김경종
55 lines
2.2 KiB
Markdown
55 lines
2.2 KiB
Markdown
---
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type: concept
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title: "Uniform Optimal Convergence"
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complexity: advanced
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domain: computational-mechanics
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aliases:
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- uniform optimal convergence
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- thickness-uniform convergence
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- optimal shell convergence
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created: 2026-05-28
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updated: 2026-05-28
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address: c-000046
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tags:
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- concept
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- finite-element-method
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- shell-elements
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- convergence
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status: current
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related:
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- "[[On-the-Finite-Element-Analysis-of-Shell-Structures]]"
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- "[[Shell Locking Phenomenon]]"
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- "[[Shell Structure Asymptotic Behavior]]"
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- "[[Shell Element Benchmark Testing]]"
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- "[[Mixed Finite Element Formulations]]"
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sources:
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- "[[On-the-Finite-Element-Analysis-of-Shell-Structures]]"
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---
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# Uniform Optimal Convergence
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## Definition
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Uniform optimal convergence means that a shell finite element converges at its expected approximation rate and that this behavior remains stable as shell thickness changes and as the problem moves between membrane, bending, and mixed-dominated regimes.
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## How It Works
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For shell elements, optimal convergence alone is not enough if it holds only for one fixed thickness or one convenient benchmark. The paper frames the ideal shell element as one that keeps optimal convergence uniformly across shell shapes, boundary conditions, loads, and asymptotic behavior classes.
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For mixed shell formulations, this requirement is closely related to the inf-sup condition. For practical benchmarking, the source uses convergence curves and S-norm style global error measurement rather than only point displacement comparisons.
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## Why It Matters
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A shell element can pass simple checks and still fail in thin-shell bending because of locking. Uniform optimal convergence is the stronger standard that separates a generally reliable shell element from one that only works in selected examples.
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## Connections
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- [[Shell Locking Phenomenon]] is the failure mode this criterion detects.
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- [[Shell Element Benchmark Testing]] describes the evidence needed to evaluate the criterion.
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- [[Mixed Finite Element Formulations]] provides the stability context, including inf-sup reasoning.
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- [[MITC4 Shell Element]] is a practical element family whose value is judged by convergence under locking-prone problems.
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## Sources
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- [[On-the-Finite-Element-Analysis-of-Shell-Structures]]
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