Cellular buckling in stiffened plates

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 with static finite element (FE) 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 FE methods; the latter being unable to capture cellular buckling behaviour even though the phenomenon is clearly observed in laboratory experiments.

Interactive buckling in long thin-walled rectangular hollow section struts

“…I-section struts [10,22] and stiffened plates [11]. These analytical models show very good quantitative comparisons with FE results and existing experimental results [9].…”

“…Since previous studies [31,32,10,11,26,27] have clearly demonstrated that it is essential to include the shear strain contributions into the total potential energy formulation to model the interactive buckling behaviour, Timoshenko beam theory is assumed currently. The global mode is decomposed into two components: a pure lateral displacement W and a pure rotation of the plane sections θ, see Figure 2, known as the 'sway' and 'tilt' modes [33,31] respectively.…”

“…The interaction between individual modes can lead to a profound change in the post-buckling behaviour, even though these modes may be stable when triggered in isolation. In particular, such systems can exhibit a violent destabilization after the peak load is reached [9,10,11] and, in certain parametric ranges, have been demonstrated to be highly sensitive to initial geometric imperfections [12,13,14,15,16,17,18,19].…”

Slenderness effects in thin-walled I-section struts susceptible to local–global mode interaction

“…Finally, for L < L l , the strut exhibits pure local buckling of the flange plates that is strongly stable. Note that for L l < L < L o , all interactive post-buckling equilibrium paths exhibit the sequential snap-backs signifying cellular buckling behaviour [11,7,6].…”

“…Structural members made from slender plate elements entirely under compression, or in part, are well known to be susceptible to a variety of different elastic instability phenomena [1,2,3,4,5,6,7,8,9,10]. In recent works [11,12], a variational model representing an open and doubly-symmetric thin-walled I-section strut under axial compression, made from a linear elastic material, was introduced where both local or global buckling could occur first.…”