Abstract
Our focus in this chapter is on problems wherein non-linearity arises solely due to large deformations, often referred to as geometric non-linearity. Geometric non-linearity itself can arise in two ways, and these are best understood with reference to the simple case of cylindrical bending which will be discussed first. The analysis is later extended to finite rectangular plates, and salient features associated with such non-linear behaviour are highlighted.
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Notes
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K.E. Bisshopp, D.C. Drucker, Large deflections of cantilever beams, Quarterly of Applied Mathematics, 3, 1945, 272–275.
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T.K. Varadan, Non-linear bending of a cantilever beam of variable cross-section, Jl. of the Aeronautical Society of India, 26, 1974, 1–5.
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See: A.R. Ragab, S.E. Bayoumi, Engineering Solid Mechanics, CRC Press, 1998.
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S.Levy, Bending of rectangular plates with large deflections, NACA Report No.737, 1942 (available online for open access).
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S. Levy, Bending of rectangular plates with large deflections, NACA Report No. 737, 1942 (available online for open access).
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See, for example:
C.Y. Chia, Non-linear Analysis of Plates, McGraw-Hill, 1980;
W.C. Young, R.G. Budynas, Roark’s Formulas for Stress and Strain, McGraw-Hill, 2001.
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C.Y. Chia, Non-linear Analysis of Plates, McGraw-Hill, 1980.
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See, for example: J.J. Thomsen, Vibrations and Stability, Springer, 2003.
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See, for example:
G. Anlas, O. Elbeyli, Nonlinear vibrations of a simply supported rectangular metallic plate subjected to transverse harmonic excitation in the presence of a one-to-one internal resonance, Nonlinear Dynamics, 30, 2002, 1-28;
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See, for example: M. Sathyamoorthy, Nonlinear vibrations of plates: An update of recent research developments, Applied Mechanics Reviews, 49(10), Part 2, 1996, S55–S62.
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Bhaskar, K., Varadan, T.K. (2021). Non-linear Flexure and Vibrations. In: Plates. Springer, Cham. https://doi.org/10.1007/978-3-030-69424-1_14
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DOI: https://doi.org/10.1007/978-3-030-69424-1_14
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