김경종
77 lines
3.3 KiB
Markdown
77 lines
3.3 KiB
Markdown
---
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type: source
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title: "MITC Study Notes"
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source_type: study-notes
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created: 2026-05-28
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updated: 2026-05-28
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address: c-000028
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aliases:
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- MITC공부
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- MITC shell element study notes
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- MITC formulation notes
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tags:
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- source
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- finite-element-method
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- shell-elements
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- mitc
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- nonlinear-analysis
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status: current
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confidence: medium
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raw_path: ".raw/MITC공부/"
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source_files:
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markdown_files: 2
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image_files: 107
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related:
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- "[[MITC4 Shell Element]]"
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- "[[MITC Shell Kinematics]]"
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- "[[Green-Lagrange Strain Linearization]]"
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- "[[Nonlinear Newmark-Beta Integration]]"
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- "[[Total Lagrangian Shell Formulation]]"
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- "[[Direct Time Integration Methods]]"
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---
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# MITC Study Notes
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## Summary
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`MITC Study Notes` is a local derivation-oriented note set on MITC shell elements. It starts with the motivation for MITC shell elements, then works through shell kinematics, finite element virtual work, Green-Lagrange strain expansion, constitutive matrix transformation, and nonlinear Newmark-beta time integration.
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The local source is a converted Markdown/image extraction: two Markdown files and 107 extracted images under `.raw/MITC공부/`.
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## Coverage Map
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| Section | Topic |
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|---|---|
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| 1 | MITC shell element motivation: continuum-degenerated shell behavior and transverse shear locking |
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| 2 | Shell kinematics: reference/current configurations, director vectors, nodal displacement and rotation variables |
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| 3 | FE formulation: virtual work, deformation gradient, Green-Lagrange strain, second Piola-Kirchhoff stress, residual and tangent terms |
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| 4 | Constitutive matrix: plane-stress shell material matrix and coordinate transformation to natural coordinates |
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| 5 | Nonlinear Newmark-beta integration: Newton-Raphson iteration, effective dynamic tangent, residual update, velocity and acceleration update |
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## Key Takeaways
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- MITC shell elements are presented as shell elements derived from a three-dimensional continuum description rather than from a specialized shell theory.
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- The practical reason for MITC is transverse shear locking control in thin shell analysis.
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- The kinematic derivation separates nodal translations from director-vector updates, which later feed the incremental displacement field.
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- The FE formulation uses Green-Lagrange strain and second Piola-Kirchhoff stress, then separates constant, linear, and nonlinear strain terms for tangent construction.
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- The dynamic section combines Newton-Raphson iteration with Newmark-beta kinematics to obtain an effective equation for displacement increments.
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## Concepts Introduced
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- [[MITC Shell Kinematics]]
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- [[Green-Lagrange Strain Linearization]]
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- [[Nonlinear Newmark-Beta Integration]]
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## Links To Existing Wiki
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- [[MITC4 Shell Element]] gives the compact element-level concept that these notes expand.
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- [[Assumed Transverse Shear Strain Interpolation]] is the locking remedy motivating the MITC approach.
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- [[Total Lagrangian Shell Formulation]] gives the nonlinear shell frame behind the Green-Lagrange and second Piola-Kirchhoff derivation.
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- [[Direct Time Integration Methods]] gives the broader time integration family that includes Newmark-type schemes.
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## Source Notes
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- Source path: `.raw/MITC공부/`
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- Composite source hash recorded in `.raw/.manifest.json`.
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- The extracted Markdown has OCR and encoding artifacts, but the section structure and equations are usable.
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