A Non‐Convex Partition of Unity and Stress Analysis of a Cracked Elastic Medium

Won-Tak Hong

Advances in Mathematical Physics, 2017, vol. 2017, issue 1

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) = 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.

Date: 2017
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https://doi.org/10.1155/2017/9574341

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2017:y:2017:i:1:n:9574341

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