Exact Timoshenko Pipe Element for Dynamic Analysis of Offshore Platforms

During the past three decades, problems of vibration of tubular structures have been considered by some authors, and special attention has been devoted to the Timoshenko theory. There have been considerable efforts, also, to apply the method of spectral analysis to vibration of a structure with tubular section beams. As the conventional finite element method requires many elements to model the mass distribution adequately, the computer power and time needed for dynamic analysis of large complex tubular structures is substantial. In essence, attention is paid to the alternative spectral approach, which works in the frequency domain and draws its robustness from the speed and switching capabilities of the Fast Fourier Transform. As the only way to efficiently solve problems with complicated boundaries and discontinuities is to develop a matrix methodology for use on a computer, the mathematical basis of the spectral element method can be used to develop a numerical method using matrix methodology. The purpose of this paper is to compare the results of the improved non-linear complex spectral element method for the Timoshenko theory with those derived from the conventional finite element method for an offshore structure. Using a computer program, the proposed formulation has been extended to derive the non-linear dynamic response of an offshore platform structure under dynamic loads.

Keywords:

spectral element , finite element , Timoshenko pipe element , offshore platform