Buckling of Thin Cylindrical Shells under Axial Compression

  • Zia Ul Rehman Tahir

Student thesis: Phd


Buckling of thin cylindrical shells under uniform axial compression is a long-standing problem in which the experimental buckling load is much lower than the theoretical prediction. There is a huge scatter in the experimental data of nominally equivalent shells, and failures are often catastrophic. "Imperfection-sensitivity" is the commonly accepted reason for the above. The classical theory of buckling of axially loaded thin cylindrical shells predicts that the buckling stress is directly proportional to the ratio of thickness to diameter (t/R), other things being equal. Whereas an empirical evaluation of the experimental data shows that the buckling stress is proportional to (t/R)1.5.The main aim of this research was to resolve the aforementioned paradoxical issues and develop a better understanding of the phenomenon of shell buckling. A comprehensive literature review was undertaken and an up-to-date database of previous experiments was developed. The database was systematically analysed against the reported parameters using standard regression analysis. Effect of any hidden combination of parameters was evaluated by the artificial neural network (ANN) model using the back-propagation method. A validated model was able to predict the buckling load within 10% of the experimental values. It was also observed that the load factors for metals specimens were higher than non-metals. Manufacturing techniques have a noticeable impact on buckling load, for example, shells produced by electroforming had relatively higher buckling strength.It has been reported in the literature that buckling is often initiated by initiation and growth of dimples. To test the effect of isolated dimples on buckling load, a set of experiments was undertaken. The shells were manufactured using PETE with nominal radius-to-thickness ratio of 175 and length-to-radius value of 3.125. The specimens with an isolated dimple had load factor from 0.4 to 0.5. A consistent post-buckling plateau load was observed for all the tested specimens and the failure mode consisted of two tiers of circumferential dimples. Repeated loading on specimens showed that the difference between the bifurcation load and post-buckling plateau load is high in the first test run due to the formation of sharp creases at the edges of the dimples and considerably lower in subsequent runs. This highlighted the need to use an appropriate imperfection shape in numerical simulations in order to obtain the stable post-buckling loads, which has implications for design. In this study, the effect of generalized imperfections in the form of different modes shapes was studied, and it was observed that the axisymmetric imperfection yields lowest load factor. The effect of imperfection in the form of an isolated dimple at the mid-height of the numerical model was studied using Single Perturbation Load Approach (SPLA) and the results agree well with the experimental values. Different shape and magnitude of imperfections were also introduced using asymmetric meshing technique (AMT). It was observed that asymmetric meshing in the form of band or patch affects both buckling loads and buckling mode shapes for linear eigenvalue analysis and affects buckling mode shapes and load-deflection curve behaviour in the post-buckling region for non-linear analysis. The buckling load decreases as the size of patch or band having asymmetric meshing increases, the reduction in buckling load is strongly related to the area of asymmetric meshing and has a weak relationship with the amplitude of asymmetry. The load-displacement behaviour of cylindrical shells under axial compression by using AMT has similar characteristics to that observed in conventional simulations with an initial geometric imperfection.
Date of Award1 Aug 2016
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorParthasarathi Mandal (Supervisor)


  • Cylindrical shells
  • Artificial neural network
  • Finite-element method
  • Single Perturbation Load Approach
  • Asymmetric Meshing Techniques

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