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This and the next image are from:
Erasmo Carrera, Enrico Zappino and Tommaso Cavallo (Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino 10129, Italy),
“Accurate free vibration analysis of launcher structures using refined 1D models”, International Journal of Aeronautial & Space Sciences (IJASS), Vol. 16, No. 2, pp 206-222, 2018, http://dx.doi.org/10.5139/IJASS.2015.16.2.206
ABSTRACT: This work uses different finite element approaches to the free vibration analysis of reinforced shell structures, and a simplified model of a typical launcher with two boosters is used as an example. The results obtained using a refined one-dimensional (1D) beam model are compared to those obtained with commercial finite element software. The 1D models that are used in the present work are based on the Carrera Unified Formulation (CUF), which assumes a variable kinematic displacement field over the cross-sections of the beam. Two different sets of polynomials that correspond to Taylor (TE) or Lagrange (LE) expansions were used. The analyses focused on three reinforced structures: a stiffened panel, a reinforced cylinder and the complete structure of the launcher. The frequencies and natural modes obtained using one-dimensional models are compared to those obtained from classical finite element analysis. The classical FE models were built using a beam-shell or solid elements, and the results indicate that the refined beam models can in fact be used to investigate the behavior of very complex reinforced structures. These models can predict the shell-like modes that are typical of thin-walled structures that cannot be detected using classical beam models. The refined 1D models used in the present work provide results that are as accurate as those from solid FE models, but the 1D models have a much lower computational cost.
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