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A natural approach to the introduction of finite-part integrals into crack problems of three-dimensional elasticity

โœ Scribed by N.I. Ioakimidis

Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
405 KB
Volume
16
Category
Article
ISSN
0013-7944

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โœฆ Synopsis

The classical singular integral equation for the problem of a piane crack inside an infinite isotropic elastic medium and under an arbitrary normal pressure distribution was recently modified and written without the use of the Laplace operator A or the derivatives of the unknown function, but with the use of a finite-part integral, In this paper, a second complete derivation of the same equation is made (not based on previous forms of this equation) by using a limiting procedure, which makes it clear why the finite-part integral results in this equation. It is believed that the present results ~111 be used in future for the introduction of finite-part integrals into a lot of crack problems in the theory of three-dimensional elasticity.

๐Ÿ“œ SIMILAR VOLUMES

Exact expression for a two-dimensional f
Exact expression for a two-dimensional finite-part integral appearing during the numerical solution of crack problems in three-dimensional elasticity
โœ Ioakimidis, N. I. ๐Ÿ“‚ Article ๐Ÿ“… 1985 ๐Ÿ› Wiley (John Wiley & Sons) ๐ŸŒ English โš– 381 KB ๐Ÿ‘ 1 views

An exact expression is derived for the finite-part integral #,r-'fdS over a triangular domain S . where r denotes the distance of the points of the triangle from one of its vertices and f is a linear function of the Cartesian co-ordinates. The more general case where r denotes the distance of the po