김경종
107 lines
4.7 KiB
Markdown
107 lines
4.7 KiB
Markdown
---
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type: concept
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title: "Assumed Transverse Shear Strain Interpolation"
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complexity: advanced
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domain: computational-mechanics
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aliases:
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- assumed shear strain interpolation
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- transverse shear tying
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- shear locking remedy
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created: 2026-05-28
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updated: 2026-05-28
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address: c-000020
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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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- locking
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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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- "[[Uniform Optimal Convergence]]"
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- "[[A Continuum Mechanics Based Four-Node Shell]]"
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- "[[Four-Node-Quadrilateral-Shell-Element-MITC4]]"
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- "[[MITC Study Notes]]"
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- "[[MITC4 Shell Element]]"
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- "[[Continuum Mechanics Based Four-Node Shell Element]]"
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- "[[Mixed Finite Element Formulations]]"
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- "[[Displacement-Based Finite Element Formulation]]"
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- "[[Isoparametric Finite Elements]]"
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sources:
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- "[[On-the-Finite-Element-Analysis-of-Shell-Structures]]"
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- "[[A Continuum Mechanics Based Four-Node Shell]]"
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- "[[Four-Node-Quadrilateral-Shell-Element-MITC4]]"
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- "[[MITC Study Notes]]"
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source_refs:
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- source: "[[On-the-Finite-Element-Analysis-of-Shell-Structures]]"
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raw_path: ".raw/쉘구조물의유한요소해석에대하여/"
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raw_files:
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- "쉘구조물의유한요소해석에대하여_001.md"
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- "쉘구조물의유한요소해석에대하여_002.md"
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md_indices:
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- 1
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- 2
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match: "heuristic-heading-keyword"
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confidence: low
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- source: "[[A Continuum Mechanics Based Four-Node Shell]]"
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raw_path: ".raw/AContinuumMechanicsBasedFourNodeShell/"
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raw_files:
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- "AContinuumMechanicsBasedFourNodeShell_001.md"
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md_indices:
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- 1
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match: "heuristic-heading-keyword"
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confidence: medium
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- source: "[[Four-Node-Quadrilateral-Shell-Element-MITC4]]"
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raw_path: ".raw/FourNodeQuadrilateralShellElementMITC4/"
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raw_files:
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- "FourNodeQuadrilateralShellElementMITC4_001.md"
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md_indices:
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- 1
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match: "heuristic-heading-keyword"
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confidence: medium
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- source: "[[MITC Study Notes]]"
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raw_path: ".raw/MITC공부/"
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raw_files:
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- "MITC공부_001.md"
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md_indices:
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- 1
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match: "heuristic-heading-keyword"
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confidence: low
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---
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# Assumed Transverse Shear Strain Interpolation
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## Definition
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Assumed transverse shear strain interpolation replaces the shear strains implied directly by the displacement interpolation with a separately interpolated shear strain field chosen to avoid artificial stiffness in shell bending.
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## How It Works
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In the four-node shell paper, the transverse shear strain components are interpolated in convected coordinates from selected tying locations rather than taken directly from the standard displacement field everywhere in the element. This lets the element approximate the near-zero transverse shear strains required by thin-shell bending while preserving a low-order quadrilateral element.
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The MITC4 source presents the same practical idea under the Mixed Interpolation of Tensorial Components name. Its assumed transverse shear strains are computed from values at edge-midpoint tying locations and then transformed back to Cartesian strain components.
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The MITC study notes keep this as the motivating issue: direct shell interpolation locks in thin shells, so the transverse shear strain field must be treated separately from the rest of the displacement-derived strain field.
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The Korean shell FE review generalizes the same idea: reducing selected strain interpolation can relieve locking, but the assumed field must still satisfy consistency and avoid spurious zero-energy behavior.
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## Why It Matters
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Standard displacement interpolation can cause shear locking: the element cannot represent the bending state without introducing parasitic transverse shear strain, so the computed shell becomes too stiff as thickness decreases. The assumed shear strain field is a targeted correction that keeps the four-node shell usable for thin shells without abandoning the economical element topology.
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## Connections
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- [[Continuum Mechanics Based Four-Node Shell Element]] uses this technique as a core formulation choice.
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- [[MITC4 Shell Element]] names the same locking remedy as mixed interpolation of tensorial components.
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- [[Mixed Finite Element Formulations]] provides a broader context for introducing extra or altered fields to satisfy constraints.
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- [[Displacement-Based Finite Element Formulation]] explains the displacement-only path that can lock.
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- [[Isoparametric Finite Elements]] explains the low-order quadrilateral mapping context.
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## Sources
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- [[A Continuum Mechanics Based Four-Node Shell]]
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- [[Four-Node-Quadrilateral-Shell-Element-MITC4]]
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- [[MITC Study Notes]]
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- [[On-the-Finite-Element-Analysis-of-Shell-Structures]]
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