Engineering and Technology Journal

Analytical Solution for the Static Bending Elastic Analysis of Thick Rectangular Plate Structures Using 3-D Plate Theory

Document Type : Research Paper

Authors

1 Department of Civil Engineering, Edo State University, Uzairue Department of Civil Engineering, University of Edo State+234

2 Civil Engineering Dept, Faculty of Engineering, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria

3 Civil Engineering Department, Faculty of Engineering, University of Nigeria, Enugu State, Nigeria

Abstract

In the current work, an analytical solution for static bending analysis of the thick rectangular plate structure was obtained using three-dimensional plate theory. First, the energy equation was formulated from the static elastic principles and transformed into a compatibility equation through general variation to get the slope and deflection relationship. The solution of the compatibility equation gave rise to the exact polynomial deflection function. In contrast, the coefficient of deflection and shear deformation of the plate was obtained from the governing equation through the direct variation method. These solutions were used to obtain the characteristic expression for analyzing the displacement and stresses of a rectangular plate. This formula was used for the solution of the bending problem of rectangular plate support conditions of two clamped edges, one free edge, and a simply-supported edge (CCFS). The result of the deflection and stresses decreases as the span-thickness ratio increases. More so, the aspect ratio effect of the shear stress of isotropic plates is investigated and discussed after a comparative analysis between the present work and previous studies. The result shows that the present study differs with RPT) of assumed deflection by 2.7%, whereas exact 2-D RPT by 1.9%. This shows the efficacy of the exact 3-D plate theory for rectangular plate analysis under CCFS support and loading condition.

Graphical Abstract

Highlights

  • Formulation of the energy equation.
  • Derivation of the exact displacement function
  • Bending and stress analysis of plate.

Keywords

Main Subjects

References
[1] F. C. Onyeka, B. O. Mama, C. D. Nwa-David, Application of variation method in three-dimensional stability analysis of rectangular plate using various exact shape functions, Nigerian Journal of Technology. 41 (2022) 8-20. doi: http://dx.doi.org/10.4314/njt.v41i1.2.
[2] F. C. Onyeka, T. E. Okeke, C. D. Nwa-David, Static and buckling analysis of a three-dimensional (3-D) rectangular thick plates using exact polynomial displacement function, European Journal of Engineering and Technology Research .7 (2022). doi: http://dx.doi.org/10.24018/ejeng.2022.7.2.2725.
[3] F. C. Onyeka, C. D. Nwa-David, 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, 1 (2022) 28-37. doi: https://dx.doi.org/10.55708/js0104004.
[4] F. C. Onyeka, C. D. Nwa-David, E. E. Arinze, Structural imposed load analysis of isotropic rectangular plate carrying a uniformly distributed load using refined shear plate theory, FUOYE Journal of Engineering and Technology (FUOYEJET) .6 (2021) 414-419. doi: http://dx.doi.org/10.46792/fuoyejet.v6i4.719.
[5] F. C. Onyeka, T. E. Okeke, Application of Higher Order Shear Deformation Theory in The Analysis of Thick Rectangular Plate, International Journal of Emerging Technologies ,11 (2020) 62-67. 
[6] F. C. Onyeka, B. O. Mama, C. D. Nwa-David, Analytical modelling of a three-dimensional (3-D) rectangular plate using the exact solution approach, IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE). 19 (2022) 76-88. di: 10.9790/1684-1901017688.
[7] F. C. Onyeka, B. O. Mama, T. E. Okeke, Exact three-dimensional stability analysis of plate using a direct variational energy method, Civil Engineering Journal .8 (2022) 60–80. doi: http://dx.doi.org/10.28991/CEJ-2022-08-01-05.
[8] Chandrashekhara, K. Theory of plates. University Press (India) Limited, 2001.
[9] F. C. Onyeka, F. O. Okafor, H. N. Onah, Buckling solution of a three-dimensional clamped rectangular thick plate using direct variational method, IOSR journal of mechanical and civil engineering (IOSR-JMCE). 18 (2021) 10-22.  doi: 10.9790/1684-1803031022.
[10] F. C. Onyeka, F. O. Okafor, H. N. Onah, Application of a new trigonometric theory in the buckling analysis of three-dimensional thick plate, International Journal of Emerging Technologies. 12 (2021) 228-240.
[11] Timoshenko, S. P., Gere J. M., Prager W. 1962. Theory of Elastic Stability,  Second Edition. In Journal of Applied Mechanics 2nd Ed., Vol. 29, Issue 1, McGraw-Hill Books Company, doi:10.1115/1.3636481.
[12] P. S. Gujar, K. B. Ladhane, Bending analysis of simply supported and clamped circular plate, International Journal of Civil Engineering (SSRG-IJCE). 2 (2015) 45 – 51. doi: 10.14445/23488352/IJCE-V2I5P112.
[13] F. C. Onyeka, T. E. Okeke, Analysis of critical imposed load of plate using variational calculus, Journal of Advances in Science and Engineering .4 (2020) 13–23. doi: https://doi.org/10.37121/jase.v4i1.125.
[14] C. H. Aginam, C. A. Chidolue and C. A. Ezeagu, Application of Direct Variational Method in the Analysis of Isotropic thin Rectangular Plates, ARPN Journal of Engineering and Applied Sciences. 7 (2012) 1128-1138.
[15] B. O. Mama, C. U. Nwoji, C. C. Ike, H. N. Onah, Analysis of simply supported rectangular Kirchhoff plates by the finite Fourier sine transform method, International Journal of Advanced Engineering Research and Science. 4 (2017) 285 – 291. di: https://doi.org/10.22161/ijaers.4.3.44.
[16] F. C. Onyeka, Critical lateral load analysis of rectangular plate considering shear deformation effect, Global Journal of Civil Engineering. 1 (2020) 16-27. doi: 10.37516/global.j.civ.eng.2020.012.
[17] J.  L. Mantari, A. S. Oktem,   S. C. Guedes, A new trigonometric shear deformation theory for isotropic, Laminated Composite and Sandwich Plates, Int. J. Solids Struct. 49 (2012) 43-53. doi: http://doi.org/10.1016/j.ijsolstr.2011.09.008.
[18] O. M. Ibearugbulem, F. C. Onyeka, Moment and stress analysis solutions of clamped rectangular thick plate, European Journal of Engineering Research and Science. 5 (2020) 531-534. DOI: https://doi.org/10.24018/ejers.2020.5.4.1898.
[19] E. Reissner, The effect of transverse shear deformation on the bending of elastic plates, J. Appl. Mech. 12 (1945) A69–A77. DOI:10.1115/1.4009435.
[20] R. D. Mindlin, Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, J. Appl. Mech. 18 (1951) 31–38. doi:10.1115/1.4010217.
[21] F. C. Onyeka, T. E. Okeke, Elastic bending analysis exact solution of plate using alternative i refined plate theory, Nigerian Journal of Technology (NIJOTECH). 40 (2021) 1018 –1029. doi: http://dx.doi.org/10.4314/njt.v40i6.4
[22] N. N. Osadebe. C. C. Ike, H. N. Onah, C. U. Nwoji, F. O. Okafor, Application of Galerkin-Vlasov method to the flexural analysis of simply supported rectangular kirchhoff plates under uniform loads, Nigerian Journal of Technology (NIJOTECH). 35 (2016) 732-738. doi: https://doi.org/10.4314/njt.v35i4.7.
[23] C. U. Nwoji, B. O. Mama, C. C. Ike, H. N. Onah H. N. Galerkin-Vlasov method for the flexural analysis of rectangular Kirchhoff plates with clamped and simply supported edges, IOSR Journal of Mechanical and Civil Engineering (IOSR JMCE). 14 (2017) 61-74. doi: https://doi.org/10.9790/1684-1402016174.
[24] C. C. Ike, Equilibrium approach in the derivation of differential equation for homogeneous isotropic Mindlin plates, Nigerian Journal of Technology (NIJOTECH) .36 (2017) 346-350. doi: https://doi.org/10.4314/njt.v36i2.4.
[25] R. Szilard, Theories and Applications of Plates Analysis: Classical, Numerical and Engineering Methods, John Wiley and Sons Inc., (2004).
[26] Y. M. Ghugal, P. D. Gajbhiye, Bending analysis of thick isotropic plates by using 5th order shear deformation theory, Journal of Applied and Computational Mechanics. 2 (2016) 80-95. doi: 10.22055/jacm.2016.12366.
[27] O. M. Ibearugbulem, J. C. Ezeh, L. O. Ettu, L. S. Gwarah, Bending analysis of rectangular thick plate using polynomial shear deformation theory, IOSR Journal of Engineering (IOSRJEN). 8 (2018) 53-61.
[28] F. C. Onyeka, F. O. Okafor, H. N. Onah, Application of exact solution approach in the analysis of thick rectangular plate, International Journal of Applied Engineering Research. 14 (2019) 2043-2057.
[29] F. C. Onyeka, T. E. Okeke, Analytical solution of thick rectangular plate with clamped and free support boundary condition using polynomial shear deformation theory, Advances in Science, Technology and Engineering Systems Journal. 6 (2021) 1427-1439. doi: https://dx.doi.org/10.25046/aj0601162.
[30] O. M. Ibearugbulem, U. C. Onwuegbuchulem, C. N. Ibearugbulem, Analytical three-dimensional bending analyses of simply supported thick rectangular plate, International Journal of Engineering Advanced Research (IJEAR). 3 (2021) 27–45.
[31] F. C. Onyeka, B. O. Mama, Analytical study of bending characteristics of an elastic rectangular plate using direct variational energy approach with trigonometric function, Emerging Science Journal. 5 (2021) 916-928. doi:  http://dx.doi.org/10.28991/esj-2021-01320.
[32] Gwarah, L. S. Application of Shear Deformation Theory in the Analysis of Thick Rectangular Plates using Polynomial Displacement Functions. A published PhD. Thesis Presented to the School of Civil Engineering, Federal University of Technology, Owerri, Nigeria, 2019.
[33] F. C. Onyeka and D. Osegbowa, Stress analysis of thick rectangular plate using higher order polynomial shear deformation theory. FUTO Journal Series – FUTOJNLS .6 (2020) 142-161.
Engineering and Technology Journal
Volume 40, Issue 11
Civil Engineering
, 24 Articles
November 2022
Page 1548-1559
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