A Non-Convex Partition of Unity and Stress Analysis of a Cracked Elastic Medium
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 ext...
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/9574341 |
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| author | Won-Tak Hong |
| author_facet | Won-Tak Hong |
| author_sort | Won-Tak Hong |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b9ab5f3850ba4f69844383ce87f39ea3 |
| institution | DOAJ |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-b9ab5f3850ba4f69844383ce87f39ea32025-08-20T03:23:15ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/95743419574341A Non-Convex Partition of Unity and Stress Analysis of a Cracked Elastic MediumWon-Tak Hong0Department of Mathematics & Finance, Gachon University, 1342 Seongnamdaero, Sujeong-gu, Seongnam-si, Gyeonggi-do, Republic of KoreaA 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.http://dx.doi.org/10.1155/2017/9574341 |
| spellingShingle | Won-Tak Hong A Non-Convex Partition of Unity and Stress Analysis of a Cracked Elastic Medium Advances in Mathematical Physics |
| title | A Non-Convex Partition of Unity and Stress Analysis of a Cracked Elastic Medium |
| title_full | A Non-Convex Partition of Unity and Stress Analysis of a Cracked Elastic Medium |
| title_fullStr | A Non-Convex Partition of Unity and Stress Analysis of a Cracked Elastic Medium |
| title_full_unstemmed | A Non-Convex Partition of Unity and Stress Analysis of a Cracked Elastic Medium |
| title_short | A Non-Convex Partition of Unity and Stress Analysis of a Cracked Elastic Medium |
| title_sort | non convex partition of unity and stress analysis of a cracked elastic medium |
| url | http://dx.doi.org/10.1155/2017/9574341 |
| work_keys_str_mv | AT wontakhong anonconvexpartitionofunityandstressanalysisofacrackedelasticmedium AT wontakhong nonconvexpartitionofunityandstressanalysisofacrackedelasticmedium |