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Complete Plane Strain Problem of a Nonhomogeneous Elastic Body with a Doubly-Periodic Set of Cracks.
- Source :
-
ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik . Jun2001, Vol. 81 Issue 6, p377-391. 15p. 1 Diagram. - Publication Year :
- 2001
-
Abstract
- In this paper, we wish to use complex potential methods to solve the fundamental complete plane strain (CPS) problems of a three-dimensional nonhomogeneous elastic body with a doubly-periodic set of cracks in the x1, x2 plane. We resolve the complete plane strain state, which is a special three-dimensional elastic system, into two linearly independent two-dimensional (plane) elastic systems by the superposition principle of force. Based on a suitable modification of Cauchy-type integrals, which is defined by the replacement of the Cauchy kernel 1/(t — z) by the Weierstrass zeta function ζ(t — z), the general representation for the solution is constructed, under some general restrictions the boundary value problem is reduced to a normal type singular integral equation with a Weierstrass zeta kernel, and the existence of an essentially unique solution is proved. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00442267
- Volume :
- 81
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
- Publication Type :
- Academic Journal
- Accession number :
- 13349532
- Full Text :
- https://doi.org/10.1002/1521-4001(200106)81:6<377::AID-ZAMM377>3.0.CO;2-Q