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---
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type: source
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title: "A Continuum Mechanics Based Four-Node Shell Element for General Non-Linear Analysis"
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source_type: paper
|
||||
authors:
|
||||
- "Eduardo N. Dvorkin"
|
||||
- "Klaus-Jurgen Bathe"
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||||
date_received: 1983-12
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aliases:
|
||||
- AContinuumMechanicsBasedFourNodeShell
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- four-node shell element paper
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||||
- Dvorkin Bathe four-node shell
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||||
created: 2026-05-28
|
||||
updated: 2026-05-28
|
||||
address: c-000017
|
||||
tags:
|
||||
- source
|
||||
- finite-element-method
|
||||
- shell-elements
|
||||
- nonlinear-analysis
|
||||
status: current
|
||||
confidence: high
|
||||
raw_path: ".raw/AContinuumMechanicsBasedFourNodeShell/"
|
||||
source_files:
|
||||
markdown_files: 2
|
||||
image_files: 100
|
||||
related:
|
||||
- "[[Eduardo N. Dvorkin]]"
|
||||
- "[[Klaus-Jurgen Bathe]]"
|
||||
- "[[Continuum Mechanics Based Four-Node Shell Element]]"
|
||||
- "[[Assumed Transverse Shear Strain Interpolation]]"
|
||||
- "[[Total Lagrangian Shell Formulation]]"
|
||||
- "[[Nonlinear Finite Element Analysis]]"
|
||||
- "[[Isoparametric Finite Elements]]"
|
||||
- "[[Four-Node-Quadrilateral-Shell-Element-MITC4]]"
|
||||
- "[[MITC4 Shell Element]]"
|
||||
---
|
||||
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# A Continuum Mechanics Based Four-Node Shell Element for General Non-Linear Analysis
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## Summary
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This paper presents a four-node non-flat quadrilateral shell element for general nonlinear analysis. The element is formulated from three-dimensional continuum mechanics instead of a specialized shell theory, and is intended for thin and thick shells, arbitrary shell geometries, large displacement and rotation response with small strains, and material nonlinear behavior.
|
||||
|
||||
The local source is a converted Markdown/image extraction of the paper: two Markdown files and 100 extracted images under `.raw/AContinuumMechanicsBasedFourNodeShell/`.
|
||||
|
||||
## Key Contributions
|
||||
|
||||
- The element uses a continuum-mechanics description with convected coordinates, so shell behavior is derived from the three-dimensional virtual work statement.
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||||
- The formulation separates transverse shear strain interpolation from the standard displacement interpolation to avoid shear locking in thin shell bending.
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- The paper develops a total Lagrangian nonlinear formulation for large displacements and rotations with small strains.
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- The numerical tests cover rigid-body modes, thin-shell bending, distorted meshes, cylindrical shells, pinched cylinders, large-deflection cantilevers, shallow spherical shell snap-through behavior, stiffened plate buckling, and elastoplastic circular plate response.
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- The authors report no spurious zero-energy modes with full numerical integration in the tested cases.
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||||
|
||||
## Concepts Introduced
|
||||
|
||||
- [[Continuum Mechanics Based Four-Node Shell Element]]
|
||||
- [[Assumed Transverse Shear Strain Interpolation]]
|
||||
- [[Total Lagrangian Shell Formulation]]
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|
||||
## Links To Existing Wiki
|
||||
|
||||
- [[Isoparametric Finite Elements]] supplies the geometry mapping and quadrature machinery used by the shell element.
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- [[Mixed Finite Element Formulations]] gives context for constraint-aware interpolation choices that prevent locking.
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- [[Nonlinear Finite Element Analysis]] gives the broader incremental equilibrium setting for the element's large-displacement examples.
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||||
- [[Finite Element Method]] is the parent discretization framework.
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- [[Four-Node-Quadrilateral-Shell-Element-MITC4|Four-Node Quadrilateral Shell Element MITC4]] is a later implementation-focused source that follows the same four-node shell lineage and emphasizes the MITC locking remedy.
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||||
|
||||
## Entities Mentioned
|
||||
|
||||
- [[Eduardo N. Dvorkin]]
|
||||
- [[Klaus-Jurgen Bathe]]
|
||||
|
||||
## Source Notes
|
||||
|
||||
- Source path: `.raw/AContinuumMechanicsBasedFourNodeShell/`
|
||||
- Composite source hash recorded in `.raw/.manifest.json`.
|
||||
- The source extraction contains encoding artifacts in names and symbols. Derived wiki pages normalize `Klaus-Jurgen Bathe` to the existing vault spelling.
|
||||
+85
@@ -0,0 +1,85 @@
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||||
---
|
||||
type: source
|
||||
title: "Dynamic Buckling Analysis of Shell Structures using Finite Element Method"
|
||||
source_type: thesis
|
||||
author: "Hee Jun Lee"
|
||||
institution: "Inha University"
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||||
department: "Aerospace Engineering"
|
||||
date_published: 2012-02
|
||||
created: 2026-05-28
|
||||
updated: 2026-05-28
|
||||
address: c-000032
|
||||
aliases:
|
||||
- "유한요소해석법을 이용한 쉘 구조물의 동적 좌굴 해석"
|
||||
- Dynamic Buckling Analysis of Shell Structures using FEM
|
||||
tags:
|
||||
- source
|
||||
- finite-element-method
|
||||
- shell-elements
|
||||
- dynamic-buckling
|
||||
- nonlinear-analysis
|
||||
status: current
|
||||
confidence: high
|
||||
raw_path: ".raw/유한요소해석법을이용한쉘구조물의동적좌굴해석/"
|
||||
source_files:
|
||||
markdown_files: 8
|
||||
image_files: 220
|
||||
related:
|
||||
- "[[Hee Jun Lee]]"
|
||||
- "[[Inha University]]"
|
||||
- "[[Dynamic Buckling Analysis]]"
|
||||
- "[[Dynamic Instability Region]]"
|
||||
- "[[Geometric Stiffness Matrix]]"
|
||||
- "[[MITC4 Shell Element]]"
|
||||
- "[[BLZPACK]]"
|
||||
- "[[ABAQUS]]"
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||||
---
|
||||
|
||||
# Dynamic Buckling Analysis of Shell Structures using Finite Element Method
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## Summary
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||||
This 2012 master's thesis develops and verifies a finite element program for dynamic buckling analysis of shell structures under axial dynamic compressive loading. The work uses the [[MITC4 Shell Element]], a [[Total Lagrangian Shell Formulation]] for geometric nonlinearity, a lumped mass matrix, and eigenvalue solvers for vibration, static buckling, and dynamic buckling checks.
|
||||
|
||||
The local source is a converted Markdown/image extraction: eight Markdown files and 220 extracted images under `.raw/유한요소해석법을이용한쉘구조물의동적좌굴해석/`.
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|
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## Coverage Map
|
||||
|
||||
| Section | Topic |
|
||||
|---|---|
|
||||
| 1 | Motivation for dynamic buckling analysis of shells under axial dynamic compression |
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| 2.1 | [[MITC4 Shell Element]] kinematics and transverse shear interpolation |
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| 2.2 | Geometric nonlinear formulation, finite rotation, constitutive matrix, mass matrix, and 6-DOF shell treatment |
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||||
| 2.3 | Static buckling, [[Dynamic Buckling Analysis]], and beam dynamic buckling theory |
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| 3.1 | Linear static verification: patch tests, pinched cylinder, hemispherical shell |
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| 3.2 | Geometric nonlinear verification against [[ABAQUS]] |
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| 3.3 | Static buckling verification: rectangular plate, cylindrical shell, stiffened square plate |
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| 3.4 | Dynamic buckling verification: beam, plate, and stiffened plate instability regions |
|
||||
|
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## Key Takeaways
|
||||
|
||||
- Dynamic buckling is treated as a parametric resonance problem caused by axial dynamic compressive loading.
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||||
- The thesis implements a shell finite element program rather than relying only on static buckling capability from commercial tools.
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- [[Geometric Stiffness Matrix]] terms are central because static and dynamic buckling analyses are built from eigenvalue problems involving stiffness, geometric stiffness, and mass.
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- The program is verified progressively: patch tests, static response benchmarks, geometric nonlinear response, static buckling eigenvalues, and dynamic instability regions.
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- Beam dynamic buckling shows the expected trend: with no static load, the instability frequency is around twice the natural frequency, and increasing dynamic load widens the instability region.
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- Plate and stiffened plate dynamic buckling comparisons show similar trends to experimental results, while stiffened plate discrepancies are attributed partly to imperfections in real structures.
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||||
|
||||
## Entities Mentioned
|
||||
|
||||
- [[Hee Jun Lee]] - thesis author.
|
||||
- [[Inha University]] - degree-granting institution.
|
||||
- [[BLZPACK]] - Block Lanczos eigenvalue solver used in the implementation.
|
||||
- [[ABAQUS]] - commercial finite element software used for comparison.
|
||||
|
||||
## Concepts Introduced
|
||||
|
||||
- [[Dynamic Buckling Analysis]]
|
||||
- [[Dynamic Instability Region]]
|
||||
- [[Geometric Stiffness Matrix]]
|
||||
|
||||
## Source Notes
|
||||
|
||||
- Source path: `.raw/유한요소해석법을이용한쉘구조물의동적좌굴해석/`
|
||||
- Composite source hash recorded in `.raw/.manifest.json`.
|
||||
- The converted Markdown includes OCR and encoding artifacts, but title, abstract, section structure, tables, and key Korean body text are usable.
|
||||
@@ -0,0 +1,89 @@
|
||||
---
|
||||
type: source
|
||||
title: "Finite Element Procedures"
|
||||
source_type: book
|
||||
author: "Klaus-Jurgen Bathe"
|
||||
date_published: 2014
|
||||
aliases:
|
||||
- Finite-Element-Procedures
|
||||
created: 2026-05-28
|
||||
updated: 2026-05-28
|
||||
address: c-000003
|
||||
tags:
|
||||
- source
|
||||
- finite-element-method
|
||||
- computational-mechanics
|
||||
status: current
|
||||
confidence: high
|
||||
raw_path: ".raw/FiniteElementProcedures/"
|
||||
source_files:
|
||||
markdown_files: 109
|
||||
image_files: 4874
|
||||
related:
|
||||
- "[[Klaus-Jurgen Bathe]]"
|
||||
- "[[Computational Mechanics]]"
|
||||
- "[[Finite Element Method]]"
|
||||
- "[[Displacement-Based Finite Element Formulation]]"
|
||||
- "[[Isoparametric Finite Elements]]"
|
||||
- "[[Nonlinear Finite Element Analysis]]"
|
||||
---
|
||||
|
||||
# Finite Element Procedures
|
||||
|
||||
## Summary
|
||||
|
||||
`Finite Element Procedures` is a full textbook treatment of finite element analysis, moving from mathematical modeling and linear algebra foundations into solid mechanics, isoparametric elements, nonlinear analysis, heat transfer, fluid flow, static and dynamic equation solvers, eigenproblem algorithms, and program implementation.
|
||||
|
||||
The local source is a converted Markdown/image extraction of the book: 109 Markdown files plus 4,874 extracted images under `.raw/FiniteElementProcedures/`. The conversion includes some encoding artifacts in metadata and non-ASCII characters, but the chapter and section headings are usable.
|
||||
|
||||
## Coverage Map
|
||||
|
||||
| Chapter | Topic | Local source span |
|
||||
|---|---|---|
|
||||
| 1 | Introduction to finite element procedures and the physical-modeling workflow | `FiniteElementProcedures_002.md` to `FiniteElementProcedures_004.md` |
|
||||
| 2 | Vectors, matrices, tensors, eigenproblems, Rayleigh quotient, and norms | `FiniteElementProcedures_004.md` to `FiniteElementProcedures_009.md` |
|
||||
| 3 | Engineering mathematical models, discrete and continuous systems, constraints | `FiniteElementProcedures_010.md` to `FiniteElementProcedures_017.md` |
|
||||
| 4 | Linear displacement-based finite element formulation in solids and structures | `FiniteElementProcedures_017.md` to `FiniteElementProcedures_036.md` |
|
||||
| 5 | Isoparametric element matrices, continuum elements, structural elements, numerical integration | `FiniteElementProcedures_036.md` to `FiniteElementProcedures_050.md` |
|
||||
| 6 | Nonlinear finite element analysis in solid and structural mechanics | `FiniteElementProcedures_051.md` to `FiniteElementProcedures_066.md` |
|
||||
| 7 | Heat transfer, field problems, incompressible fluid flow, and fluid-structure interaction | `FiniteElementProcedures_066.md` to `FiniteElementProcedures_071.md` |
|
||||
| 8 | Static equilibrium solvers: direct, iterative, and nonlinear equation methods | `FiniteElementProcedures_072.md` to `FiniteElementProcedures_079.md` |
|
||||
| 9 | Dynamic equilibrium solvers: direct integration, mode superposition, and nonlinear dynamics | `FiniteElementProcedures_079.md` to `FiniteElementProcedures_086.md` |
|
||||
| 10 | Preliminaries for finite element eigenproblems and error bounds | `FiniteElementProcedures_086.md` to `FiniteElementProcedures_091.md` |
|
||||
| 11 | Eigenproblem solution methods: vector iteration, transformations, Lanczos, subspace iteration | `FiniteElementProcedures_091.md` to `FiniteElementProcedures_100.md` |
|
||||
| 12 | Program implementation, element stress recovery, and STAP example program | `FiniteElementProcedures_100.md` to `FiniteElementProcedures_103.md` |
|
||||
|
||||
## Key Takeaways
|
||||
|
||||
- The finite element workflow is framed as modeling first, numerical solution second: the analyst selects the geometry, material laws, loading, constraints, and idealization before solving.
|
||||
- The main linear solid mechanics path is displacement-based: choose interpolation functions, derive element equations from virtual work or variational statements, assemble global equations, apply boundary conditions, then solve.
|
||||
- Convergence depends on approximation spaces, element compatibility, completeness, mesh refinement, and the physical meaning of computed stresses.
|
||||
- Mixed formulations and inf-sup stability are central for incompressible or nearly incompressible behavior, where displacement-only elements can lock or create pressure artifacts.
|
||||
- Isoparametric elements connect geometry mapping, interpolation, Jacobians, numerical integration, and element matrix construction into a programmable element routine.
|
||||
- Nonlinear finite element analysis is organized around incremental equilibrium, tangent matrices, constitutive updates, contact constraints, and convergence criteria.
|
||||
- Solver chapters treat the finite element model as a sparse algebraic system, separating static, dynamic, and eigenvalue workflows.
|
||||
- The implementation chapter makes the data flow explicit: nodes and elements enter first, element matrices are calculated locally, global arrays are assembled, equations are solved, and stresses are recovered.
|
||||
|
||||
## Entities Mentioned
|
||||
|
||||
- [[Klaus-Jurgen Bathe]] - author and MIT professor of mechanical engineering.
|
||||
|
||||
## Concepts Introduced
|
||||
|
||||
- [[Finite Element Method]]
|
||||
- [[Engineering Mathematical Models]]
|
||||
- [[Displacement-Based Finite Element Formulation]]
|
||||
- [[Isoparametric Finite Elements]]
|
||||
- [[Mixed Finite Element Formulations]]
|
||||
- [[Nonlinear Finite Element Analysis]]
|
||||
- [[Finite Element Heat Transfer and Field Problems]]
|
||||
- [[Static Equilibrium Equation Solvers]]
|
||||
- [[Direct Time Integration Methods]]
|
||||
- [[Finite Element Eigenproblem Solvers]]
|
||||
- [[Finite Element Program Implementation]]
|
||||
|
||||
## Source Notes
|
||||
|
||||
- Source path: `.raw/FiniteElementProcedures/`
|
||||
- Composite source hash recorded in `.raw/.manifest.json`.
|
||||
- Keep the raw folder immutable. Add derived notes under `wiki/`.
|
||||
@@ -0,0 +1,79 @@
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||||
---
|
||||
type: source
|
||||
title: "Four-Node Quadrilateral Shell Element MITC4"
|
||||
source_type: paper
|
||||
authors:
|
||||
- "Edita Dvorakova"
|
||||
- "Borek Patzak"
|
||||
doi: "10.4028/www.scientific.net/AMM.825.99"
|
||||
container: "Applied Mechanics and Materials"
|
||||
created: 2026-05-28
|
||||
updated: 2026-05-28
|
||||
address: c-000022
|
||||
aliases:
|
||||
- FourNodeQuadrilateralShellElementMITC4
|
||||
- MITC4 paper
|
||||
- Four-Node Quadrilateral Shell Element MITC4
|
||||
tags:
|
||||
- source
|
||||
- finite-element-method
|
||||
- shell-elements
|
||||
- mitc
|
||||
- implementation
|
||||
status: current
|
||||
confidence: high
|
||||
raw_path: ".raw/FourNodeQuadrilateralShellElementMITC4/"
|
||||
source_files:
|
||||
markdown_files: 1
|
||||
image_files: 21
|
||||
related:
|
||||
- "[[Edita Dvorakova]]"
|
||||
- "[[Borek Patzak]]"
|
||||
- "[[OOFEM]]"
|
||||
- "[[MITC4 Shell Element]]"
|
||||
- "[[Scordelis-Lo Shell Benchmark]]"
|
||||
- "[[Continuum Mechanics Based Four-Node Shell Element]]"
|
||||
- "[[Assumed Transverse Shear Strain Interpolation]]"
|
||||
---
|
||||
|
||||
# Four-Node Quadrilateral Shell Element MITC4
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|
||||
## Summary
|
||||
|
||||
This paper presents a four-node quadrilateral MITC4 shell element applicable to both thick and thin shells. The formulation starts from a three-dimensional continuum description degenerated to shell behavior, follows the Dvorkin-Bathe four-node shell element lineage, and uses MITC, Mixed Interpolation of Tensorial Components, to overcome transverse shear locking in thin shell analysis.
|
||||
|
||||
The local source is a converted Markdown/image extraction: one Markdown file and 21 extracted images under `.raw/FourNodeQuadrilateralShellElementMITC4/`.
|
||||
|
||||
## Key Contributions
|
||||
|
||||
- The source explains the MITC4 geometry and displacement interpolation using four shell vertices, director vectors, three translational degrees of freedom, and two rotational degrees of freedom per node.
|
||||
- It identifies shear locking as the key weakness of direct low-order shell interpolation for thin shells.
|
||||
- It uses assumed transverse shear strain components evaluated from edge-midpoint tying locations to construct a locking-resistant MITC strain field.
|
||||
- It describes implementation in [[OOFEM]] and reports patch-test verification for pure bending, pure shear, pure twist, and three membrane stress states.
|
||||
- It validates the implementation with the [[Scordelis-Lo Shell Benchmark]], where MITC4 converges close to the reference displacement and performs competitively against an RDKT reference element.
|
||||
|
||||
## Concepts Introduced
|
||||
|
||||
- [[MITC4 Shell Element]]
|
||||
- [[Scordelis-Lo Shell Benchmark]]
|
||||
|
||||
## Links To Existing Wiki
|
||||
|
||||
- [[Continuum Mechanics Based Four-Node Shell Element]] is the parent shell formulation lineage.
|
||||
- [[Assumed Transverse Shear Strain Interpolation]] captures the locking remedy also used by MITC4.
|
||||
- [[Finite Element Program Implementation]] connects the formulation to practical implementation in a finite element code.
|
||||
- [[Isoparametric Finite Elements]] supplies the quadrilateral mapping and element-matrix framework.
|
||||
|
||||
## Entities Mentioned
|
||||
|
||||
- [[Edita Dvorakova]]
|
||||
- [[Borek Patzak]]
|
||||
- [[OOFEM]]
|
||||
- [[Klaus-Jurgen Bathe]]
|
||||
- [[Eduardo N. Dvorkin]]
|
||||
|
||||
## Source Notes
|
||||
|
||||
- Source path: `.raw/FourNodeQuadrilateralShellElementMITC4/`
|
||||
- Composite source hash recorded in `.raw/.manifest.json`.
|
||||
- The source extraction contains encoding artifacts in author names and Czech text. Derived pages normalize names to ASCII transliterations.
|
||||
@@ -0,0 +1,76 @@
|
||||
---
|
||||
type: source
|
||||
title: "MITC Study Notes"
|
||||
source_type: study-notes
|
||||
created: 2026-05-28
|
||||
updated: 2026-05-28
|
||||
address: c-000028
|
||||
aliases:
|
||||
- MITC공부
|
||||
- MITC shell element study notes
|
||||
- MITC formulation notes
|
||||
tags:
|
||||
- source
|
||||
- finite-element-method
|
||||
- shell-elements
|
||||
- mitc
|
||||
- nonlinear-analysis
|
||||
status: current
|
||||
confidence: medium
|
||||
raw_path: ".raw/MITC공부/"
|
||||
source_files:
|
||||
markdown_files: 2
|
||||
image_files: 107
|
||||
related:
|
||||
- "[[MITC4 Shell Element]]"
|
||||
- "[[MITC Shell Kinematics]]"
|
||||
- "[[Green-Lagrange Strain Linearization]]"
|
||||
- "[[Nonlinear Newmark-Beta Integration]]"
|
||||
- "[[Total Lagrangian Shell Formulation]]"
|
||||
- "[[Direct Time Integration Methods]]"
|
||||
---
|
||||
|
||||
# MITC Study Notes
|
||||
|
||||
## Summary
|
||||
|
||||
`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.
|
||||
|
||||
The local source is a converted Markdown/image extraction: two Markdown files and 107 extracted images under `.raw/MITC공부/`.
|
||||
|
||||
## Coverage Map
|
||||
|
||||
| Section | Topic |
|
||||
|---|---|
|
||||
| 1 | MITC shell element motivation: continuum-degenerated shell behavior and transverse shear locking |
|
||||
| 2 | Shell kinematics: reference/current configurations, director vectors, nodal displacement and rotation variables |
|
||||
| 3 | FE formulation: virtual work, deformation gradient, Green-Lagrange strain, second Piola-Kirchhoff stress, residual and tangent terms |
|
||||
| 4 | Constitutive matrix: plane-stress shell material matrix and coordinate transformation to natural coordinates |
|
||||
| 5 | Nonlinear Newmark-beta integration: Newton-Raphson iteration, effective dynamic tangent, residual update, velocity and acceleration update |
|
||||
|
||||
## Key Takeaways
|
||||
|
||||
- MITC shell elements are presented as shell elements derived from a three-dimensional continuum description rather than from a specialized shell theory.
|
||||
- The practical reason for MITC is transverse shear locking control in thin shell analysis.
|
||||
- The kinematic derivation separates nodal translations from director-vector updates, which later feed the incremental displacement field.
|
||||
- The FE formulation uses Green-Lagrange strain and second Piola-Kirchhoff stress, then separates constant, linear, and nonlinear strain terms for tangent construction.
|
||||
- The dynamic section combines Newton-Raphson iteration with Newmark-beta kinematics to obtain an effective equation for displacement increments.
|
||||
|
||||
## Concepts Introduced
|
||||
|
||||
- [[MITC Shell Kinematics]]
|
||||
- [[Green-Lagrange Strain Linearization]]
|
||||
- [[Nonlinear Newmark-Beta Integration]]
|
||||
|
||||
## Links To Existing Wiki
|
||||
|
||||
- [[MITC4 Shell Element]] gives the compact element-level concept that these notes expand.
|
||||
- [[Assumed Transverse Shear Strain Interpolation]] is the locking remedy motivating the MITC approach.
|
||||
- [[Total Lagrangian Shell Formulation]] gives the nonlinear shell frame behind the Green-Lagrange and second Piola-Kirchhoff derivation.
|
||||
- [[Direct Time Integration Methods]] gives the broader time integration family that includes Newmark-type schemes.
|
||||
|
||||
## Source Notes
|
||||
|
||||
- Source path: `.raw/MITC공부/`
|
||||
- Composite source hash recorded in `.raw/.manifest.json`.
|
||||
- The extracted Markdown has OCR and encoding artifacts, but the section structure and equations are usable.
|
||||
@@ -0,0 +1,85 @@
|
||||
---
|
||||
type: source
|
||||
title: "On the Finite Element Analysis of Shell Structures"
|
||||
source_type: paper
|
||||
authors:
|
||||
- "Phill-Seung Lee"
|
||||
- "Hyuk-Chun Noh"
|
||||
date_published: 2007
|
||||
created: 2026-05-28
|
||||
updated: 2026-05-28
|
||||
address: c-000040
|
||||
aliases:
|
||||
- "쉘구조물의 유한요소해석에 대하여"
|
||||
- "Finite Element Analysis of Shell Structures"
|
||||
tags:
|
||||
- source
|
||||
- finite-element-method
|
||||
- shell-elements
|
||||
- locking
|
||||
- benchmark
|
||||
status: current
|
||||
confidence: medium
|
||||
raw_path: ".raw/쉘구조물의유한요소해석에대하여/"
|
||||
source_files:
|
||||
markdown_files: 2
|
||||
image_files: 78
|
||||
related:
|
||||
- "[[Phill-Seung Lee]]"
|
||||
- "[[Hyuk-Chun Noh]]"
|
||||
- "[[Basic Shell Mathematical Model]]"
|
||||
- "[[Shell Structure Asymptotic Behavior]]"
|
||||
- "[[Shell Locking Phenomenon]]"
|
||||
- "[[Uniform Optimal Convergence]]"
|
||||
- "[[Shell Element Benchmark Testing]]"
|
||||
- "[[MITC4 Shell Element]]"
|
||||
---
|
||||
|
||||
# On the Finite Element Analysis of Shell Structures
|
||||
|
||||
## Summary
|
||||
|
||||
This paper is a Korean review of finite element analysis for shell structures. It connects three layers that must be understood together: physical shell behavior, the [[Basic Shell Mathematical Model]], and finite element discretization. The paper focuses on thin-shell difficulty: as thickness decreases, shell problems split into bending-dominated, membrane-dominated, and mixed-dominated asymptotic behavior, and unreliable elements show [[Shell Locking Phenomenon]] in convergence curves.
|
||||
|
||||
The local source is a converted Markdown/image extraction: two Markdown files and 78 extracted images under `.raw/쉘구조물의유한요소해석에대하여/`.
|
||||
|
||||
## Coverage Map
|
||||
|
||||
| Section | Topic |
|
||||
|---|---|
|
||||
| Abstract and 1 | Why shell finite element analysis needs integrated physical, mathematical, and numerical understanding |
|
||||
| 2 | [[Basic Shell Mathematical Model]] from midsurface geometry, covariant bases, director kinematics, and variational equations |
|
||||
| 3 | [[Shell Structure Asymptotic Behavior]] under decreasing thickness and load scaling |
|
||||
| 4 | [[Shell Locking Phenomenon]], S-norm error measurement, and convergence curves |
|
||||
| 5 | [[Uniform Optimal Convergence]], ideal shell element requirements, MITC/ANS/EAS remedies, and consistency/ellipticity tradeoffs |
|
||||
| 5.3 | [[Shell Element Benchmark Testing]] using basic tests, S-norm, layers, Gaussian curvature, asymptotic classes, and mesh patterns |
|
||||
| 6 | Conclusion that shell mathematical models and asymptotic behavior are prerequisites for reliable shell FE interpretation |
|
||||
|
||||
## Key Takeaways
|
||||
|
||||
- Shell FE reliability is not only an implementation issue; it depends on matching physical behavior, shell mathematical model, and discretization.
|
||||
- The basic shell model captures bending, membrane, transverse shear, and coupling terms and is the mathematical model beneath continuum-mechanics-based shell finite elements.
|
||||
- The load scaling factor `rho` classifies thin-shell behavior: membrane-dominated near `1`, bending-dominated near `3`, and mixed-dominated between them.
|
||||
- Locking appears as thickness-dependent loss of convergence and artificial stiffness, especially for displacement-based shell elements in bending or mixed-dominated problems.
|
||||
- MITC-style mixed interpolation is presented as a strong locking remedy, but the paper emphasizes the balance between locking control, consistency, and ellipticity.
|
||||
- Shell element benchmarking should include basic tests, global error norms, asymptotic behavior classes, Gaussian curvature, layer behavior, and mesh distortion sensitivity.
|
||||
|
||||
## Entities Mentioned
|
||||
|
||||
- [[Phill-Seung Lee]] - author.
|
||||
- [[Hyuk-Chun Noh]] - author.
|
||||
- [[Klaus-Jurgen Bathe]] - thanked and repeatedly cited as a core shell finite element source.
|
||||
|
||||
## Concepts Introduced
|
||||
|
||||
- [[Basic Shell Mathematical Model]]
|
||||
- [[Shell Structure Asymptotic Behavior]]
|
||||
- [[Shell Locking Phenomenon]]
|
||||
- [[Uniform Optimal Convergence]]
|
||||
- [[Shell Element Benchmark Testing]]
|
||||
|
||||
## Source Notes
|
||||
|
||||
- Source path: `.raw/쉘구조물의유한요소해석에대하여/`
|
||||
- Composite source hash recorded in `.raw/.manifest.json`.
|
||||
- The converted Markdown contains OCR and encoding artifacts, but the title, authors, abstract, section structure, equations, tables, and conclusions are usable.
|
||||
@@ -0,0 +1,71 @@
|
||||
---
|
||||
type: source
|
||||
title: "Solid Element Notes"
|
||||
source_type: study-notes
|
||||
created: 2026-05-28
|
||||
updated: 2026-05-28
|
||||
address: c-000048
|
||||
aliases:
|
||||
- SolidElement
|
||||
- "등매개 선형 솔리드 요소"
|
||||
tags:
|
||||
- source
|
||||
- finite-element-method
|
||||
- solid-elements
|
||||
- isoparametric-elements
|
||||
status: current
|
||||
confidence: high
|
||||
raw_path: ".raw/SolidElement/"
|
||||
source_files:
|
||||
markdown_files: 1
|
||||
image_files: 65
|
||||
related:
|
||||
- "[[Isoparametric Linear Solid Elements]]"
|
||||
- "[[Solid Element Shape Functions]]"
|
||||
- "[[Solid Element Strain-Displacement Matrix]]"
|
||||
- "[[Solid Element Stiffness Integration]]"
|
||||
- "[[Incompatible Mode Solid Elements]]"
|
||||
- "[[Isoparametric Finite Elements]]"
|
||||
---
|
||||
|
||||
# Solid Element Notes
|
||||
|
||||
## Summary
|
||||
|
||||
These local notes derive linear isoparametric solid elements for three-dimensional continuum modeling. They cover nodal displacement interpolation, common first-order solid element topologies, natural-coordinate shape functions, the strain-displacement matrix, Hooke-law material stiffness, Gaussian integration for element stiffness, and incompatible modes for locking relief.
|
||||
|
||||
The local source is a converted Markdown/image extraction: one Markdown file and 65 extracted images under `.raw/SolidElement/`.
|
||||
|
||||
## Coverage Map
|
||||
|
||||
| Section | Topic |
|
||||
|---|---|
|
||||
| 1 | [[Isoparametric Linear Solid Elements]] and practical modeling notes |
|
||||
| 2.1 | Position and displacement interpolation with shape functions |
|
||||
| 2.1 | [[Solid Element Shape Functions]] for 4-node tetrahedron, 5-node pyramid, 6-node wedge, and 8-node hexahedron |
|
||||
| 2.2 | [[Solid Element Strain-Displacement Matrix]] and Jacobian derivative mapping |
|
||||
| 2.3 | Three-dimensional Hooke-law stress-strain matrix |
|
||||
| 2.4 | [[Solid Element Stiffness Integration]] using `B^T D B` and element-specific Gauss points |
|
||||
| 2.5 | [[Incompatible Mode Solid Elements]] and static condensation of internal mode degrees of freedom |
|
||||
|
||||
## Key Takeaways
|
||||
|
||||
- Linear solid elements model three-dimensional volume response with three translational degrees of freedom per node and no rotational degrees of freedom.
|
||||
- The same shape functions interpolate both geometry and displacement, making the notes a direct extension of [[Isoparametric Finite Elements]] into 3D continuum elements.
|
||||
- The Jacobian maps derivatives from natural coordinates to physical coordinates, allowing the `B` matrix to be assembled in global coordinates.
|
||||
- The element stiffness follows the standard displacement-based form `K = integral B^T D B dV`, evaluated in natural coordinates with the Jacobian determinant.
|
||||
- Incompatible modes add internal displacement modes to selected wedge and hexahedral elements, then eliminate those extra degrees of freedom by static condensation.
|
||||
|
||||
## Concepts Introduced
|
||||
|
||||
- [[Isoparametric Linear Solid Elements]]
|
||||
- [[Solid Element Shape Functions]]
|
||||
- [[Solid Element Strain-Displacement Matrix]]
|
||||
- [[Solid Element Stiffness Integration]]
|
||||
- [[Incompatible Mode Solid Elements]]
|
||||
|
||||
## Source Notes
|
||||
|
||||
- Source path: `.raw/SolidElement/`
|
||||
- Composite source hash recorded in `.raw/.manifest.json`.
|
||||
- The note contains a few OCR/math transcription issues in the quadrature expressions, but the formulation sequence and element topology coverage are usable.
|
||||
+31
-3
@@ -11,19 +11,32 @@ related:
|
||||
- "[[index]]"
|
||||
- "[[log]]"
|
||||
- "[[entities/_index]]"
|
||||
- "[[Andrej Karpathy]]"
|
||||
- "[[Finite Element Procedures]]"
|
||||
- "[[A Continuum Mechanics Based Four-Node Shell]]"
|
||||
- "[[Four-Node-Quadrilateral-Shell-Element-MITC4]]"
|
||||
- "[[MITC Study Notes]]"
|
||||
- "[[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method]]"
|
||||
- "[[On-the-Finite-Element-Analysis-of-Shell-Structures]]"
|
||||
- "[[Solid Element Notes]]"
|
||||
---
|
||||
|
||||
# Sources Index
|
||||
|
||||
Navigation: [[index]] | [[concepts/_index|Concepts]] | [[entities/_index|Entities]]
|
||||
|
||||
All source pages — summaries of ingested documents, transcripts, articles, and data.
|
||||
All source pages: summaries of ingested documents, transcripts, articles, and data.
|
||||
|
||||
---
|
||||
|
||||
## Books
|
||||
|
||||
- [[Finite Element Procedures]] - finite element analysis textbook by [[Klaus-Jurgen Bathe]]
|
||||
|
||||
---
|
||||
|
||||
## Transcripts
|
||||
|
||||
<!-- Add transcript source pages here -->
|
||||
|
||||
---
|
||||
|
||||
@@ -35,7 +48,22 @@ All source pages — summaries of ingested documents, transcripts, articles, and
|
||||
|
||||
## Papers
|
||||
|
||||
<!-- Add paper source pages here -->
|
||||
- [[A Continuum Mechanics Based Four-Node Shell]] - continuum-mechanics-based four-node shell element paper by [[Eduardo N. Dvorkin]] and [[Klaus-Jurgen Bathe]]
|
||||
- [[Four-Node-Quadrilateral-Shell-Element-MITC4|Four-Node Quadrilateral Shell Element MITC4]] - MITC4 shell implementation paper by [[Edita Dvorakova]] and [[Borek Patzak]]
|
||||
- [[On-the-Finite-Element-Analysis-of-Shell-Structures|On the Finite Element Analysis of Shell Structures]] - Korean shell FE review by [[Phill-Seung Lee]] and [[Hyuk-Chun Noh]]
|
||||
|
||||
---
|
||||
|
||||
## Study Notes
|
||||
|
||||
- [[MITC Study Notes]] - derivation notes for MITC shell kinematics, Green-Lagrange linearization, and nonlinear Newmark-beta integration
|
||||
- [[Solid Element Notes]] - local formulation notes for linear isoparametric solid elements, Gauss integration, and incompatible modes
|
||||
|
||||
---
|
||||
|
||||
## Theses
|
||||
|
||||
- [[Dynamic-Buckling-Analysis-of-Shell-Structures-using-Finite-Element-Method|Dynamic Buckling Analysis of Shell Structures using Finite Element Method]] - 2012 Inha University thesis by [[Hee Jun Lee]]
|
||||
|
||||
---
|
||||
|
||||
|
||||
Reference in New Issue
Block a user