In this thesis, a computational thin-walled beam model is presented which can be used in various engineering applications and whose computer implementation is straightforward. The model is applicable to beams with both open and closed cross sections, including multicellular beams. The dimensions and topology of the beam‟s cross sections may arbitrarily (and possibly even abruptly) vary along the length of the beam. Anisotropic material properties are allowed, and they may vary both within the cross section and along the beam‟s length.
Compared to many existing models, the only assumption the model presented in this thesis retains is in-plane rigidity of the cross section. In particular, it does not require any definition of cross-sectional warping, which is typically needed in the present thin-walled beam models. Instead, in this model, a finite element mesh is used in which a carefully chosen set of degrees of freedom describes warping. The deformation pattern that this finite element mesh describes is superposed on the bending deformation described by Euler-Bernoulli beam theory. Consequently, in the model presented here the warping pattern is not predetermined but results from the solution of the final system of equations. This is particularly important for beams with variable cross section. The presented model is tested through several numerical examples. Comparisons with independently obtained results, including the results obtained by much more sophisticated models, demonstrate the validity and accuracy of the formulation.
University of Minnesota M.S. thesis. October 2011. Major: Civil Engineering. Advisor: Henryk K. Stolarski. 1 computer file (PDF); vi, 63 pages, appendices A-B.
Dahl, Ariel M..
A computational model for thin-walled structures with variable cross sections.
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