김경종
57 lines
2.2 KiB
Markdown
57 lines
2.2 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: 2026-05-29
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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 Element Library]]"
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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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---
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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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## 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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- [[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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