Vol. 6 No. 02 (2025)
Articles

New Mathematical Models For Biaxial Buckling Analysis Of Thin Rectangular Plates Under Large Deflection For Various Boundary Conditions

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  • Edward Adah,
  • Hycienth Edubi,
  • Stanley Ubi
Edward Adah
University of Calabar
Hycienth Edubi
Department of Civil Engineering, University of Cross River State
Stanley Ubi
Department of Civil Engineering, University of Cross River State
DOI: https://doi.org/10.38094/jocef602120

Published 2025-11-08

Keywords

  • Large Deflection,
  • Buckling ratio,
  • Biaxial in-plane Loading,
  • Aspect Ratio,
  • Thin isotropic plates

How to Cite

[1]
E. Adah, H. Edubi, and S. Ubi, “New Mathematical Models For Biaxial Buckling Analysis Of Thin Rectangular Plates Under Large Deflection For Various Boundary Conditions”, JoCEF, vol. 6, no. 02, pp. 103 - 115, Nov. 2025.

Copyright (c) 2025

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Abstract

Thin rectangular plates are widely used in civil, mechanical, and aeronautical engineering, where accurate prediction of buckling behaviour is critical for structural reliability. While most classical analyses focus on small-deflection conditions, such approaches neglect the nonlinear effects induced by large out-of-plane displacements. This study aims to apply the new general mathematical model for biaxial buckling of a thin isotropic plate with large deflection to formulate new specific equations for six plate boundary conditions. The nonlinear buckling behaviour is investigated for plates with boundary conditions CCCC (clamped - clamped - clamped - clamped), CSSS (clamped - simply supported - simply supported - simply supported), CSCS (clamped - simply supported - clamped - simply supported), CCSS (clamped - clamped - simply supported - simply supported), CCCS (clamped - clamped - clamped - simply supported) and SSSS (simply supported all-round)) subjected to biaxial compressive loads. The new specific equations of this work allow for the evaluation of buckling load coefficients across varying aspect ratios, biaxial buckling ratios (n), and deflection-to-thickness ratios (w/t). The results obtained reveal that the biaxial buckling load coefficient (and load) decreases with increasing ‘n’ but increases with an increase in w/t. This highlights the combined influence of loading distribution and geometric nonlinearity. Deducing from the new biaxial equations for the uniaxial loading case for the purpose of comparison in square plates, the large-deflection buckling coefficients compared showed negligible deviation (~0%) from prior works, validating the proposed equations’ accuracy. Comparative analysis on values of buckling and postbuckling loads of CCCS plates against existing work under biaxial loading shows percentage differences between 0% and 5.56%, with the present results consistently upper bound but within acceptable engineering tolerances. The further comparison of biaxial buckling and post-buckling load coefficients of Sthe SSS plate with existing works has also shown the adequacy of this new model.  The findings demonstrate that the proposed linear and nonlinear buckling equations not only align with established studies but also offer enhanced predictive capability for large deflection analysis of thin isotropic rectangular plates.

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