An investigation on structural stability of ring stiffened cylindrical shells subjected to external pressure load

In this thesis, structural stability of ring stiffened cylindrical shells subjected to external pressure is investigated by using different methods. The reason why buckling of ring stiffened cylindrical shells under external pressure is chosen to study is that these type of structures are widely used as main structural component of submarine pressure hulls. Submarine pressure hulls generally consist of some basic structures. These are ring stiffened cylindrical and conical shells and unstiffened domes. In this study, only cylindrical shells are investigated. Ring stiffened cylindrical shells under external pressure cannot maintain their structural stability and collapse when the external pressure reaches to critical buckling pressure of the structure. The pressure that causes a submarine pressure hull to collapse is called as collapse pressure and it is a very important calculation for a submarine pressure hull design. This calculation is an ultimate strength calculation and one can find the limit load capacity of the ring stiffened cylindrical shells by applying this calculation and also several methods are available to perform this calculation. Analytical methods which some of the classification societies serving about classification of submarines, numerical methods (finite element method) and experimental methods are the methods used in this thesis. These methods were applied to twenty one small-scale ring stiffened cylindrical pressure hull models. Twenty of these models were generated with same material and only one parameter, distance between adjacent stiffeners, was changed when producing models. Twenty first model was produced with different material so its results were presented with discrete graphics. Both analytical and numerical methods were applied to determine the collapse pressures of 20 models and their results were presented graphically. Five models (model numbers: 5, 8, 10, 12, 21) were also manufactured with lathe and critical buckling pressures of these 5 models were determined experimentally by using a pressure chamber and their experimental results were compared with the results obtained by using analytical and numerical methods. In addition, divergences between the results were explained. Ring stiffeners in submarine pressure hulls are usually connected to cylindrical shells with a welding process. However, if very small-scale models are used, it is very difficult to satisfy enough similarity between small-scale and full-scale model. In addition, manufacturing welded very small-scale models is another challenge because welding includes heating process that can seriously affect shells in small thickness. Small-scale models were produced without a welding process for above reasons. They were manufactured by using a lathe machine. Firstly, thick drawn steel pipes are bought and their thickness is reduced with lathe machine. Therefore it was possible to have ring stiffened cylindrical shell models without using a welding machine. First of all, a pressure chamber was designed and manufactured in order to apply uniform external pressure to the models produced as ring stiffened cylindrical shells. Manufactured models are put in the pressure chamber that is already filled with water and the water inside pressure chamber is pressured gradually with a hand pump. While pressure in the tank is increasing, it is measured with a pressure sensor and it is recorded instantly to a computer. When reaching the critical pressure of the ring stiffened cylinder, the model buckles and pressure in the pressure chamber decreases simultaneously. The critical buckling pressure belonging to any model can be determined sensitively from the records on the computer. Ultimate strength problems require knowing the material properties in detail because of its considerable effects to the results. Therefore, tensile tests for the materials used to manufacture the models are performed. Reports of these tensile tests can be found in the annex of the thesis. Results of these tests are used in the analytical and numerical calculations. Ring stiffened cylindrical shells subjected to external pressure can buckle with three basic buckling modes. These buckling modes are asymmetric buckling, symmetric buckling and general instability and there are several analytical methods to calculate buckling pressure related to above buckling modes. Formulations belonging to Reynolds T.E., Lunchick M.E. and Bryant A.R. are used in order to determine critical buckling pressures belonging to above buckling modes respectively for the models generated in this thesis. Main principles of the above solutions are explained in this study. Buckling mode of ring stiffened cylindrical shell is said to be the minimum buckling pressure determined with above solutions. Finite element method was chosen as a numerical method to solve the problem numerically and ABAQUS packaged software was used in order to realize the analysis. Linear buckling analysis and nonlinear buckling analysis are performed with ABAQUS software. Elastic buckling load of a structure is determined by performing a linear buckling analysis (eigenvalue buckling analysis) but the load determined with this analysis is always higher than the load capacity of the real structure. Therefore, a nonlinear buckling analysis including nonlinear effects and initial shape imperfections that may appear in the manufacturing processes should be performed. Firstly, linear buckling analysis for all the models in this thesis performed and deformations obtained from these analyses are scaled in order to have a new imperfect geometry. Those geometries are used in the nonlinear buckling analysis. Modified Riks Method (Arc-Length Method) is used as a nonlinear solution technique. It is an iterative solution technique in order to investigate post-buckling behavior of unstable structures. Because finite element method is a numerical method which solves the problem with defined number of finite elements, it is necessary to determine right element size for reliable analysis. When decreasing element size, solution comes closer to real value. In buckling analysis, buckling load decreases through the actual value if element size decreases. On the other hand, decreasing element size increases computational time. Nonlinear buckling analysis is a time consuming analysis so it requires optimizing finite element size. In this study,optimization of element size was done by running a linear buckling analysis with model-5 and effects of element size to solutions and solution time were presented graphically. Solution time increases dramatically below 5 mm element size according to the graphics. Also, 5 mm element size was thought to be small enough to have a sensitive solution and this element size was used in all finite element analysis of all the models. One edge of ring stiffened model was closed with a 20 mm thick circular plate and displacements and rotations at the other edge of cylinder is assumed to be zero. Then, uniform external pressure is applied to all the surfaces including circular plate. Megapascal was used as a pressure unit in the finite element analysis so buckling pressure units of results of finite element analysis is also MPa but when comparing it was converted to another pressure unit called bar. It is possible to determine critical buckling pressure of ring stiffened cylindrical shells subjected to external pressure with experimental methods by using small-scale models. When producing a small-scale model, it is necessary to scale all dimensions with the same scale factor determined. Therefore, all the flaws in full-scale model should be similar in small-scale model. When a small-scale model satisfies all the requirements so that it can be similar to related full-scale model, critical buckling pressures of small-scale model is equal to critical buckling pressures of full-scale model. Thickness of the cylindrical shells of the models is wanted to be 1.5 millimeters and the buckling pressures of twenty one piece of models are calculated according to this thickness value. The results of this situation are presented in the comparison part of the thesis. On the other hand, models used in the experiments were wanted to have above thickness value (1.5 mm) but it was not possible to manufacture the models with the same and exact thickness value. Thus, pieces of shells were cut from the models to measure the real thickness values. The analytical and numerical results are updated according to measured thickness values. As a result, buckling mode of the models that are manufactured or not was estimated to be asymmetric buckling of shell between ring stiffeners from the analytical calculations and it was validated with the experimental results. It was observed that there is a very good consistency between analytical and numerical results. On the other hand, when analyzing the results of five model which were tested experimentally, it was observed that experimental buckling pressure of model-10 and model-12 have a very good agreement with the analytical and numerical calculations and experimental buckling pressures of model-5, model-8 and model-21 were remained under expected buckling pressures. Structural stability problems are considerably affected by initial geometric imperfections and defects in material. Therefore, Germanisher Lloyd presents the asymmetric buckling pressure formulation used in this study by multiplying with a reduction factor and all the experimental results of this study were higher than the final formulation of Germanisher Lloyd. Therefore, it can be said that dimensions of shells of the models used in this thesis are considered having enough thickness to meet the requirements of Germanisher Lloyd.