Rozkład naprężeń cieplnych w belce z płaską szczeliną
Distribution of thermal stresses in a beam with a plane crack
The stress distribution in the vicinity of a Griffith type of crack situated in a rectangular beam of isotropic homogeneous elastic material occupying the region –δ ≤ x ≤ δ, –π ≤ y ≤ π –∞ ≤ z ≤ ∞ has been discussed, when the beam is subject to an internal pressure in the crack and a thermal field, under the usual assumptions of infinitesimal theory of elasticity appropriate to the plane strain. Use is made of the technique developed by Srivastav [1] for solving dual series relations.
References
R.P. Srivastav, Dual series relations, III, Proc. Roy. Soc. Edin., 1964, A 66, 173-184.
C.E. Inglis, Stresses in a plate due to pressure of cracks and sharp corners, Trans. Inst. Noval Arch., 1913, 55, 219.
A.A Griffith, The phenomena of rupture and flow in solids, Phil. Trans., 1921, A 221, 163.
I.N. Sneddon, H.A. Elliot, The opening of the crack under internal pressure, Quart. App. Math., 1946, 4, 262.
H.M. Westergaard, Bearing pressures and cracks, J. App. Mech., 1939, A-49.
A.H. England, A.E. Green, Some two dimensional punch and crack problems in classical elasticity, Proc. Camb. Phil. Soc., 1963, 59, 489-500.
W.T. Korraa, An infinite row of collinear cracks in an infinite elastic sheet, Ing. Arch., 1959, 28, 168-172.
R.J. Tarr, Some problems in the mathematical theory of elasticity, Ph. D. Thesis, 1962, Glasgow University.
I.N. Sneddon, R.P. Srivastav, The stress in the vicinity of an infinite row of collinear cracks in an elastic body, A 67, 1965, 39-49.
L.N. Sneddon, Z. Olesiak, The distribution of stress in an infinite elastic solid containing a penny shaped crack, Arch. Prat. Mech. and Anal., 4, 1960, 3, 238-254.
P. Narain, R.P. Srivastav, A two-dimensional indentation problems of a heated punch, Proc. Eighth Congress, Theoretical and Applied Mechanics, Delhi 1963, 1-10.