IX.—The Propagation of Thermal Stresses in Thin Metallic Rods

1959 ◽  
Vol 65 (2) ◽  
pp. 121-142 ◽  
Author(s):  
I. N. Sneddon
Keyword(s):  
Boundary Value Problems ◽  
Approximate Method ◽  
Finite Length ◽  
Thermal Stresses ◽  
Boundary Value ◽  
Elastic Rod ◽  
Time Dynamic ◽  
Simple Waves ◽  
Set Up

SynopsisIf the temperature in an elastic rod is not uniform and if it varies with time, dynamic thermal stresses are set up in the rod. This paper is concerned with the calculation of the distribution of temperature and stress in an elastic rod when its ends are subjected to mechanical or thermal disturbances. Simple waves in an infinite rod are first discussed and then boundary value problems for semi-infinite rods and rods of finite length. The paper concludes with an account of an approximate method of solving the equations of thermoelasticity.

Some Mixed Boundary-Value Problems of the Semi-Infinite Strip

1957 ◽  
Vol 24 (2) ◽  
pp. 261-268
Author(s):  
G. Horvay ◽  
J. S. Born
Keyword(s):  
Shear Stress ◽  
Boundary Value Problems ◽  
Approximate Method ◽  
Normal Stress ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Normal Displacement ◽  
Infinite Strip ◽  
Elastic Strip ◽  
Variational Solutions

Abstract Rigorous and approximate (variational) solutions are given for the semi-infinite elastic strip, traction-free along the long edges, when the short edge is subjected (a) to a quadratic shear displacement, zero normal stress, (b) to a cubic normal displacement, zero shear stress. The approximate method of self-equilibrating functions is extended.

Certain two-dimensional problems of stress distribution in wedge-shaped elastic solids under discontinuous load

1965 ◽  
Vol 61 (4) ◽  
pp. 945-954 ◽  
Author(s):  
R. P. Srivastav ◽  
Prem Narain
Keyword(s):  
Integral Equation ◽  
Stress Field ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Wedge Angle ◽  
Theory Of Elasticity ◽  
Polar Coordinates ◽  
Dual Integral Equations ◽  
Fredholm Equations ◽  
Set Up

In this paper we consider the problem of distribution of stress in an infinite wedge of homogeneous elastic isotropic solid under the usual assumptions pertaining to plane strain in classical (infinitesimal) theory of elasticity. The wedge is supposed to occupy the region 0 ≤ ρ ≤ ∞, − α ≤ θ ≤ α (in plane polar coordinates) where the pole is taken on the apex of the wedge with the line bisecting the wedge angle as the initial line. We report here the investigations of two types of stress fields: (i) the stress field which is set up by the application of known pressure to inner surfaces of a crack situated on the bisector of the wedge angle, and (ii) the stress field generated by the indentation of the plane faces of the wedge by the rigid punch. The corresponding boundary-value problems are shown to be equivalent to the problem of solving dual integral equations involving inverse Mellin-transforms. Similar equations have been discussed by Srivastav ((l)) in a recent paper. The method of (1) is easily modified to reduce the dual equations to single Fredholm equations of the second kind which are best solved numerically. The boundary-value problems discussed here are of the mixed type and appear to have been considered only recently by Matczynski ((2)) who has investigated a contact problem. He identifies the problem with a Wiener-Hopf integral equation and solves the integral equation approximately using a method due to Koiter ((3)). The method presented here seems to have the advantage that it requires no elaborate tools of analysis which are necessary for resolving the problem of Wiener-Hopf and numerical results may be obtained comparatively easily.

Sign in / Sign up

Export Citation Format

Share Document