Dynamic Analysis of Large Shell Structures: Complex Damped Spectral Element Method

Abstract

The purpose of this paper is to present the Complex Damped Spectral Element method (CDSEM) for dynamic analysis of large shell structures. Most shell structures can be analysed and designed by using the conventional finite element (FE) method. However, in order to guarantee stability and accuracy of the solution, the number of elements used to model a structure may be very large indeed; more precisely, accurate results can be obtained only after a substantial computational effort. As a consequence, it appears that for designing a large shell structure it may be more effective to use alternative mathematical modelling techniques. In this respect, attention is paid to an alternative complex spectral approach which works in the frequency domain, and draws its robustness from the speed and switching capabilities of the Fast Fourier Transform (FFT). The spectral formulation starts at the same starting point as the conventional finite element formulation. However, it is formulated in the frequency domain. Consequently, spectral analysis concerns the synthesis of waveforms from the superposition of many frequency components. Using a fractional derivative model to describe the damping characteristic of materials, the non-linear damping behaviour of structural material has been modelled. The assembled system of equations is solved in the frequency domain, and is then transformed to the time domain using a FFT. The method is then used to analyse a large cooling tower structure.