김경종
94 lines
3.9 KiB
Markdown
94 lines
3.9 KiB
Markdown
---
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type: concept
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title: "Reduced Integration and Hourglass Control"
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complexity: advanced
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domain: computational-mechanics
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created: 2026-05-29
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updated: 2026-06-01
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address: c-000057
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aliases:
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- reduced integration
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- hourglass control
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- under-integration
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tags:
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- concept
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- finite-element-method
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- numerical-integration
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- locking
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status: current
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related:
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- "[[Abaqus Theory Manual]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]]"
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- "[[Abaqus Element Library]]"
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- "[[Abaqus Element Selection and Formulation]]"
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- "[[Abaqus Continuum Element Families]]"
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- "[[Isoparametric Finite Elements]]"
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- "[[Solid Element Stiffness Integration]]"
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- "[[Shell Locking Phenomenon]]"
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- "[[Hybrid Incompressible Elements]]"
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sources:
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- "[[Abaqus Theory Manual]]"
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- "[[Abaqus-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]]"
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source_refs:
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- source: "[[Abaqus Theory Manual]]"
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raw_path: ".raw/AbaqusTheoriesManual/"
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raw_files:
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- "AbaqusTheoriesManual_029.md"
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- "AbaqusTheoriesManual_044.md"
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- "AbaqusTheoriesManual_045.md"
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- "AbaqusTheoriesManual_027.md"
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md_indices:
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- 29
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- 44
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- 45
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- 27
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match: "heuristic-heading-keyword"
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confidence: high
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- source: "[[Abaqus-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]]"
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raw_path: ".raw/AbaqusAnalysisUserGuide4/"
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raw_files:
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- "AbaqusAnalysisUserGuide4_047.md"
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- "AbaqusAnalysisUserGuide4_025.md"
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- "AbaqusAnalysisUserGuide4_010.md"
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- "AbaqusAnalysisUserGuide4_008.md"
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md_indices:
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- 47
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- 25
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- 10
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- 8
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match: "heuristic-heading-keyword"
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confidence: high
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---
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# Reduced Integration and Hourglass Control
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## Definition
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Reduced integration evaluates an element with fewer integration points than full quadrature. Hourglass control adds stabilization to suppress spurious zero-energy deformation modes that reduced integration can introduce.
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## How It Works
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Reduced integration can reduce computational cost and, in some element families, improve accuracy at special strain-sampling locations. It can also soften elements that otherwise become overly stiff in bending-dominated or nearly incompressible situations.
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The risk is rank deficiency: some displacement patterns can produce little or no strain energy at the reduced integration points. These patterns appear as hourglass or zero-energy modes. Abaqus controls them by adding artificial stiffness or related stabilization terms so the element remains usable without losing the intended benefits of reduced quadrature.
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[[Abaqus-Analysis-User-s-Guide-Volume-IV|Volume IV]] shows how this becomes a naming and selection issue. Many Abaqus element names use `R` to mark reduced integration, such as `C3D8R` and `S4R`, and the element family determines which hourglass-control assumptions are appropriate.
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## Why It Matters
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Reduced integration is not just a cheaper quadrature rule. It changes the numerical behavior of the element and must be judged together with element topology, mesh distortion, material behavior, contact, and expected deformation mode.
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## Connections
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- [[Isoparametric Finite Elements]] supplies the quadrature framework.
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- [[Abaqus Element Library]] places reduced integration among full, selective, and hybrid element choices.
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- [[Abaqus Element Selection and Formulation]] connects reduced integration to element suffixes and analysis-product availability.
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- [[Abaqus Continuum Element Families]] shows where reduced-integration solid and coupled-field variants appear.
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- [[Shell Locking Phenomenon]] is one reason under-integration or assumed-strain methods are introduced.
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- [[Hybrid Incompressible Elements]] is a more explicit mixed alternative for incompressible response.
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## Sources
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- [[Abaqus Theory Manual]]
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- [[Abaqus-Analysis-User-s-Guide-Volume-IV|Abaqus Analysis User's Guide Volume IV]]
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