Dear all
How spectral finite element differ from finite element method with respect to formulation? how it is useful in vibration analysis
The Spectral Element Method has been introduced by Patera in 1984 (A. T. Patera. Journal of Computational Physics, 54:468--488, 1984). This method is based on the weak/variational formulation of the differential problem and allows to increase the number collocation points inside each element. This strategy is similar to the well-known p-FEM.
If you want to know what are the advantages of using such formulation with respect to the vibration problem please take a look at review paper attached.
Moreover I suggest you to have a look at the work YUFENG XING, BO LIU, and GUANG LIU, Int. J. Appl. Mechanics 02, 207 (2010). DOI: 10.1142/S1758825110000470
Please note that weak form differential quadrature element method and spectral element methods are the same approach which may use different basis functions.
Which kind of problems would you like to solve using SEM?
Article Strong Formulation Finite Element Method Based on Differenti...
thank you for your useful information and suggestions.
Spectral Element Method (SEM) is one of the most efficient and accurate frequency-domain based methods. In this method, time-domain quantities of differential equations are transformed into frequency domain using the discrete Fourier transform (DFT) theory. the most important point in SEM is obtaining dynamic stiffness matrix.
I prefer to use force-displacement approach to obtain dynamic stiffness matrix. in this method, The relationship between nodal displacements and nodal force vectors should be determined to obtain the dynamic stiffness matrix.
I think all of the questions you may have, are answered in this book:
Lee, U. Spectral Element Method in Structural Dynamics. (1st Ed.). Singapore: John Wiley and Sons, 2009.
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