---
type: source
title: "Dynamic Buckling Analysis of Shell Structures using Finite Element Method"
source_type: thesis
author: "Hee Jun Lee"
institution: "Inha University"
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]]"
---

# Dynamic Buckling Analysis of Shell Structures using Finite Element Method

## Summary

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/`.

## Coverage Map

| Section | Topic |
|---|---|
| 1 | Motivation for dynamic buckling analysis of shells under axial dynamic compression |
| 2.1 | [[MITC4 Shell Element]] kinematics and transverse shear interpolation |
| 2.2 | Geometric nonlinear formulation, finite rotation, constitutive matrix, mass matrix, and 6-DOF shell treatment |
| 2.3 | Static buckling, [[Dynamic Buckling Analysis]], and beam dynamic buckling theory |
| 3.1 | Linear static verification: patch tests, pinched cylinder, hemispherical shell |
| 3.2 | Geometric nonlinear verification against [[ABAQUS]] |
| 3.3 | Static buckling verification: rectangular plate, cylindrical shell, stiffened square plate |
| 3.4 | Dynamic buckling verification: beam, plate, and stiffened plate instability regions |

## Key Takeaways

- Dynamic buckling is treated as a parametric resonance problem caused by axial dynamic compressive loading.
- The thesis implements a shell finite element program rather than relying only on static buckling capability from commercial tools.
- [[Geometric Stiffness Matrix]] terms are central because static and dynamic buckling analyses are built from eigenvalue problems involving stiffness, geometric stiffness, and mass.
- The program is verified progressively: patch tests, static response benchmarks, geometric nonlinear response, static buckling eigenvalues, and dynamic instability regions.
- 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.
- 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.

## 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.