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.
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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 lik...
»
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