Hypersingular integral equations and applications to porous elastic materials with periodic cracks

Michele Ciarletta; Gerardo Iovane

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 2, page 415-420
  • ISSN: 0392-4033

Abstract

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In this work a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions, is presented. The first goal of the present study is the development of an efficient analytical and direct numerical collocation method. The second one is the application of the method to the porous elastic materials when a periodic array of co-planar cracks is present. Starting from Cowin- Nunziato model and by applying Fourier integral transform the problem is reduced to some integral equations. For the plane-strain problem we operate with a direct numerical treatment of a hypersingular integral equation. We also study stress-concentration factor, and investigate its behaviour versus porosity of the material.

How to cite

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Ciarletta, Michele, and Iovane, Gerardo. "Hypersingular integral equations and applications to porous elastic materials with periodic cracks." Bollettino dell'Unione Matematica Italiana 8-B.2 (2005): 415-420. <http://eudml.org/doc/194826>.

@article{Ciarletta2005,
abstract = {In this work a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions, is presented. The first goal of the present study is the development of an efficient analytical and direct numerical collocation method. The second one is the application of the method to the porous elastic materials when a periodic array of co-planar cracks is present. Starting from Cowin- Nunziato model and by applying Fourier integral transform the problem is reduced to some integral equations. For the plane-strain problem we operate with a direct numerical treatment of a hypersingular integral equation. We also study stress-concentration factor, and investigate its behaviour versus porosity of the material.},
author = {Ciarletta, Michele, Iovane, Gerardo},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {415-420},
publisher = {Unione Matematica Italiana},
title = {Hypersingular integral equations and applications to porous elastic materials with periodic cracks},
url = {http://eudml.org/doc/194826},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Ciarletta, Michele
AU - Iovane, Gerardo
TI - Hypersingular integral equations and applications to porous elastic materials with periodic cracks
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/6//
PB - Unione Matematica Italiana
VL - 8-B
IS - 2
SP - 415
EP - 420
AB - In this work a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions, is presented. The first goal of the present study is the development of an efficient analytical and direct numerical collocation method. The second one is the application of the method to the porous elastic materials when a periodic array of co-planar cracks is present. Starting from Cowin- Nunziato model and by applying Fourier integral transform the problem is reduced to some integral equations. For the plane-strain problem we operate with a direct numerical treatment of a hypersingular integral equation. We also study stress-concentration factor, and investigate its behaviour versus porosity of the material.
LA - eng
UR - http://eudml.org/doc/194826
ER -

References

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  1. IOVANE, G. - LIFANOV, I. K. - SUMBATYAN, M. A., On direct numerical treatment of hypersingular integral equations arising in mechanics and acoustics, Acta Mechanica (accepted). Zbl1051.65130
  2. COWIN, S. C. - NUNZIATO, J. W., Linear elastic materials with voids, J. Elasticity, 13 (1983), 125-147. Zbl0523.73008
  3. SCALIA, A. - SUMBATYAN, M. A., Contact problem for porous elastic half-plane, J. Elasticity, 60 (2000), 91-102. Zbl1055.74028

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