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An Augmented Beam Element for Structural Dynamics Using Unit Deflection Shapes Gained on a 2D Finite Element Mesh of the Cross Section
Author(s) -
Müller Gerhard,
Kreutz Johannes
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310268
Subject(s) - finite element method , deflection (physics) , torsion (gastropod) , wavenumber , eigenvalues and eigenvectors , beam (structure) , torsion spring , computation , physics , geometry , mathematical analysis , structural engineering , mathematics , classical mechanics , optics , engineering , algorithm , medicine , surgery , quantum mechanics
Wave behaviour of line shaped structures can be analysed if 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 but reasonable deflection shapes of the cross section can be covered. The unit deflection shapes are defined and computed on the basis of a 2D finite element mesh of the beam cross section: warpshapes for primary and secondary torsion and shear forces, Eigenmodes for the problem of a plate in membrane and a plate in bending action, derived warpshapes for in plane shapes and shapes which cover the lateral strains. By this transformation of unknowns the number of system degrees of freedom can be reduced considerably. Expensive pre‐ and postprocessing steps can be done in parallel which opens the gate for massive performance gains. This method was validated in previous publications of the authors and shall now be extended using unit deflection shapes gained from eigenmodes of an infinite Fourier transformed structure obtained by solving a quadratic eigenvalue problem for the wavenumber k x . The results of both methods shall be compared. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)