Finite Tube Method for buckling analysis of tubular members using Fourier-approximation for the displacements

In this paper an efficient numerical method for the static analysis of cylindrical tubes is introduced. The method is designed for the linear buckling analysis of wind turbine support towers which are, most typically, built up from conical and/or cylindrical cans. Accordingly, the developed method uses cylindrical tube segments as elementary building blocks, along with specialized shape functions, and is named the Finite Tube Method. Within a tube segment the displacements are approximated by two-dimensional Fourier series. The curved nature of the surface is directly considered in the kinematic equations. The segments are joined and/or supported to the ground by constraint equations or by elastic links. In the current implementation internal stresses are determined in a simplified way: the circumferential stress distributions are calculated from the internal forces/moment by classic strength of material formulae, while the longitudinal distribution within each segment is quadratic. The considered internal forces/moments are: normal force, shear force, bending moment, and torsional moment. The internal forces can be arbitrarily combined. In the paper the underlying derivations are briefly summarized, then the method is demonstrated and validated by numerical examples, comparing the results to analytical and alternative numerical solutions. The authors are actively developing the method and will provide future work on utilization of the method for buckling mode identification and decomposition, as well as practical advancements to make the method a useful tool in the engineering design and analysis of wind turbine support towers.