Stress Analysis of Transversely Loaded Isotropic Three-Dimensional Plates Using a Polynomial Shear Deformation Theory

Onyeka, Festus C.; Mama, B. O.; Nwa-David, Chidobere D.

doi:10.30684/etj.2023.137410.1345

	Stress Analysis of Transversely Loaded Isotropic Three-Dimensional Plates Using a Polynomial Shear Deformation Theory
Engineering and Technology Journal
Article 1, Volume 41, Issue 5, May 2023, Pages 603-618 PDF (994.32 K)
Document Type: Research Paper
DOI: 10.30684/etj.2023.137410.1345
Authors
Festus C. Onyeka^* ¹; B. O. Mama^* ²; Chidobere D. Nwa-David³
¹Department of Civil Engineering, Edo State University, Uzairue Department of Civil Engineering, University of Edo State+234
²Civil Engineering Dept., Faculty of Engineering, University of Nigeria, Enugu State, Nigeria.
³Civil Engineering Dept., Faculty of Engineering, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria.
Abstract
An exact solution for the bending attributes of a thick rectangular plate under transverse loading is modeled herein using three-dimensional (3-D) elasticity plate theory and fourth-order polynomial shear deformation function. Precluding coefficients of shear correction, this model captured the effect of shear deformation along with the transverse normal strain stress. The expression for total potential energy was derived from a 3-D kinematic and constitutive relation the equilibrium equation was developed and employed from the energy functional transformation to get the relationship between slope and deflection. Exact polynomial functions were obtained from the outcome of the equilibrium equation and with the aid of the direct variation approach, the coefficient of deflection of the plate was generated from the governing equation. The expression for computing the displacement, bending moments, and stress components along the three axes of the plate was established from these solutions for the assessment of the bending characteristics of a rectangular plate. The result of a simply supported at one edge, free at one edge and clamped at the two outer edges (SCFC) was evaluated using the obtained functions in this study. The report of this study confirms the exactness and consistency of the 3-D model unlike the refined plate theories applied by previous authors in the available literature. The value of 8.05% is the comprehensive average percentage variation of the values for center deflection obtained by Onyeka and Okeke (2020) and Gwarah (2019). It is established that at the 92 % confidence level, this model is worthy of adoption for safe, cost-effective and accurate bending analysis of thick plates of any support condition.
Highlights
A 3-D total potential energy was developed. A derived shape function of the plate was obtained. An expression for stress and moment of the plate was formulated.
Keywords
Three-dimensional plate theory; Fourth-order polynomial shear deformation and displacement function; Exact Solution for bending analysis; SCFC Thick Plate

References
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