- Two dimensional plane unbounded in three dimensional space series#
- Two dimensional plane unbounded in three dimensional space crack#
In this paper, we propose a simple method to construct accurate ABCs for peridynamic scalar wave-type problems in viscous media.
Moreover, application of Fourier and Laplace transforms, which are essential for the majority of available methods for ABCs, to nonlocal models is complicated. (ORNL), Oak Ridge, TN (United States) Sponsoring Org.: USDOE Laboratory Directed Research and Development (LDRD) Program German Research Foundation (DFG) OSTI Identifier: 1959608 Grant/Contract Number: AC05-00OR22725 470246804 Resource Type: Accepted Manuscript Journal Name: Computer Methods in Applied Mechanics and Engineering Additional Journal Information: Journal Volume: 407 Journal Issue: N/A Journal ID: ISSN 0045-7825 Publisher: Elsevier Country of Publication: United States Language: English Subject: 42 ENGINEERING peridynamics absorbing boundary conditions dynamic fracture unbounded domain elastic = ,Ĭonstruction of absorbing boundary conditions (ABCs) for nonlocal models is generally challenging, primarily due to the fact that nonlocal operators are commonly associated with volume constrained boundary conditions. Publication Date: Research Org.: Oak Ridge National Lab. Helmholtz-Zentrum Hereon (Germany) Hamburg University of Technology (Germany).(SNL-NM), Albuquerque, NM (United States)
Two dimensional plane unbounded in three dimensional space crack#
So our investigation shows that the proposed ABCs perform stably in time with an appropriate level of accuracy even in problems characterized by highly-dispersive propagating waves, including crack propagation in semi-unbounded brittle solids. We scrutinize the performance of the proposed ABCs through several examples. At the discrete level, the modes satisfy the same numerical dispersion relations of the near field, which makes the far-field solution compatible with that of more » the near field. They are constructed in the time and space domains and thus application of Fourier and Laplace transforms, cumbersome for nonlocal models, is not required. They are of Dirichlet-type, hence their implementation is relatively simple as no derivatives of the field variables are required.
The proposed ABCs offer appealing advantages, which facilitate their application to PD. This is accomplished through a collocation procedure at subregions (clouds) around each absorbing point.
Two dimensional plane unbounded in three dimensional space series#
The corresponding unknown coefficients of the series are found in terms of the displacement field at a layer of points adjacent to the absorbing boundary. The modes are adjusted to transmit the energy from the interior region (near field) to the exterior region (far field). This solution is made up of a finite series of plane waves, as fundamental solutions (modes), which satisfy the PD dispersion relations. We construct absorbing boundary conditions (ABCs) derived from a semi-analytical solution of the PD governing equation at the exterior region. The focus of this paper is on application of peridynamics (PD) to propagation of elastic waves in unbounded domains.
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