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.
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Coverage Map
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Topic
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Motivation for dynamic buckling analysis of shells under axial dynamic compression
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.
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