Buckling Analysis of a Three-Dimensional Rectangular Plates Material Based on Exact Trigonometric Plate Theory
by Onyeka Festus Chukwudi 1,3, Okeke Thompson Edozie 2,* 
, Nwa-David Chidobere 3
1 Department of Civil Engineering, Edo State University Uzairue, Edo State, 312102, Nigeria.
2 Department of Civil Engineering, University of Nigeria, Nsukka, Enugu State, 410101, Nigeria.
3 Department of Civil Engineering, Michael Okpara University of Agriculture, Umudike, Abia State, 440109, Nigeria.
* Author to whom correspondence should be addressed.
Journal of Engineering Research and Sciences, Volume 1, Issue 3, Page # 106-115, 2022; DOI: 10.55708/js0103011
Keywords: CCCS rectangular thick plate, exact trigonometric deflection function, three-dimensional plate theory, critical buckling load under uniaxial compression
Received: 27 January 2022, Revised: 08 March 2022, Accepted: 11 March 2022, Published Online: 17 March 2022
AMA Style
Chukwudi OF, Edozie OT, Chidobere N-D. Buckling analysis of a three-dimensional rectangular plates material based on exact trigonometric plate theory. Journal of Engineering Research and Sciences. 2022;1(3):106-115. doi:10.55708/js0103011
Chicago/Turabian Style
Chukwudi, Onyeka Festus, Okeke Thompson Edozie, and Nwa-David Chidobere. “Buckling Analysis of a Three-Dimensional Rectangular Plates Material Based on Exact Trigonometric Plate Theory.” Journal of Engineering Research and Sciences 1, no. 3 (2022): 106–15. https://doi.org/10.55708/js0103011.
IEEE Style
O. F. Chukwudi, O. T. Edozie, and N.-D. Chidobere, “Buckling analysis of a three-dimensional rectangular plates material based on exact trigonometric plate theory,” Journal of Engineering Research and Sciences, vol. 1, no. 3, pp. 106–115, 2022.
In this study, exact trigonometric displacement function was used to solve the buckling problem of a three-dimensional (3-D) rectangular plate that is clamped at the first-three edges and the other remaining edge simply supported (CCCS) under uniaxial compressive load. Employing 3-D constitutive relations which consist of entire components, the functional for total potential energy was obtained. After that, the rotation and deflection at x-axis and y-axis were formulated from the established compatibility equations to get an exact trigonometric deflection function. The characteristics equation was obtained by differentiating energy equation with respect to deflect to obtain the relations between deflection and rotation. The equation of the total potential energy is minimized with respect to the deflection coefficient after incorporating the deflection and rotation function, the critical buckling load formula was established. The solution for the buckling problem gotten shown that the structure of the plate is safe when the plate thickness is increased as the outcome of the study showed that the critical buckling load increased as the span- thickness ratio increased. The overall difference in form of percent between the present work and previous studies recorded is 5.4%. This shows that at about 95% certainty, the present work is perfect. The comparison of this study with the results of previous similar studies revealed the uniformity 3-D plate theory and the variations of CPT and RPT theories in the exact buckling analysis of a rectangular plate. However, this approach which includes all the six stress elements of the plate material in the analysis produced an exact deflection function unlike the previous studies which used assumed functions. Furthermore, the theoretical analysis of this study demonstrates a novel approach to solve the buckling problem rectangular plate which is capable of analyzing rectangular plates of any thickness configuration.
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