Experimental investigation of buckling of wind turbine tower cylindrical shells with opening and stiffening under bending
Introduction
Shells, due to their importance as structural elements in many engineering structures, have been receiving a great attention by scientists. Their response has been investigated both experimentally and numerically, especially when it comes to cylindrical shells under axial compression or bending.
Axial compression tests in the elastic region were conducted by Lundquist [1], Tennyson [2], Weingarten et al. [3], Schneider et al. [4] and Athiannan and Palaninathan [5] just to name a few. In the inelastic region some experimental work on axially compressed shells is that of Lee [6], Batterman [7], Osgood [8], Horton et al. [9], Bardi et al. [10] and Bardi and Kyriakides [11].
It is well known nowadays that the experimental buckling loads of very thin shells in compression, which buckle in the elastic region, exhibit a wide scatter and may be significantly lower than the classical analytical predictions. This phenomenon can be attributed mainly to the inevitable geometrical imperfections and secondarily to loading eccentricities, boundary conditions and variability in thickness and material properties. As the shell slenderness decreases the effect of those factors on the collapse loads becomes less significant.
As far as the bending loading is concerned, some experimental work on thin shells is that of Mossman and Robinson [12], Rhode and Lundquist [13], Imperial [14], Lundquist [15], [16], Donnell [17]. In the studies of Suer et al. [18] and Mathon and Limam [19], the effect of the internal pressure was also taken into account. In the inelastic region, experiments for the case of pure bending have been carried out by Moore and Clark [20], Jirsa et al. [21], Sherman [22], Tuggu and Schroeder [23], Reddy [24], Kyriakides and Shaw [25] and Kyriakides and Ju [26]. In the work of Johns et al. [27], Corona and Kyriakides [28] and Ju and Kyriakides [29] the effect of external pressure on the bending strength of the shells was also included.
The aforementioned references concerned shells without any geometrical discontinuity on their surface. However, in some engineering structures, such as wind turbine towers, chimneys and tanks, it is mandatory to provide openings in order to fulfill various practical needs, such as manholes. The effect of openings on the shell strength was investigated in a number of experimental works. In some cases, the effect of stiffening of the opening on the collapse load of shells was also considered due to its practical importance. Typical experimental studies of axially compressed shells with openings are those of Starnes [30], [31], [32], [33], Tennyson [34], Toda [35], [36], [37], [38], Schulz [39], Almroth and Holmes [40], Bennet et al. [41], Han et al. [42] and Shariati and Rokhi [43].
In the case of shells with openings under bending, experimental work has been carried out by Yeh et al. [44], Poursaedi et al. [45] and Knödel and Schulz [46]. Yeh et al. [44] studied the elasto-plastic buckling of aluminum cylindrical shells with unreiforced cut-outs with orthogonal or circular shape under the state of pure bending, both experimentally and numerically. The ratio of diameter to thickness was equal to 50 while the ratio of length to diameter was equal to 7.9. Poursaedi et al. [45] studied the plastic buckling of stainless steel cylindrical shell with rectangular or circular cut-outs under bending. The diameter to thickness ratio of the specimens was 40.4 and their length to diameter ratio was 7.94. In contrary to previous work, Knödel and Schulz [46] studied experimentally the strength of cylindrical steel shells with rectangular cut-outs, with chamfered angles, under bending. The effect of stringer stiffeners of various cross-section profiles on the strength was also studied. However, the slenderness of their specimens was, in general, significantly larger than values corresponding to wind turbine towers. Moreover, in the few cases with lower slenderness, the angles of their openings was significantly larger (in the order of 120°) than the typical openings of wind turbine towers (approximately 25°).
More experimental work on steel cylindrical shells with reinforced or unreinforced rectangular cutouts under bending are those of Baehre and Knödel [47] and Öry et al. [48]. As in the case of Knödel and Schulz experiments [46], in these two studies, either the angles of the openings and/or the slenderness of the specimens are generally larger than those encountered in wind turbine towers.
To the authors’ knowledge no previous experimental work has been carried out that is especially designed so as to correspond to wind turbine towers, which exhibit specific geometrical and loading characteristics. In order to cover this gap, an experimental study is presented in this paper which focuses on the buckling behavior of cantilever shells with opening and stiffening that reflect the main geometric characteristics of wind turbine towers. The specimens are loaded with a prescribed transverse displacement at the end of the cantilever, thus making bending the predominant action. Both load–displacement curves as well as strain measurements at a number of characteristic positions of the external surface of the shells are presented. These results are compared with numerical analyses performed with the commercial finite element program ABAQUS [49]. Three different refinement levels of numerical modeling are presented, which are characterized by different levels of accuracy. In the less satisfactory model, the presence of bolts tying the flanges is neglected and the support is considered to be fully clamped. In the most accurate model, the interaction of bolts and flanges and the interaction between flanges as well as a partially clamped support are taken into account.
Section snippets
Geometric characteristics of specimens and experimental set-up
A total number of six shells with the same overall geometry were tested, among which the first two had no opening, the next two had an unstiffened opening near their base, while in the last two the opening was stiffened. The shape of the opening was rectangular with elliptical ends and the stiffening, when used, was a frame welded around the opening. The geometrical characteristics of these shells (external diameter, thickness, cut-out dimensions and stiffening) were chosen in such a manner as
Material characteristics of specimens
Due to the overstrength of all other parts, only the material properties of the second part have been extracted through tensile tests. The true stress–plastic strain plots for the material of the three blocks are given in Fig. 9. This material behavior was used in the numerical simulation described below. For the shells of parts “Block 14” and “Block 16” the Young’s Modulus was equal to 206 GPa while the yield stress, taken equal to the 0.2% proof stress, was equal to 272 MPa. The stiffeners of
Description of numerical models
For the numerical computations, the commercial finite element analysis program ABAQUS [49] has been used. In order to maintain an acceptable level of accuracy and at the same time build a numerical model that is computationally effective in terms of computation resources and solution time, in the basic numerical model the presence of the test frame and the interaction of the plate of block 10 with the frame column were ignored. This type of interaction was, however, found to be important when
Numerical estimation of support flexibility
For the estimation of the support flexibility, the numerical model of Section 4.1 has been analyzed and the results obtained are described in Fig. 13, Fig. 14. Both geometrical and material nonlinearities were taken into account. The concentrated vertical force that loaded the structure was equal to one half of the collapse load obtained from a pre-test numerical analysis of the cantilever specimen. The applied horizontal bending moment was calculated using the concentrated load multiplied by
Effect of buckling mode imperfection on shell strength
All previous numerical analyses referred to a perfect structure (GMNA analyses). In this section the results of a numerical study based on GMNIA analyses are presented. In these analyses the first buckling mode was considered as initial imperfection, which is a common choice in nonlinear analyses as it is computed easily with finite element codes and leads in many cases to the lowest ultimate load. Despite these obvious advantages, it is well known that this type of imperfection may not be the
Effect of cut-out position on the collapse load
As mentioned above, the effect of the direction of the bending moment with respect to the cut-out was studied by Yeh et al. [44], where the buckling due to bending of an elastoplastic cylindrical shell with unstiffened cut-out was studied both experimentally and numerically. The most severe case leading to the lowest collapse bending moment was found to be the case where the cut-out was situated on the compression side. The maximum collapse load was obtained when the cut-out was on the neutral
Conclusions
The effect of opening and stiffening on the strength of cylindrical shells has been investigated both experimentally and numerically. The geometrical parameters of the shells as well as those of opening and stiffening were chosen in such a manner so that they reflect the main geometric characteristics of wind turbine towers. The shell specimens were of a cantilever type and the type of loading was a transverse imposed displacement at the end of the cantilever.
The experimental study revealed
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Alternative ring flange models for buckling verification of tubular steel wind turbine towers via advanced numerical analyses and comparison to code provisions
2023, StructuresCitation Excerpt :Local buckling of shells is discussed in traditional textbooks [26,27]), but continues to attract the attention of researchers, both in a generic manner [28–32] and also targeted specifically to tubular wind turbine towers [33,34]. Specifically, the effect on buckling strength of an unstiffened or stiffened cutout, such as the man door near the base of tubular wind turbine towers, has been studied experimentally as well as numerically in [35–37] and under dynamic loads in [38–41]. The behavior and design of ring flange connections between sections are addressed in [42] and [43], while their beneficial effect to buckling strength, associated with their action as stiffeners, is studied in [44].
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