A Non-Convex Partition of Unity and Stress Analysis of a Cracked Elastic Medium. (7th February 2017)

• Record Type: Journal Article
• Authors: Hong, Won-Tak
• Other Names: Mei Ming Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2017(2017)
• Publication Date: 2017-02-07
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2017/9574341
• Languages: English
• ISSNs: 1687-9120

Abstract

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, θ ) = r λ g ( 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.