A Non-Convex Partition of Unity and Stress Analysis of a Cracked Elastic Medium
- Authors
- Hong, Won-Tak
- Issue Date
- 2017
- Publisher
- HINDAWI LTD
- Citation
- ADVANCES IN MATHEMATICAL PHYSICS
- Journal Title
- ADVANCES IN MATHEMATICAL PHYSICS
- URI
- https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/7436
- DOI
- 10.1155/2017/9574341
- ISSN
- 1687-9120
- Abstract
- 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, theta) = r(lambda) g(theta), 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.
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