김경종
69 lines
2.7 KiB
Markdown
69 lines
2.7 KiB
Markdown
---
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type: concept
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title: "Axisymmetric Finite Elements"
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complexity: intermediate
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domain: computational-mechanics
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created: 2026-05-29
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updated: 2026-05-29
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address: c-000067
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aliases:
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- axisymmetric element
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- triangular torus element
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- body of revolution finite element
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tags:
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- concept
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- finite-element-method
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- continuum-elements
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- axisymmetric-analysis
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status: current
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related:
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- "[[Plane Stress and Plane Strain Elements]]"
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- "[[Isoparametric Finite Elements]]"
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- "[[Finite Element Thermal Stress Analysis]]"
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- "[[Finite Element Modeling and Convergence Checks]]"
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sources:
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- "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
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source_refs:
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- source: "[[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]"
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raw_path: ".raw/AFirstCourseInTheFiniteElementMethod/"
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raw_files:
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- "AFirstCourseInTheFiniteElementMethod_044.md"
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- "AFirstCourseInTheFiniteElementMethod_043.md"
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- "AFirstCourseInTheFiniteElementMethod_045.md"
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- "AFirstCourseInTheFiniteElementMethod_082.md"
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md_indices:
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- 44
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- 43
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- 45
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- 82
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match: "heuristic-heading-keyword"
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confidence: high
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---
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# Axisymmetric Finite Elements
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## Definition
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Axisymmetric finite elements model bodies of revolution when the geometry, material behavior, boundary conditions, and loading are symmetric about an axis.
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## How They Work
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The simplest axisymmetric element is a triangular ring, or triangular torus, formed by rotating a triangular cross section around the axis of symmetry. The unknowns are radial and axial displacements in the cross section, but the strain state includes radial, axial, circumferential, and shear components.
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The stiffness and load terms include the circumferential integration effect, commonly appearing through a radius-weighted area integral. This lets a two-dimensional mesh represent a three-dimensional body of revolution such as a thick pressure vessel, circular footing problem, or axisymmetric solid.
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## Why It Matters
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Axisymmetric elements are efficient when their assumptions hold. They avoid the cost of a full 3D mesh while retaining the hoop strain and hoop stress behavior that plane stress or plane strain idealizations would miss.
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## Connections
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- [[Plane Stress and Plane Strain Elements]] are also 2D idealizations, but they do not represent circumferential strain.
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- [[Finite Element Thermal Stress Analysis]] includes an axisymmetric thermal strain case.
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- [[Isoparametric Finite Elements]] generalizes the same cross-section mapping idea to higher-order or quadrilateral axisymmetric elements.
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## Sources
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- [[A-First-Course-in-the-Finite-Element-Method|A First Course in the Finite Element Method]]
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