigenequations were derived, but also the explicit solutions of displacement and singular stress fields were obtained. At the end, the correctness of the formulas of the singular stress field near the tip of the V-notch has been verified by FEM analysis.     

A point heat source on the surface of a semi-infinite transversely isotropic electro-magneto-thermo-elastic material

We use the compact mono-harmonic general solutions of transversely isotropic electro-magneto-thermo-elastic material to construct the three-dimensional Green’s function for a steady point heat source on the surface of a semi-infinite transversely isotropic electro-magneto-thermo-elastic material by five newly introduced mono-harmonic functions. All components of coupled field are expressed in terms of elementary functions and are convenient to use. Numerical results are given graphically by contours.     

Numerical investigation of free convection from an instantaneous heat source in viscous fluid

A formulation is given, as well as results of the numerical solution, of the self-consistent problem of free convection from an instantaneous heat source in a viscous incompressible fluid.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 4, pp. 700–704, October, 1977.     

Thermal stresses in an elastic solid weakened by two coplanar circular cracks

Some linear thermoelastic problems are studied for the thermal stress and displacement fields in an infinite elastic medium weakened by cracks occupying the space interior to two coplanar circular regions with equal radii. The thermal stresses are caused by the uniform heating or heat flow disturbed by the presence of the coplanar cracks. The problem is reduced to the determination of the solution of infinite sets of Fredholm integral equations. Attention is given to the case when the plane occupying the space external to the cracks is insulated from uniform heat flow. The sets of integral equations are solved iteratively by assuming the spacing between the center of the cracks is large as compared to the radii. Physical quantity of interest such as crack-opening displacement is investigated.     

Enlargement of a circular hole in a disc of plastically compressible material

A semi-analytic solution for the elastic/plastic distribution stress and strain in a thin annular disc subject to pressure over its inner radius is presented. It is assumed that a pressure-dependent yield criterion and its associated flow rule are valid in the plastic zone. Thus, the material is plastically compressible, which is a distinguished feature of the solution. Also, in contrast to most studies on elastic/plastic deformation of thin plates and discs under plane stress conditions, the flow theory of plasticity is adopted in conjunction with a smooth yield surface. Numerical methods are only necessary to evaluate ordinary integrals and to solve simple transcendental equations. It is shown that the stress path is not proportional and, therefore, the application of deformation theories of plasticity widely used to calculate the distribution of stresses and strains in thin plates and discs is not justified.     

Temperature-rate-dependent thermoelastic interactions due to a line heat source

Summary Temperature-rate-dependent thermoelasticity theory is employed to study thermoelastic interactions due to a continuous line source in a linear, homogeneous and isotropic unbounded solid. Laplace and Hankel transforms are employed to solve the problem. Explicit expressions for temperature and stress fields are obtained for small time approximation. Numerical results for a copper material are presented.     

Response of orthotropic micropolar elastic medium due to time harmonic source

The present paper is concerned with the plane strain problem in homogeneous micropolar orthotropic elastic solids. The disturbance due to time harmonic concentrated source is investigated by employing eigen-value approach. The integral transforms have been inverted by using a numerical technique to obtain the component of displacement, force stress and couple stress in the physical domain. The results of these quantities are given and illustrated graphically.