The dynamic modeling of open thin-walled beams as applied in heavy automotive frames

Heavy automotive frames including those used for trucks consist of beams formed from thick gage sheet steel. Open shapes dominate the construction due to the ease of manufacturing. Therefore, the structural modeling of these frames depend on accurate mathematical approximations of open beam behaviors. Warping effects associated with torsion are extremely important for the determination of deflection and dynamic responses (i.e. establishing natural frequencies and mode shapes.) In addition, to reduce the cost and time associated with modeling, it is advantageous to use one dimensional finite element beam shapes.; This study focuses on the development of an appropriate one dimensional finite element formulation which will improve the modeling of deflection and dynamics of straight and curved beams with open cross-sections. It is known that two dimensional shell models approximate these characteristics much better than current beam models. Therefore, the results of this study were compared with results obtained from a shell model. A currently used beam model is also presented to highlight the differences found in current modeling practices.; The analytical work presented herein focuses on the modeling of curved beams with open thin-walled cross-sections. The strain formulation, which establishes stress resultants, is developed and accounts for the initial curvature and shear center location. The formulation of the warping constants that account for the initial curvature effects is also developed. The governing partial differential equations are obtained using the stress resultants and the equilibrium conditions. These equations are solved using the method of weighted residuals with standard finite element procedures.; The developed finite element approximation applied to the straight beam matches the shell model approximation very well. In addition, the correction factors introduced into the beam model correspond to the beam deflection and dynamics computed by a standard shell model for open curved beams with an accuracy not possible using current beam modeling techniques. It is believed that these results provide structural engineers a more effective beam formulation that gives exceptional accuracy at reduced cost and time for the analysis.