Cracks of any size may occur at various locations and orientations throughout thin-walled structures. The presence of cracks in such structures can considerably affect their load bearing behaviour. This paper addresses a finite element study on the buckling strength of a cracked plate with simple supports subjected to an axial compressive edge load. The effects of crack location, crack orientation, crack length and plate aspect ratio are analysed. The size of the crack as well as its location and orientation are shown to have significant effects on the buckling behaviour of the plate under compressive loading. Some new results are also discussed in detail.
Plates are the most common structural elements used in the majority of thin-walled structures, dealing with the fields of naval architecture, civil, mechanical, and aerospace engineering. Ships and offshore structures are some examples of intricate thin-walled structures that consist of plate elements, which are subjected to a variety of load combinations. An ageing thin-walled structure is vulnerable to various types of defects and damages induced by different phenomena such as corrosion and fatigue cracking. It is of crucial importance, from many design and safety aspects, to study and understand both behaviour and strength of such plate elements in intact, defected and damaged conditions. The importance is well understood on the failure events that have led to the loss of life.
The strength characteristics and behaviour of plates with a crack have received some attention by numerous investigators in recent years. Some of the researchers have studied the problem under tensile loads [1], [2], [3], [4], [5] and [6]. Brighenti [5] and [6] in his latest works has calculated the critical load multiplier for a cracked plate in tension. In his studies, some parameters were changed and finally an approximate theoretical model to explain and predict the buckling phenomena in cracked plates under tension was proposed. Crack influences on the vibration and parametric instability of plates were also studied by some of the researchers [7], [8], [9], [10] and [11]. Paik et al. in his extensive work [12] made a numerical/experimental study on the collapse behaviour of plates with crack under both tensile and compressive loads. They finally derived the ultimate strength formulations for such cases. The influence of central cracks on buckling and post-buckling behaviour of shear panels was studied by Alinia et al. [13]. They have reached the conclusion that the mesh density at crack tips exceptionally plays a dominant role in the numerical accuracy, but the vicinity of crack sides may have the mesh refinement similar to uncracked panels.
Besides, the problem of cracked plate elements under compression was the subject of few research studies [1], [5], [6], [10], [11] and [14]. Most of these studies were performed on the plates with either central or perpendicular-to-one-edge crack of varying crack length. A crack in a plate element may be generally observed at any location and orientation. The initiation of such a crack may be due to fatigue, impact, imperfections and so on. No extensive studies have been published yet, according to the authors’ knowledge and literature survey, on the buckling analysis of cracked plate elements under compression, including all affecting parameters such as crack location, orientation and size. In this regard, the objectives of the present study are: (i) to investigate the buckling strength characteristics of a cracked plate under monotonically applied axial compression and (ii) to study the sensitivity of the buckling strength of cracked plate elements under axial compression to the crack size, location and orientation.
To do so, a series of eigenvalue buckling analysis on cracked plate elements under axial compression is carried out using an in-house finite element (FE)-based program. Due attention has been focused on FE modelling of the problem and the significance of various parameters such as the crack size, location and orientation. The research findings by Javidruzi and his collaborators in their earlier works [10] and [11], are incorporated into the FE modelling of the problem. The present study does not aim to address crack propagation scenarios and fracture related to the critical crack length considerations.
In the present paper, the elastic buckling phenomena of variously cracked plates under compression has been considered.
An in-house general purpose FE program is developed in order to perform elastic buckling analyses to determine the buckling coefficients, by varying some cracked plates’ parameters. In particular, the effects of the crack length, crack orientation and crack location on the buckling phenomena have been investigated. Two distinct cases, in which the cracks are located either on the edge or inside the plate, have been studied. Also, effect of the plate aspect ratio on its buckling characteristics in the cracked situation has been investigated.
Numerical investigations have shown that the behaviours of the cracked plate are entirely different when the crack is either on the edge or inside the plate. For an internally cracked plate, the buckling behaviours and coefficients change at the orientation angle θ=45°. In other words, the plate with an internal crack behaves in different ways when the crack orientation is less or more than 45°.
For an edge-cracked plate, it is observed that with the increase of the orientation angle, buckling coefficient first increases and then decreases. The amount of increase is a direct function of the orientation of the crack.
In both cases, for cracks either on the edge or inside the plate, the plate aspect ratio is also an influencing parameter. Changing the plate aspect ratio leads to different rates and extents of changes in the sensitivity curves of the buckling coefficient of the cracked plate.
Also in the case of an internally cracked plate, the crack parameters (crack size, crack orientation and crack location) may have large effects on the buckling mode of the plate, causing some irregularities in it. Depending on the relative size and orientation, the crack may fall within the buckling half-wave with the largest amplitude, thus leading to the increase in the crack gap.
