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A Non-Convex Partition of Unity and Stress Analysis of a Cracked Elastic Medium
Author
Source
Advances in Mathematical Physics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-02-07
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
A stress analysis using a mesh-free method on a cracked elastic medium needs a partition of unity for a non-convex domain whether it is defined explicitly or implicitly.
Constructing such partition of unity is a nontrivial task when we choose to create a partition of unity explicitly.
We further extend the idea of the almost everywhere partition of unity and apply it to linear elasticity problem.
We use a special mapping to build a partition of unity on a non-convex domain.
The partition of unity that we use has a unique feature: the mapped partition of unity has a curved shape in the physical coordinate system.
This novel feature is especially useful when the enrichment function has polar form, f(r,θ)=rλg(θ), because we can partition the physical domain in radial and angular directions to perform a highly accurate numerical integration to deal with edge-cracked singularity.
The numerical test shows that we obtain a highly accurate result without refining the background mesh.
American Psychological Association (APA)
Hong, Won-Tak. 2017. A Non-Convex Partition of Unity and Stress Analysis of a Cracked Elastic Medium. Advances in Mathematical Physics،Vol. 2017, no. 2017, pp.1-9.
https://search.emarefa.net/detail/BIM-1123352
Modern Language Association (MLA)
Hong, Won-Tak. A Non-Convex Partition of Unity and Stress Analysis of a Cracked Elastic Medium. Advances in Mathematical Physics No. 2017 (2017), pp.1-9.
https://search.emarefa.net/detail/BIM-1123352
American Medical Association (AMA)
Hong, Won-Tak. A Non-Convex Partition of Unity and Stress Analysis of a Cracked Elastic Medium. Advances in Mathematical Physics. 2017. Vol. 2017, no. 2017, pp.1-9.
https://search.emarefa.net/detail/BIM-1123352
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1123352