Proposal for an advanced wave guide element

Traditionally wave behaviour of line shaped structures can be analysed in case they are simply shaped (beams, rods, etc.) and if the frequency or wavelength is within a range where the underlying theories are still applicable. If the frequencies and wavelengths exceed these limits, the modelling of these line or beam shaped structures is only possible using volume elements which results in considerably high computation time and modelling effort. The idea of this work is to keep the beam like modelling of structures but enhance the solution space such that arbitrary, reasonable deflection shapes of the cross section can be covered. The concept is in analogy with the concept of warping torsion of beam elements. New degrees of freedom are introduced at the nodes which correspond to the contribution of a unit deflection shape at each node. The unit deflection shapes can contain either out of plane or in plane deflections which are defined on the basis of a 2D finite element mesh of the cross section. With the help of this mesh also the stiffness matrix entries for the degrees of freedom are computed. The shapes for the unit deflection modes are obtained with various procedures making use of the Finite Element mesh of the cross section. The number of considered shapes can be chosen according to the requirements on accuracy, the expected deflection shape and frequency range of excitation. "Higher modes" can be neglected and thus an adaptive and efficient solution scheme is obtained. Due to the structure of the problem with its comparably small number of system's unknowns it is computationally inexpensive. The setup of the system stiffness- and mass matrices and the computation of stresses (postprocessing) is computationally expensive but well suited for parallelisation. This property opens the gate for massive performance gains since also modern core architectures can be made use of in an optimal way.