김경종
62 lines
2.2 KiB
Markdown
62 lines
2.2 KiB
Markdown
---
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type: concept
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title: "Green-Lagrange Strain Linearization"
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complexity: advanced
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domain: computational-mechanics
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created: 2026-05-28
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updated: 2026-05-28
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address: c-000030
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aliases:
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- Green Lagrange strain expansion
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- nonlinear strain linearization
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- total Lagrangian tangent strain terms
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tags:
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- concept
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- finite-element-method
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- nonlinear-analysis
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- shell-elements
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status: current
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related:
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- "[[MITC Study Notes]]"
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- "[[Total Lagrangian Shell Formulation]]"
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- "[[Nonlinear Finite Element Analysis]]"
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- "[[MITC Shell Kinematics]]"
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sources:
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- "[[MITC Study Notes]]"
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source_refs:
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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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- "MITC공부_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: medium
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---
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# Green-Lagrange Strain Linearization
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## Definition
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Green-Lagrange strain linearization separates the nonlinear strain measure into terms that can be used to form residual forces and tangent stiffness contributions during incremental nonlinear finite element analysis.
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## How It Works
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The study notes use Green-Lagrange strain with second Piola-Kirchhoff stress in a reference-configuration virtual work statement. The strain expression is expanded with respect to the current displacement state and an incremental displacement. This separates terms associated with the existing strain state, terms linear in the increment, and terms nonlinear in the increment. The variation of the strain then produces internal force and tangent terms for Newton-Raphson iteration.
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## Why It Matters
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In nonlinear shell analysis, the element stiffness is not a fixed matrix. The tangent must account for both material response and geometry-dependent stress terms. Linearizing the Green-Lagrange strain is the step that turns the nonlinear virtual work equation into a solvable incremental system.
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## Connections
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- [[Total Lagrangian Shell Formulation]] provides the reference configuration and stress/strain pair.
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- [[MITC Shell Kinematics]] defines the displacement and director variables being linearized.
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- [[Nonlinear Finite Element Analysis]] supplies the Newton iteration context.
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## Sources
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- [[MITC Study Notes]]
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