Selection of best beam theories based on natural frequencies and dynamic response obtained through mode superposition method

–

Selection of best beam theories based on natural frequencies and dynamic response obtained through mode superposition method

Pierluigi Iannotti

Abstract. Simplified formulations, particularly 1D models, are fundamental for reducing the computational cost typically required by structural analyses. The use of a limited number of nodal degrees of freedom has inevitable implications for the model’s capabilities and accuracy. Furthermore, the performance of a reduced formulation is strictly problem-dependent, and the choice of a specific set of primary unknowns must be weighted considering their influence on the accuracy of the results of interest. In this work, a procedure for the selection of the best 1D models to adopt for time-response analyses is investigated. Through the Axiomatic/Asymptotic Method (AAM), the influence of single unknowns is evaluated for a specific structural configuration, which can be described as a combination of aspect ratio, material, geometry, and boundary conditions. The finite element governing equations for every considered set of variables are obtained through the Carrera Unified Formulation (CUF). The main indicator for the quality of a theory is based on the evaluation of a certain number of natural frequencies. Dynamic response analyses are then carried out using the modal superposition method to further asses the performance of the selected best theories.

Keywords
CUF, Best Theories, Beam Models, AAM, Dynamic

Published online 6/1/2024, 5 pages
Copyright © 2024 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Pierluigi Iannotti, Selection of best beam theories based on natural frequencies and dynamic response obtained through mode superposition method, Materials Research Proceedings, Vol. 42, pp 5-9, 2024

DOI: https://doi.org/10.21741/9781644903193-2

The article was published as article 2 of the book Aerospace Science and Engineering

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

References
[1] E. Carrera, A. Pagani, M. Petrolo, E. Zappino, Recent developments on refined theories for beams with applications, Mechanical Engineering Reviews 2.2 (2015) 14-00298. https://doi.org/10.1299/mer.14-00298
[2] J.N. Reddy, On locking-free shear deformable beam finite elements, Computational Methods in Applied Mechanics and Engineering, 149 (1997) 113–132. https://doi.org/10.1016/S0045-7825(97)00075-3
[3] K. Kapania, S. Raciti, Recent advances in analysis of laminated beams and plates, part I: shear effects and buckling, AIAA Journal 27.7 (1989) 923–935. https://doi.org/10.2514/3.10202
[4] K. Kapania, S. Raciti, Recent advances in analysis of laminated beams and plates, part II: vibrations and wave propagation, AIAA Journal 27.7 (1989) 935–946. https://doi.org/10.2514/3.59909
[5] E. Carrera, M. Petrolo, On the effectiveness of higher-order terms in refined beam theories, Journal of Applied Mechanics 78.2 (2011) 021013. https://doi.org/10.1115/1.4002207
[6] E. Carrera, F. Miglioretti, M. Petrolo, Computations and evaluations of higher-order theories for free-vibration analysis of beams, Journal of Sound and Vibration 331 (2012) 4269-4284. https://doi.org/10.1016/j.jsv.2012.04.017
[7] S. Candiotti, J. L. Mantari, J. Yarasca, M. Petrolo, E. Carrera, An axiomatic/asymptotic evaluation of best theories for isotropic metallic and functionally graded plates employing non-polynomic functions, Aerospace Science and Technology 68 (2017) 179-192. https://doi.org/10.1016/j.ast.2017.05.003
[8] M. Petrolo, P. Iannotti, Best Theory Diagrams for laminated composite shells based on failure indexes, Aerotecnica Missili & Spazio 102 (2023), 199-218. https://doi.org/10.1007/s42496-023-00158-5
[9] E. Carrera, M. Cinefra, M. Petrolo, E. Zappino, Finite element analysis of structures through unified formulation, Wiley & Sons Ltd, 2014.
[10] K.J. Bathe, Finite element procedures, Klaus-Jurgen Bathe, 2006.
[11] O. E. Hansteen, K. Bell, On the accuracy of mode superposition analysis in structural dynamics, Earthquake Engineering & Structural Dynamics, 7.5 (1979) 405-411. https://doi.org/10.1002/eqe.4290070502
[12] M. Dan, A. Pagani, E. Carrera, Free-vibration analysis of simply-supported beams with solid and thin-walled cross-sections using higher-order theories based on displacement variables, Thin-Walled Structures 98 (2016), 478-495. https://doi.org/10.1016/j.tws.2015.10.012