An approximate analysis of an internally loaded elastic plate containing an infinite row of closely spaced parallel cracks

✍ Scribed by A.P.S. Selvadurai

• Publisher: Elsevier Science
• Year: 1979
• Tongue: English
• Weight: 468 KB
• Volume: 11
• Category: Article
• ISSN: 0013-7944
• DOI: 10.1016/0013-7944(79)90005-5

✦ Synopsis

The stress transfer which occurs in an internally loaded infinite elastic plate containing an array of closely spaced parallel cracks of finite width is examined. The internal loading corresponds to a doublet of concentrated forces which act at finite distances from the cracked region. The solution presented is approximate to the extent that the state of stress in the strip regions contained between adjacent cracks is considered to be one-dimensional. Such a simplification enables the derivation of certain general results for the stress distribution in a strip region contained within internally loaded half-planes of differing elastic characteristics. These solutions are obtained by Fourier lransform methods. Attention is particularly focussed on the estimation of the stress magnification which occurs in the strip region. NOTATION b x. Y W,(Y) W,(5) G Y s(r4 d(f) PI, p2 %(Y) 4 (0 k ES r Ei(-)i: E,(A) so A. 6 f crack length crack spacing Cartesian coordinates surface displacement of the halfplane in the x-direction due lo normal surface traction Fourier cosine transform of w,(y) linear elastic shear modulus Poisson's ratio length parameter tensile traction: stress distribution in the strip region Fourier cosine transform of q(y) concentrated forces surface displacement of halfplane due lo internal load Fourier cosine transform of w,(y) one-dimensional stiffness constant elastic modulus of the strip region non-dimensional stiffness parameter location of internal loading exponential integral function modified exponential integral function stress magnification factor substitution parameters integration parameter