The first basic problem for a notch at the apex of an infinite wedge

✍ Scribed by A. A. Khrapkov

• Book ID: 104656542
• Publisher: Springer Netherlands
• Year: 1971
• Tongue: English
• Weight: 525 KB
• Volume: 7
• Category: Article
• ISSN: 1573-2673
• DOI: 10.1007/bf00189109

✦ Synopsis

In this paper it is shown that the first basic problem of the plane theory of elasticity for an infinite triangular wedge with a notch at its apex can be reduced to a non-homogeneous Hilbert problem for the Mellin transform of a vector function made up of stress and displacement components. The possibility of solving this problem depends on the matrix factor of the non-homogeneous Hilbert problem. When certain matrix components are polynomials in the parameter of the Mellin transform, it is possible to factorize the matrix in question, and hence to obtain a solution of the problem. In this way the solutions of the basic problem for three different geometries are obtained: (a) an arbitrarily oriented notch on the boundary of a half-plane ; (b) a notch on the line of contact of an arbitrary wedge with a half-plane (c) a semi-infinite notch with an arbitrarily oriented branch. These three cases are illustrated graphically in Figs. l(a), (b), (c) respectively.

The calculation of the stress intensity factors in case (a) when the loading on the notch can be expressed by power series is considered in more detail.