Nonlinear analysis of imperfect metallic and laminated cylinders under bending loads

The nonlinear buckling of imperfect metallic and laminated cylindrical shells under axial compression, bending, and a combination of compression and bending is investigated. The effects of length-to-rad ius ratio, radius-tothickness ratio, imperfection shape and amplitude, and boundary conditions on critical loads are considered. The finite element method is employed and the ANSYS computer code is selected to generate results. The effect of transverse shear deformation is included in the analysis. To acquire confidence in the solution methodology, results are produced and compared with those available by other solution techniques (analytical verification). Then, numerical results reflecting a wide range of length-to-radius ratios, radius-to-thickness ratios, and various imperfection shapes and amplitudes are presented and discussed. Among all conclusions, the most important one is that imperfection shapes substantially affect the critical loads. For each cylindrical configuration analyzed, certain imperfection shapes can be found, which make the cylinder extremely imperfection sensitive. HE primary consideration for designing and sizing jet engine casings is buckling under dynamic conditions. The loads that cause buckling are generated by the large forces resulting from rotor unbalance as a result of bladeout (loss of one or more blades during operation). These loads induce an end bending moment on the casing that is time dependent both in magnitude and direction. This bending moment is of finite but small duration. The time in which this moment reaches a peak value and vanishes is very short. The engine casing geometry can be approximated by a cylindrical shell. This configuration has numerous applications in real world structures. Airplane fuselages, submarine hulls storage bins, and missiles are but a few examples. Many times during service these systems are subjected to suddenly applied loads, such as blast loads on airplanes and submarine hulls and gust loads on storage bins and missiles. All of these situations can be simulated by cylindrical shells under dynamic bending moment or a combination of compressive and bending loads (Fig. 1). For jet engine casings, the current practice is to estimate the peak moment, consider it as a static bending moment, and compare it with the static critical condition (buckling) of cylindrical shell under bending moment. This procedure has led to designs that are very conservative according to data from experimental verification studies. The weight penalty in most cases is in the 30-50% range. Moreover, since a large number of new casings are made of polymeric matrix composite materials and since the static analytical methods for these configurations are of questionable value, the weight penalty can exceed the 30-50% range. Therefore, it is necessary to predict the static and dynamic critical loads of cylindrical shells under aforementioned loading conditions and to provide information that can be used in designs of cylindrical structures. In this paper, the static stability of metallic and laminated cylinders is studied and the following points are emphasized. 1) Cylindrical shells are subjected to axial compression, bending moment, or a combination of both loads. 2) Cylinders are geometrically imperfect. The effects of imperfect shapes and amplitudes on critical loads are discussed. Also,