Thin-walled carbon fiber reinforced plastic (CFRP) shells are increasingly used in aerospace industry. Such shells are prone to the loss of stability under compressive loads. Furthermore, the instability onset of monocoque shells exhibits a pronounced imperfection sensitivity. The vibration correlation technique (VCT) is being developed as a nondestructive test method for evaluation of the buckling load of the shells. In this study, accuracy and robustness of an existing and a modified VCT method are evaluated. With this aim, more than 20 thin-walled unstiffened CFRP shells have been produced and tested. The results obtained suggest that the vibration response under loads exceeding 0.25 of the linear buckling load needs to be characterized for a successful application of the VCT. Then the largest unconservative discrepancy of prediction by the modified VCT method amounted to ca. 22% of the critical load. Applying loads exceeding 0.9 of the buckling load reduced the average relative discrepancy to 6.4%.

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Nondestructive methods, to calculate the buckling load of imperfection sensitive thin-walled structures, such as large-scale aerospace structures, are one of the most important techniques for the evaluation of new structures and validation of numerical models. The vibration correlation technique (VCT) allows determining the buckling load for several types of structures without reaching the instability point, but this technique is still under development for thin-walled plates and shells. This paper presents and discusses an experimental verification of a novel approach using vibration correlation technique for the prediction of realistic buckling loads of unstiffened cylindrical shells loaded under axial compression. Four different test structures were manufactured and loaded up to buckling: two composite laminated cylindrical shells and two stainless steel cylinders. In order to characterize a relationship with the applied load, the first natural frequency of vibration and mode shape is measured during testing using a 3D laser scanner. The proposed vibration correlation technique allows one to predict the experimental buckling load with a very good approximation without actually reaching the instability point. Additional experimental tests and numerical models are currently under development to further validate the proposed approach for composite and metallic conical structures.

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With the evolution of composite materials and moreover of the manufacturing process of large composite structures, a new window of possibilities is opened from the optimization point of view. Currently, one has great materials and reliable manufacturing processes than can be used for extremely optimized structures. The problem is that even nowadays some calculation processes make use of design guidelines based on data from 50 years ago, which limits the optimization process due to outdated allowables and process tolerances, increasing the final cost of the structure and putting on the edge the reliability of the entire design process. Currently, imperfection sensitive shell structures prone to buckling are designed according to the NASA SP-8007 guideline, dating from 1968, using its conservative lower bound curve. In this guideline the structural behaviour of composite materials is not appropriately considered, since the imperfection sensitivity and the buckling load of shells made of such materials depend among other things on the layup design as well. In this context, a numerical investigation about the different methodologies to characterize the behaviour of imperfection sensitive composite structures subjected to compressive loads up to buckling is presented. A benchmark test is developed using a 500 mm diameter unstiffened composite cylindrical shell. A series of non-linear analyses considering geometric and thickness imperfection, obtained from real measurements, are carried-out to characterize the knock-down factor of the benchmark test. The effect of each type of imperfection on the knock-down factor is compared against the experimental results.@en

Nondestructive methods, to calculate the buckling load of imperfection sensitive thin-walled structures, are one of the most important techniques for the validation of new structures and numerical models of large scale aerospace structures. The vibration correlation technique (VCT) allows determining the buckling load for several types of structures without reaching the instability point, but this technique is still under development for thin-walled plates and shells. This paper presents and discusses an experimental and numerical validation of a novel approach, using the vibration correlation technique, for the prediction of realistic buckling loads on unstiffened cylindrical shells loaded in compression. From the experimental point of view, a batch of three composite laminated cylindrical shells are fabricated and loaded in compression up to buckling. An unsymmetric laminate is adopted in order to increase the sensitivity of the test structure to initial geometric imperfections. In order to characterize a relationship with the applied load, the first natural frequency of vibration and mode shape is measured during testing using a 3D laser scanner. The proposed vibration correlation technique allows one to predict the experimental buckling load with a very good approximation, without actually reaching the instability point. Furthermore, a series of numerical models, including non-linear effects such as initial geometric and thickness imperfection, are carried-out in order to characterize the variation of the natural frequencies of vibration with the applied load and compare the results with the experiment findings. Additional experimental tests are currently under development to further validate the proposed approach for metallic and balanced composite structures.

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Imperfection sensitive structures such as unstiffened or skin-dominant shell structures are commonly used for aeronautic and aerospace applications. Cylindrical shells are dominating satellite launcher structures and a reliable methodology to calculate their behaviour in the early stages of design is fundamental to achieve optimum results. Launcher design requires fast and precise prediction of structural weight as well its weight distribution already in the early design phase, because in that phase different concepts of the whole launcher system have to be evaluated in order to identify the optimal one. The prediction has to be precise, because less reliable ones might lead to basic changes, later in the detailed design phase, which might also influence the design of the whole system. Such changes in later design phases are extremely costly in terms of time and money; they definitely have to be avoided. The dimensioning criterion with the design of launcher structures is buckling not before ultimate load, thus they do not have an exploitable post-buckling area. The most critical aspect for numerical buckling prediction is the structure's sensitivity to geometric and loading imperfections. Currently, imperfection sensitive shell structures prone to buckling are designed according to the NASA SP-8007 guideline [1], from 1968, using its conservative lower bound curve. In this guideline the structural behaviour of composite materials is not appropriately considered, since the imperfection sensitivity and the buckling load of shells made of such materials depend on the lay-up design. There is no specific design guideline for imperfection sensitive composite structures prone to buckling. NASA performed high investments for the last 5 years with one project called "Shell Buckling Knock-down Factor" (SBKF) in order to develop a new guideline to calculate the knock-down factor of cylindrical shells prone to buckling [2], and also the European project DESICOS [3] (New Robust DESign Guideline for Imperfection Sensitive Composite Launcher Structures) is working on new methodologies to estimate the ultimate load of such structures. An example of applicability of these new design guidelines could be the next generation of the European launchers family "Ariane" in order to maintain the actual position in the satellite launchers market [4].

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Nondestructive experimental methods to calculate the buckling load of imperfection sensitive thin-walled structures are one of the most important techniques for the validation of new structures and numerical models of large scale aerospace structures. Vibration correlation technique (VCT) allows determining equivalent boundary conditions and buckling load for several types of structures without reaching the instability point. VCT is already widely used for beam structures, but the technique is still under development for thin-walled plates and shells. This paper intends to explain the capabilities and current limitations of this technique applied to two types of structures under buckling conditions: flat plates and cylindrical shells prone to buckling. Experimental results for a flat plate and a cylindrical shell are presented together with reliable finite element models for both cases. Preliminary results showed that the VCT can be used to determine the realistic boundary conditions of a given test setup, providing valuable data for the estimation of the buckling load by finite element models. Also numerical results herein presented show that VCT can be used as a nondestructive tool to estimate the buckling load of unstiffened cylindrical shells. Experimental tests are currently under development to further validate the approach proposed herein.

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