김경종
141 lines
8.1 KiB
Markdown
141 lines
8.1 KiB
Markdown
---
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type: overview
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title: "Wiki Overview"
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created: 2026-04-07
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updated: 2026-05-28
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tags:
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- meta
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- overview
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status: current
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related:
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- "[[index]]"
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- "[[hot]]"
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- "[[log]]"
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- "[[dashboard]]"
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- "[[Finite Element Procedures]]"
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- "[[A Continuum Mechanics Based Four-Node Shell]]"
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- "[[Four-Node-Quadrilateral-Shell-Element-MITC4]]"
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- "[[MITC Study Notes]]"
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- "[[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method]]"
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- "[[On-the-Finite-Element-Analysis-of-Shell-Structures]]"
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- "[[Solid Element Notes]]"
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- "[[Computational Mechanics]]"
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sources:
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- "[[Finite Element Procedures]]"
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- "[[A Continuum Mechanics Based Four-Node Shell]]"
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- "[[Four-Node-Quadrilateral-Shell-Element-MITC4]]"
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- "[[MITC Study Notes]]"
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- "[[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method]]"
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- "[[On-the-Finite-Element-Analysis-of-Shell-Structures]]"
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- "[[Solid Element Notes]]"
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---
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# Wiki Overview
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Navigation: [[index]] | [[hot]] | [[log]] | [[dashboard]]
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---
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## Purpose
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This vault is currently focused on computational mechanics, seeded from [[Finite Element Procedures]] by [[Klaus-Jurgen Bathe]], solid element notes, shell element sources, MITC derivation notes, shell buckling analysis, and [[On-the-Finite-Element-Analysis-of-Shell-Structures|On the Finite Element Analysis of Shell Structures]] by [[Phill-Seung Lee]] and [[Hyuk-Chun Noh]].
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---
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## Current Seed Content
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**Domain:**
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- [[Computational Mechanics]] - finite element analysis, numerical methods, and engineering simulation
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**Concepts:**
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- [[Finite Element Method]] - central computational mechanics workflow
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- [[Engineering Mathematical Models]] - how physical problems become solvable models
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- [[Displacement-Based Finite Element Formulation]] - primary solid mechanics derivation
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- [[Isoparametric Finite Elements]] - element construction and integration framework
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- [[Isoparametric Linear Solid Elements]] - 3D continuum element formulation with translational nodal DOFs
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- [[Solid Element Shape Functions]] - linear solid element interpolation functions
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- [[Solid Element Strain-Displacement Matrix]] - 3D strain-displacement relation and Jacobian mapping
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- [[Solid Element Stiffness Integration]] - Gauss integration of solid element stiffness matrices
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- [[Incompatible Mode Solid Elements]] - internal-mode enrichment for solid element flexibility
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- [[Mixed Finite Element Formulations]] - pressure and constraint-aware formulations
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- [[Nonlinear Finite Element Analysis]] - incremental nonlinear solution workflow
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- [[Continuum Mechanics Based Four-Node Shell Element]] - four-node shell formulation derived from continuum mechanics
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- [[Assumed Transverse Shear Strain Interpolation]] - transverse shear locking remedy for shell elements
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- [[Total Lagrangian Shell Formulation]] - large displacement and rotation shell analysis framework
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- [[MITC4 Shell Element]] - mixed-interpolation four-node shell element implementation
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- [[MITC Shell Kinematics]] - shell director kinematics for MITC derivations
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- [[Green-Lagrange Strain Linearization]] - nonlinear strain expansion for tangent construction
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- [[Nonlinear Newmark-Beta Integration]] - Newmark time stepping with Newton iterations
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- [[Dynamic Buckling Analysis]] - finite element stability analysis under time-varying axial compression
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- [[Dynamic Instability Region]] - instability boundary in excitation/load parameter space
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- [[Geometric Stiffness Matrix]] - stress stiffness contribution needed for buckling eigenproblems
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- [[Scordelis-Lo Shell Benchmark]] - shell element convergence benchmark
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- [[Basic Shell Mathematical Model]] - general shell model beneath continuum shell finite elements
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- [[Shell Structure Asymptotic Behavior]] - bending, membrane, and mixed behavior as thickness decreases
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- [[Shell Locking Phenomenon]] - thickness-dependent artificial stiffness in shell finite element results
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- [[Uniform Optimal Convergence]] - convergence target that remains stable across shell thickness regimes
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- [[Shell Element Benchmark Testing]] - benchmark methodology for shell element reliability
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- [[Finite Element Heat Transfer and Field Problems]] - FE treatment beyond structural mechanics
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- [[Static Equilibrium Equation Solvers]] - linear and nonlinear static equation solution
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- [[Direct Time Integration Methods]] - transient dynamics and time integration
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- [[Finite Element Eigenproblem Solvers]] - modal and eigenvalue algorithms
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- [[Finite Element Program Implementation]] - FE code data flow and STAP-style implementation
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**Entity:**
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- [[Klaus-Jurgen Bathe]] - author of [[Finite Element Procedures]] and co-author of [[A Continuum Mechanics Based Four-Node Shell]]
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- [[Eduardo N. Dvorkin]] - co-author of [[A Continuum Mechanics Based Four-Node Shell]]
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- [[Edita Dvorakova]] - co-author of [[Four-Node-Quadrilateral-Shell-Element-MITC4|Four-Node Quadrilateral Shell Element MITC4]]
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- [[Borek Patzak]] - co-author of [[Four-Node-Quadrilateral-Shell-Element-MITC4|Four-Node Quadrilateral Shell Element MITC4]]
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- [[OOFEM]] - finite element code used in the MITC4 implementation
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- [[Hee Jun Lee]] - author of the dynamic shell buckling thesis
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- [[Phill-Seung Lee]] - author of the shell finite element review
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- [[Hyuk-Chun Noh]] - author of the shell finite element review
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- [[Inha University]] - degree-granting institution for the thesis
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- [[BLZPACK]] - Block Lanczos eigenvalue solver used in the thesis
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- [[ABAQUS]] - validation comparison software used in the thesis
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**Source:**
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- [[Finite Element Procedures]] - finite element analysis textbook
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- [[A Continuum Mechanics Based Four-Node Shell]] - shell element formulation paper
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- [[Four-Node-Quadrilateral-Shell-Element-MITC4|Four-Node Quadrilateral Shell Element MITC4]] - MITC4 implementation and validation paper
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- [[MITC Study Notes]] - local MITC shell derivation notes
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- [[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method|Dynamic Buckling Analysis of Shell Structures using Finite Element Method]] - thesis on MITC4 shell dynamic buckling analysis
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- [[On-the-Finite-Element-Analysis-of-Shell-Structures|On the Finite Element Analysis of Shell Structures]] - review of shell mathematical models, asymptotic behavior, locking, convergence, and benchmark testing
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- [[Solid Element Notes]] - local notes on linear isoparametric solid elements
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---
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## Current State
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- Sources ingested: 7
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- Wiki pages: 63
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- Last activity: 2026-05-28 (ingested solid element notes)
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---
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## Canvases
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- [[main]] - default visual reference canvas with a General zone
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---
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## Key Themes
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**Model first, solve second.** The finite element result is only meaningful relative to the selected mathematical model, boundary conditions, materials, loads, and discretization.
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**Formulation controls reliability.** Displacement, mixed, isoparametric, nonlinear, transient, and eigenproblem formulations each impose different stability and accuracy requirements.
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**Solid elements ground the 3D continuum path.** The solid element notes connect natural-coordinate interpolation, Jacobian derivative mapping, `B`/`D` matrices, stiffness integration, and incompatible-mode enrichment.
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**Shell elements expose formulation tradeoffs.** Low-order shell elements need careful shear strain interpolation and nonlinear kinematics to avoid locking while preserving computational economy.
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**Benchmarks close the loop.** The MITC4 source ties formulation to implementation by using patch tests and the Scordelis-Lo shell benchmark before comparing convergence.
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**Derivations connect formulations to solvers.** The MITC study notes link shell director kinematics, Green-Lagrange strain linearization, tangent construction, and nonlinear Newmark-beta dynamics.
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**Stability analysis closes the structural loop.** The dynamic buckling thesis connects MITC4 shell modeling, geometric stiffness, eigenvalue solvers, validation benchmarks, and instability-region prediction.
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**Thin-shell asymptotics explain shell FE failure modes.** The shell FE review connects basic shell models, bending/membrane/mixed asymptotic behavior, locking, uniform convergence, and benchmark design.
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**Implementation matters.** Element-level calculations, assembly, storage, solvers, and stress recovery are part of the method, not afterthoughts.
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