Displacement-based formulation of Koiter's method: Application to multi-modal post-buckling finite element analysis of plates

Castro, Saullo G.P.; Jansen, E. L.

doi:10.1016/j.tws.2020.107217

Displacement-based formulation of Koiter's method

Title

Displacement-based formulation of Koiter's method: Application to multi-modal post-buckling finite element analysis of plates

Author

Castro, Saullo G.P. (TU Delft Aerospace Structures & Computational Mechanics)
Jansen, E. L. (Rotterdam University of Applied Sciences)

Date

2021

Abstract

Koiter's asymptotic method enables the calculation and deep understanding of the initial post-buckling behaviour of thin-walled structures. For the single-mode asymptotic analysis, Budiansky (1974) presented a clear and general formulation for Koiter's method, based on the expansion of the total potential energy function. The formulation from Budiansky is herein revisited and expanded for the multi-modal asymptotic analysis, of primordial importance in structures with clustered bifurcation modes. Given the admittedly difficult implementation of Koiter's method, especially for multi-modal analysis and during the evaluation of the third– and fourth–order tensors involved in Koiter's analysis; the presented study proposes a formulation and notation with close correspondence with the implemented algorithms. The implementation is based on state-of-the-art collaborative tools: Python, NumPy and Cython. The kinematic relations are specialized using von Kármán shell kinematics, and the displacement field variables are approximated using an enhanced Bogner-Fox-Schmit (BFS) finite element, modified to reach third-order interpolation also for the in-plane displacements, using only 4 nodes per element and 10 degrees-of-freedom per node, aiming an accurate representation of the second-order fields. The formulation and implementation are verified by comparing results for isotropic and composite plates against established literature. Finally, results for multi-modal displacement fields with up to 5 modes and corresponding post-buckling factors are reported for future reference.

Subject

Buckling
Classical formulation
Displacement-based
Finite elements
Koiter method
Plate
Post-buckling

To reference this document use:

http://resolver.tudelft.nl/uuid:65f1ef2d-0928-4477-9437-558dfe7732ab

DOI

https://doi.org/10.1016/j.tws.2020.107217

ISSN

0263-8231

Source

Thin-Walled Structures, 159

Part of collection

Institutional Repository