شبیه سازی عددی پانل های سخت آلومینیومی تحت فشار محوری: تجزیه و تحلیل حساسیت اولیه از عیوب هندسی و خواص مواد

In the present work, a set of finite element analyses (FEA) was carried out, using Abaqus to reproduce the mechanical behaviour of integrally stiffened panels when subject to longitudinal compression. Since most fabrication processes, such as welding, introduce distortions and affect the material properties, the sensitivity to these defects was assessed. Different shapes and magnitudes of the initial geometrical imperfections were tested and a high sensitivity was observed to both factors on the ultimate load. The existence of a heat affected material showed no influence on the ultimate strength of the tested panels.

Stiffened panels are often the basic structural building blocks of airplanes, vessels and other structures with high requirements of strength-to-weight ratio. They typically consist of a plate with equally spaced longitudinal stiffeners on one side, and often with intermediate transverse stiffeners [1]. Large aeronautical and naval parts are primarily designed based on their longitudinal compressive strength. The structural stability of such thin-walled structures, when subjected to compressive loads, is highly dependent on the buckling strength of the structure as a whole and of each structural member. A typical load vs. end-shortening curve, as obtained from a stiffened panel subjected to longitudinal comprehensive loads, is illustrated in Fig. 1, where distinct load–displacement regions are visible. The stiffness of a panel is reduced after buckling, as the panel enters a post-buckling regime after the ultimate load is reached, with the consequent failure or collapse [2]. After the start of buckling, a phenomenon of “mode-switching” may occur, with the panel changing the buckling patterns for increasing load levels [3] and [4]. Full-size image (22 K) Fig. 1. Typical behaviour of a stiffened panel subjected to longitudinal compressive loads (adapted from Ref. [7]). Figure options Aluminium stiffened panels have been used for a long time in airplane structures, as aluminium alloys have been the primary material of choice in the aeronautical industry since the 1930s [5]. Design methods in this field were initially based on Euler's column buckling theory as well as on Timoshenko's theory on the elastic stability of plates and shells. The use of aluminium in the construction of high speed commercial and military vessels rapidly expanded since the early 1990s, mostly due to their higher strength-to-weight ratio when compared to steel structures [6]. Naval structural design analyses have been typically simplified and experience-based [2], mainly relying on empirical methods. In the meanwhile, specific software packages have been developed (e.g. DNV PULS, ALPS/ULPAC, Hypersizer) in order to reduce the calculation time of the ultimate load on stiffened panels. The EUROCODE 9 [8] and the US Aluminium Association Specifications [9] design codes also take into account the calculation of the ultimate strength of a stiffened panel. However, some of the previously referred methods have limitations related to the simplicity of boundary conditions that can be used, constitutive behaviours (often assumed as elastic) and geometrical configuration of the panels. Therefore, the prediction of critical loads does not always show good accuracy when compared to experimental results [2]. The use of the finite element method (FEM) can lead to higher levels of accuracy and generality, being suitable for generic case studies. Distinct FEM models, with different element formulations and mesh densities were used to study the behaviour of aluminium panels in a number of works in the literature (e.g. Abaqus [10], [11], [12], [13], [14] and [15], ANSYS [1], [16], [17] and [18], LS-DYNA [18], ULSAS [18] and MSC Marc [18], to name but a few). The manufacturing process of stiffened panels often involves welding operations necessary to join the stiffeners to the skin plates (as in build-up panels), or to join together integrally stiffened panels (ISP), that are basically modular structures including the base plate (skin) and the stiffener (stringer) in a single component directly obtained by extrusion operations. The heat added and conducted in the pieces to be joined can influence the structural efficiency of the final set, since it affects the quality of the panels in terms of: geometrical distortions, build-up of residual stresses and significant changes in the properties of the materials in the heat affected zone (HAZ) [19]. These changes are less significant for the friction stir welding (FSW) process than in the traditional welding processes, like MIG [19] and [20]. One main concern using the FEM in the study of the behaviour of such structures is the initial imperfection modelling. Imperfections are normally introduced into finite element models in order to provide a triggering for the initiation of buckling in the numerical simulation. Considering the use of geometrical imperfections, several authors have concluded that the shape and magnitude of the initial imperfections significantly affect the behaviour of a stiffened plate [16], [18], [21] and [22]. Different methods were used to take into consideration these initial imperfections in the analysis of aluminium stiffened panels, such as: – previous deflection of the panel using pressure in one side of the plate [1], [16] and [18]; – from the analysis of buckling modes [11]; – displacement of the transversal central nodes of the panel [10] and [14]; – displacement of the nodes based on equations (as used by Paik et al. [17]). Examples of those equations are presented and used by Zhang et al. [23] for steel panels analyses and – displacement based on measured imperfection in the experimental panels [21] and [22]. In concerning the properties of the HAZ materials, their modelling properties have been presented by several authors [1], [14], [16], [18], [20] and [24]. They were considered in some FEM models in order to study their influence in the panels' strength behaviour. Literature reported that it can significantly reduce the ultimate strength of the panels when compared to those with original unaltered material properties [1], [14], [16] and [18]. In order to provide a comprehensive and global analysis of the behaviour of ISP under compressive loads, the present work proposes and describes a methodology and the corresponding finite element formulations and models able to reproduce the behaviour of these structures. The sensitivity of the obtained results to the shape and magnitude of the initial geometrical imperfection fields is assessed, as well as the influence of a heat-affected material in the HAZ.

The shell finite elements models developed in the present work were shown to be able to correctly predict the complex behaviour of stiffened panels when subjected to compressive loads, and particularly the ultimate load level, in the presence of elasto-plasticity. Although for the model L the post-buckling load evolution coming from numerical simulations did not perfectly correlate to the available experimental data, the ultimate load was nevertheless predicted with very good accuracy. Additionally, it was shown that both tested models (models TR and L) were highly sensitive to initial imperfections, either in terms of their shape or in terms of their magnitude. Maximum variations of 14.9% and 22.4% were observed using the same 2 mm magnitude and different shapes for model TR and L, respectively. It was also observed that the increase of the magnitude of the imperfections has a significant influence in the variation trend of the ultimate load levels, depending on the shape chosen for the imperfection. For most of the initial imperfection shapes, a decrease on the ultimate load as the magnitude of the imperfection increases was observed, although for some shapes the opposite trend was also verified. The imperfection shapes obtained from the pre-performed analyses without imperfection, from the moment of collapse (COL), led to the determination of the minimum ultimate load values, or closer, for a defined imperfection magnitude. This kind of imperfection shape led to ultimate load variations of up to 14.4%, when considering a magnitude interval in the range of 0–2 mm. The inclusion of a material with heat-affected properties in the HAZ was shown to not significantly affect the ultimate load value, when compared to the results obtained from models considering the original plate material properties in the same zone. Therefore, as an overall conclusion, it was demonstrated that a reliable ultimate load prediction in the presence of compressive loads should be preceded by a careful assessment of geometric imperfections that are used in the initial model, being their influence more significant than the one coming from the constitutive parameters in the HAZ in the studied panels.