An accurate and refined nonlinear beam model accounting for the Poisson effect

An accurate and refined nonlinear beam model accounting for the Poisson effect

E. Ruocco, J.N. Reddy

download PDF

Abstract. In this paper, an enhanced beam model based on a 5-parameter displacement field, recently proposed by the authors and able to reproduce the Poisson effect in transverse direction is presented, and utilized to simulate the fully geometrically nonlinear response of elastic beam structures. The adoption of the linear solution as approximation functions for the nonlinear case allows prediction of nonlinear response of problems involving complex geometries with a relatively small computational effort. Several numerical examples of benchmark problems are analyzed, highlighting the characteristic features of the proposed five-parameter model and comparing the results with those obtained using the classical Bernoulli beam model and 3D finite element model.

Keywords
Nonlinear Beam Model, Poisson Effect, Large Deformation Analysis, Snap-Back/Through Behavior

Published online 3/17/2022, 6 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: E. Ruocco, J.N. Reddy, An accurate and refined nonlinear beam model accounting for the Poisson effect, Materials Research Proceedings, Vol. 26, pp 85-90, 2023

DOI: https://doi.org/10.21741/9781644902431-14

The article was published as article 14 of the book Theoretical and Applied Mechanics

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] J.N. Reddy, Theories and Analyses of Beams and Axisymmetric Circular Plates, CRC Press, Boca Raton, FL, 2022. https://doi.org/10.1201/9781003240846
[2] J.N. Reddy, A simple higher order theory for laminated composite plates, ASME J. Appl. Mech. 51 (4) (1984) 745–752. https://doi.org/10.1115/1.3167719
[3] C. Polizzotto, From the Euler–Bernoulli beam to the Timoshenko one through a sequence of Reddy-type shear deformable beam models of increasing order, Eur.J. Mech. A Solids 53 (2015) 62–74. https://doi.org/10.1016/j.euromechsol.2015.03.005
[4] E. Ruocco, J.N. Reddy, C. Wang, An enhanced hencky bar-chain model for bending, buckling and vibration analyses of Reddy beams, Eng. Struct. 221(2020) 111056, https://doi.org/10.1016/j.engstruct.2020.111056
[5] M. Di Paola, J.N. Reddy, E. Ruocco, On the application of fractional calculus for the formulation of viscoelastic reddy beam, Meccanica 55 (3) (2020) 1–14. https://doi.org/10.1007/s11012-020-01177-3
[6] W. Castañeda, J. Yarasca, J. Mantari, Best shear deformation theories based on polynomial expansions for sandwich beams, Eng. Struct. 190 (2019) 422–434. https://doi.org/10.1016/j.engstruct.2019.04.022
[7] W. Su, C.E. Cesnik, Strain-based geometrically nonlinear beam formulation for modeling very flexible aircraft, Int. J. Solids Struct. 48 (16) (2011) 2349–2360. https://doi.org/10.1016/j.ijsolstr.2011.04.012
[8] E. Turco, Modeling nonlinear beams for metamaterials design in a dynamic setting, Mech. Res. Commun. 117 (2021) 103786. https://doi.org/10.1016/j.mechrescom.2021.103786
[9] J. Wen, A. Hamid Sheikh, M. Uddin, B. Uy, Analytical model for flexural response of two-layered composite beams with interfacial shear slip using a higher order beam theory, Compos. Struct. 184 (2018) 789–799. https://doi.org/10.1016/j.compstruct.2017.10.023
[10] E.P.R. Vieira, F. Virtuoso, Buckling of thin-walled structures through a higher order beam model, Compos. Struct. 180 (2019) 104–116. https://doi.org/10.1016/j.compstruc.2016.01.005
[11] A.S. Sayyad, Y.M. Ghugal, Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature, Compos. Struct. 171 (2017) 486–504. https://doi.org/10.1016/j.compstruct.2017.03.053
[12] K. Evans, Auxetic polymers: a new range of materials, Endeavour 15 (4) (1991) 170–174. https://doi.org/10.1016/0160-9327(91)90123-S
[13] E. Ruocco, J.N. Reddy, E. Sacco, Analytical solution for a 5-parameter beam displacement model, Int. J. Mech. Sci. 201 (2021) 106496. https://doi.org/10.1016/j.ijmecsci.2021.106496
[14] E. Ruocco, J.N. Reddy, A new nonlinear 5-parameter beam model accounting for the Poisson effect. Int. J. of Non-Linear Mech. 142 (2022) 103996. https://doi.org/10.1016/j.ijnonlinmec.2022.103996
[15] M. Gutierrez Rivera, J.N. Reddy, Stress analysis of functionally graded shells using a 7-parameter shell element, Mech. Res. Commun. 78 (2016) 60–70. https://doi.org/10.1016/j.mechrescom.2016.02.009
[16] S. Lee, F. Manuel, E. Rossow, Large deflections and stability of elastic frames, J. Eng. Mech. 94 (1968) 521–547. https://doi.org/10.1061/JMCEA3.0000966
[17] C. Cichon, Large displacements in-plane analysis of elastic-plastic frames, Comput. Struct. 19 (5–6) (1984) 737–745, http://dx.doi.org/10.1016/0045-7949(84)90173-1. https://doi.org/10.1016/0045-7949(84)90173-1
[18] J. Simo, L. Vu-Quoc, A three-dimensional finite strain rod model: Part 2: Computational aspects, Comput. Methods Appl. Mech. Engrg. 58 (1986) 79–116. https://doi.org/10.1016/0045-7825(86)90079-4
[19] B. Coulter, R. Miller, Numerical analysis of a generalized plane ’elastica’ with non-linear material behaviour, Int. J. Numer. Methods Eng. 26 (1988) 617–630. https://doi.org/10.1002/nme.1620260307