M. Fleischmann, A. Heinrich:
"Beitrag zur Theorie der Wölbkrafttorsion I. Ordnung für abgeknickte Stabzüge und Durchführung von grundlegenden Vergleichsrechnungen mit Hilfe der Methode der Finiten Elemente"; TU Wien, Institut für Stahlbau, 2000.
Vlasov's warping torsion theory (first order theory) is only applicable for straight thin-walled beams of uniform cross-sections.In this master's thesis the classical theory is modified for thin-walled composite beams of arbitrary cross-sections using the transfer-matrix-method. The entire transfer matrix is made up of field transfer matricies and dot matricies (chapter 3). Field matricies are obtained by integrating the differential equations. Dot matricies include compatibility conditions, equilibrium conditions, single-loads and springs acting at the nodal points.
In chapter 4 two numerical examples are presented. In both cases thin-walled composed beams of I-shaped cross-sections under warping torsion are analysed using the program Mathematica Version 4.0. A numerical comparison of the analytic results and a finite element computation (program Marc Version K6.2) show large differences at both examples. (Results obtained with the finite element computation are not included in this master's thesis).
In chapter 5 basic cases for straight thin-walled beams of open cross-section under torsion are investigated by finite element computation. After numerous studies in which e.g. mesh divisions or the used element type are varied it is explained that in any case stiffeners must be used at least at the beginning and end of each member until the computed solution should come near to the analytic results.
Keywords: Methode der Finiten Elemente, Reduktionsverfahren, Stabzug, Wölbkrafttorsion