zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Wave propagation in cracked elastic slabs and half-space domains-TBEM and MFS approaches. (English) Zbl 1195.74090

Summary: In this paper, the traction boundary element method (TBEM) and the method of fundamental solutions (MFS), formulated in the frequency domain, are used to evaluate the 3D scattered wave field generated by 2D empty cracks embedded in an elastic slab and a half-space. Both models overcome the thin-body difficulty posed when the classical BEM is applied.

The crack exhibits arbitrary cross section geometry and null thickness. In neither model are the horizontal formation surfaces discretized, since appropriate fundamental solutions are used to take them into consideration.

The TBEM models the crack as a single line. The singular and hypersingular integrals that arise during the TBEM model’s implementation are computed analytically, which overcomes one of the drawbacks of this formulation. The results provided by the proposed TBEM model are verified against responses provided by the classical BEM models derived for the case of an empty cylindrical circular cavity.

The MFS solution is approximated in terms of a linear combination of fundamental solutions, generated by a set of virtual sources simulating the scattered field produced by the crack, using a domain decomposition technique. To avoid singularities, these fictitious sources are not placed close to the crack, and the use of an enriched function to model the displacement jumps across the crack is unnecessary.

The performances of the proposed models are compared and their limitations are shown by solving the case of a C-shaped crack embedded in an elastic slab and a half-space domain.

The applicability of these formulations is illustrated by presenting snapshots from computer animations in the time domain for an elastic slab containing an S-shaped crack, after applying an inverse Fourier transformation to the frequency domain computations.

74J25Inverse problems (waves in solid mechanics)
74S15Boundary element methods in solid mechanics
74S30Other numerical methods in solid mechanics
74R10Brittle fracture
65N80Fundamental solutions, Green’s function methods, etc. (BVP of PDE)