김경종
52 lines
2.1 KiB
Markdown
52 lines
2.1 KiB
Markdown
---
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type: concept
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title: "Geometric Stiffness Matrix"
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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-000039
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aliases:
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- initial stress stiffness matrix
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- stress stiffness matrix
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- 기하 강성 행렬
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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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- buckling
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status: current
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related:
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- "[[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method]]"
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- "[[Dynamic Buckling Analysis]]"
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- "[[Green-Lagrange Strain Linearization]]"
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- "[[Total Lagrangian Shell Formulation]]"
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- "[[Finite Element Eigenproblem Solvers]]"
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sources:
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- "[[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method]]"
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---
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# Geometric Stiffness Matrix
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## Definition
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The geometric stiffness matrix is a stiffness contribution that arises from the current stress state and geometry of a structure, and is essential in buckling and geometric nonlinear analysis.
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## How It Works
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In the dynamic buckling thesis, the geometric stiffness matrix is derived through a [[Total Lagrangian Shell Formulation]] for the [[MITC4 Shell Element]]. The nonlinear strain terms are separated so that material stiffness and initial-stress stiffness contributions can be assembled. Static buckling then appears as an eigenvalue problem involving structural stiffness and geometric stiffness, while dynamic buckling also involves mass and time-varying load parameters.
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## Why It Matters
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Without geometric stiffness, a finite element model may predict ordinary elastic response but cannot capture the loss of stability associated with compressive pre-stress. It is the bridge from stress state to buckling load, mode shape, and dynamic instability boundary.
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## Connections
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- [[Green-Lagrange Strain Linearization]] explains how nonlinear strain terms feed tangent construction.
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- [[Finite Element Eigenproblem Solvers]] are needed once stiffness and geometric stiffness form a buckling eigenproblem.
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- [[Dynamic Buckling Analysis]] uses separate geometric stiffness terms for static and dynamic load components.
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## Sources
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- [[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method]]
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