Cellular buckling in stiffened plates

TL;DR

This paper develops an analytical model for cellular buckling in stiffened plates under compression, revealing complex unstable mode interactions and snap-back phenomena, and compares it with finite element models.

Contribution

It introduces a variational principles-based analytical model that captures cellular buckling and mode interactions, outperforming standard finite element methods in certain conditions.

Findings

Identification of unstable local-global mode interactions.

Observation of snap-back responses indicating cellular buckling.

Analytical model aligns better with experimental results than finite element models.

Abstract

An analytical model based on variational principles for a thin-walled stiffened plate subjected to axial compression is presented. A system of nonlinear differential and integral equations is derived and solved using numerical continuation. The results show that the system is susceptible to highly unstable local--global mode interaction after an initial instability is triggered. Moreover, snap-backs in the response showing sequential destabilization and restabilization, known as cellular buckling or snaking, arise. The analytical model is compared to static finite element models for joint conditions between the stiffener and the main plate that have significant rotational restraint. However, it is known from previous studies that the behaviour, where the same joint is insignificantly restrained rotationally, is captured better by an analytical approach than by standard finite element methods; the latter being unable to capture cellular buckling behaviour even though the phenomenon is clearly observed in laboratory experiments.