Study on Stability Analysis of Rectangular Plates Section Using a Three-Dimensional Plate Theory with Polynomial Function
by Festus Chukwudi Onyeka 1,2, Chidobere David Nwa-David 2 and Thompson Edozie Okeke 3,* 
1 Department of Civil Engineering, Edo State University Uzairue, Edo State, 312102, Nigeria.
2 Department of Civil Engineering, Michael Okpara University of Agriculture, Umudike, Abia State, 440109, Nigeria.
3 Department of Civil Engineering, University of Nigeria, Nsukka, Enugu State, 410101, Nigeria.
* Author to whom correspondence should be addressed.
Journal of Engineering Research and Sciences, Volume 1, Issue 4, Page # 28-37, 2022; DOI: 10.55708/js0104004
Keywords: SSFS rectangular plate, Energy variation method, 3-D plate theory, Exact polynomial deflection function, Stability analysis of thick plate
Received: 09 February 2022, Revised: 22 March 2022, Accepted: 28 March 2022, Published Online: 12 April 2022
APA Style
Onyeka, F. C., Nwa-David, C. D., & Okeke, T. E. (2022, April). Study on Stability Analysis of Rectangular Plates Section Using a Three-Dimensional Plate Theory with Polynomial Function. Journal of Engineering Research and Sciences, 1(4), 28–37. https://doi.org/10.55708/js0104004
Chicago/Turabian Style
Onyeka, Festus Chukwudi, Chidobere David Nwa-David, and Thompson Edozie Okeke. “Study on Stability Analysis of Rectangular Plates Section Using a Three-Dimensional Plate Theory with Polynomial Function.” Journal of Engineering Research and Sciences 1, no. 4 (April 2022): 28–37. https://doi.org/10.55708/js0104004.
IEEE Style
F. C. Onyeka, C. D. Nwa-David, and T. E. Okeke, “Study on Stability Analysis of Rectangular Plates Section Using a Three-Dimensional Plate Theory with Polynomial Function,” Journal of Engineering Research and Sciences, vol. 1, no. 4, pp. 28–37, Apr. 2022, doi: 10.55708/js0104004.
In this paper, a polynomial displacement function is developed to evaluate the stability of rectangular thick plate that is freely supported at the third edge and other three edges simply supported (SSFS). Employing three-dimensional (3-D) constitutive relations which consist of entire stress components, the functional for total potential energy was obtained. The governing equations plate was obtained through the variation of the 3-D theory of elasticity to get the slope and deflection relations. The solution of equilibrium equations gives an exact polynomial deflection and rotation function which was gotten after replacement of the variables of total potential energy while the solution of the governing equation gave the expression for the deflection coefficient of the plate. The direct variation method through deflection coefficient was applied to get the formula for calculation of the critical buckling load. Furthermore, the model followed strictly from the first principle of 3-D theory of elasticity without state of stress assumption through the thickness axis of the plate, so that it is able to eliminate the stress under-estimation problem from the approximation and 2-D refined plate theory approach, when the thickness becomes thicker. The result of the present study using the established 3-D model yields an exact solution which shows that it can be used with confidence in the stability analysis of any type of plate boundary condition.
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