Thermal Stresses in Transversely Isotropic Semi-Infinite Elastic Solids

1958 ◽  
Vol 25 (1) ◽  
pp. 86-88
Author(s):  
Brahmadev Sharma
Keyword(s):  
Thermal Stress ◽  
Steady State ◽  
Thermal Stresses ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Elastic Solids ◽  
Stress Problem ◽  
Method Of Solution ◽  
General Method

Abstract A general method of solution of the steady-state thermal-stress problem of a transversely isotropic semi-infinite elastic solid is given in this paper.

Thermal Stresses in an Orthotropic Elastic Semispace

1972 ◽  
Vol 39 (1) ◽  
pp. 87-90 ◽  
Author(s):  
A. Y. Ako¨z ◽  
T. R. Tauchert
Keyword(s):  
Temperature Field ◽  
Green's Functions ◽  
Thermal Stresses ◽  
Green’S Functions ◽  
Elastic Solid ◽  
Displacement Boundary ◽  
Steady State Temperature ◽  
Method Of Solution ◽  
Displacement Potentials ◽  
General Method

The thermal stresses in an orthotropic semi-infinite elastic solid subject to plane strain are investigated. A general method of solution based upon displacement potentials is presented for the case of a steady-state temperature field. Results are presented for both stress-free and zero-displacement boundary conditions. The stresses are written in terms of Green’s functions, where the Green’s functions represent stresses induced by a line source of temperature on the bounding plane.

Steady-state thermal stresses in an elastic solid containing an insulated penny-shaped crack

1975 ◽  
Vol 10 (1) ◽  
pp. 19-24 ◽  
Author(s):  
J R Barber
Keyword(s):  
Thermal Stress ◽  
Steady State ◽  
Heat Flow ◽  
Thermal Stresses ◽  
Mixed Boundary ◽  
Elastic Solid ◽  
Mixed Boundary Value Problem ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Axisymmetric Problems

A solution is given for the steady-state thermal stress and displacement field in an infinite elastic solid containing an insulated penny-shaped crack. The problem is reduced to a mixed-boundary-value problem for the half-space, making use of Green's isothermal solution for the thick elastic plate in complex harmonic potentials and a particular thermoelastic solution due to Williams. In the axisymmetric case, the complex potential reduces to the real harmonic function used by Shail in his solution for the external crack. To illustrate the use of the method in both axisymmetric and non-axisymmetric problems, complete solutionsare given for (1) a uniform heat flow and (2) a linearly varying heat flow disturbed by an insulated penny-shaped crack.

Steady-State Thermal Stresses in Wedge-Shaped Cutting Tools

1975 ◽  
Vol 97 (3) ◽  
pp. 1060-1066
Author(s):  
P. F. Thomason
Keyword(s):  
Thermal Stress ◽  
Steady State ◽  
Metal Cutting ◽  
Thermal Stresses ◽  
Heat Conduction Problem ◽  
Equivalent Stress ◽  
Cutting Tools ◽  
Thermoelastic Stress ◽  
Plastic State ◽  
Steady State Heat

Closed form expressions for the steady-state thermal stresses in a π/2 wedge, subject to constant-temperature heat sources on the rake and flank contact segments, are obtained from a conformal mapping solution to the steady-state heat conduction problem. It is shown, following a theorem of Muskhelishvili, that the only nonzero thermal stress in the plane-strain wedge is that acting normal to the wedge plane. The thermal stress solutions are superimposed on a previously published isothermal cutting-load solution, to give the complete thermoelastic stress distribution at the wedge surfaces. The thermoelastic stresses are then used to determine the distribution of the equivalent stress, and this gives an indication of the regions on a cutting tool which are likely to be in the plastic state. The results are discussed in relation to the problems of flank wear and rakeface crater wear in metal cutting tools.

scholarly journals Existence of solutions of plane traction problems for inextensible transversely isotropic elastic solids

1975 ◽  
Vol 19 (1) ◽  
pp. 40-54 ◽  
Author(s):  
L. W. Morland
Keyword(s):  
Existence Of Solutions ◽  
Lateral Displacement ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Elastic Solids ◽  
Standard Potential ◽  
Linear Elastic ◽  
Axis Of Symmetry ◽  
Uniqueness And Existence ◽  
Traction Boundary Conditions

AbstractA plane strain or plane stress configuration of an inextensible transversely isotropic linear elastic solid with the axis of symmetry in the plane, leads to a harmonic lateral displacement field in stretched coordinates. Various displacement and mixed displacement-traction boundary conditions yield standard boundary-value problems of potential theory for which uniqueness and existence of solutions are well established. However, the important case of prescribed tractions at each boundary point gives a non-standard potential problem involving linking of boundary values at opposite ends of chords parallel to the axis of material symmetry. Uniqueness and existence of solutions, within arbitrary rigid motions, are now established for the traction problem for general domains.

scholarly journals AN ANTICRACK IN A TRANSVERSELY ISOTROPIC SPACE

2013 ◽  
Vol 7 (3) ◽  
pp. 140-147
Author(s):  
Andrzej Kaczyński
Keyword(s):  
Complete Solution ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Point Of View ◽  
Newtonian Potential ◽  
Stress Jump ◽  
Elastic Symmetry ◽  
Governing System ◽  
The Fourier Transform ◽  
General Method

Abstract An absolutely rigid inclusion (anticrack) embedded in an unbound transversely isotropic elastic solid with the axis of elastic symmetry normal to the inclusion plane is considered. A general method of solving the anticrack problem is presented. Effective results have been achieved by constructing the appropriate harmonic potentials. With the use of the Fourier transform technique, the governing system of two-dimensional equations of Newtonian potential type for the stress jump functions on the opposite surfaces of the inclusion is obtained. For illustration, a complete solution to the problem of a penny-shaped anticrack under perpendicular tension at infinity is given and discussed from the point of view of material failure.

Thermal Stress in a Finitely Deformed Incompressible Elastic Medium Containing a Penny-Shaped Crack

2003 ◽  
Vol 19 (1) ◽  
pp. 143-147
Author(s):  
Y. M. Tsai
Keyword(s):  
Stress Intensity Factor ◽  
Thermal Stress ◽  
Stress Intensity ◽  
Thermal Stresses ◽  
Elastic Solid ◽  
Crack Plane ◽  
Lateral Stress ◽  
Penny Shaped Crack ◽  
Shaped Crack ◽  
Small Deformations

ABSTRACTThe thermal stress for a penny-shaped crack contained in an infinite isotropic elastic solid initially subjected to an axisymmetrical tension of any amount at infinity is investigated using the techniques of Hankel transforms and multiplying factors. The effect that the lateral normal stress has on the thermal stresses is studied on the basis of the theory of small deformations superposed on finite deformation. Symmetrical thermal loadings are applied over the crack surfaces. For the case of constant temperature over the crack surfaces, expressions for the crack shape and thermal stresses in the crack plane are obtained in closed forms. The stress intensity factor is also obtained and shown to be dependent on the lateral stress.

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