Non-linear bending and stress analysis of a transversely loaded isotropic plates material using 3-D plate theory

Keywords: 3-D plate theory, CCSS rectangular plate, Isotropic plate material, Polynomial shape function

Abstract

This paper presents the bending stress analysis of anisotropic plate material under transverse loading using a three-dimensional (3-D) plate theory. The static elastic theory was used to formulate the total energy expression of the plate thereafter, transformed into a compatibility equation through general variation to get the slope and deflection relationship. The solution of equations of the equilibrium gave rise to the exact polynomial deflection function while the coefficient of deflection and shear deformation of the plate was gotten 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 the rectangular plate. This formula was used for the solution of the bending problem of the rectangular plate that is clamped at the first-two edge and the other edges simply supported (CCSS). The result of the deflection and stresses decrease 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 from that refined plate theory (RPT) of assumed deflection by 5.5% whereas exact 2-D RPT by 5.3%. This shows the efficacy of the exact 3-D plate theory for flexural characteristics of CCSS isotropic rectangular thick plate.

Downloads

Download data is not yet available.

References

F. C. Onyeka, F. O. Okafor, H. N. Onah, “Buckling solution of a three-dimensional clamped rectangular thick plate using direct variational method,” IOSR J. Mech. Civ. Eng., vol. 18, no. 3 Ser. III, pp. 10-22, 2021.

F. C. Onyeka, F. O. Okafor, H. N. Onah, “Application of a new trigonometric theory in the buckling analysis of three-dimensional thick plate,” Int. J. Emerg. Technol. vol. 12, no. 1, pp. 228-240, 2021.

F. C. Onyeka and T. E. Okeke, “Elastic bending analysis exact solution of plate using alternative I refined plate theory,” Niger. J. Technol., vol. 40, no. 6, pp. 1018 –1029, 2021.

G. R. Kirchhoff, “On the equilibrium and the motion of an elastic disk,” J. Pure Appl. Math., vol. 40, pp. 51-88, 1850.

R. D. Mindlin, “Influence of rotary inertia and shear on flexural motion of isotropic elastic plates,” ASME J. Appl. Mech., vol. 18, pp. 31 – 38, 1951.

R. B. Pipes, N. J. Pagano, “Interlinear stresses in composite laminates under axial extension,” J. Compos Mater, vol. 4, pp. 538–648, 1970.

F. C. Onyeka, “Critical lateral load analysis of rectangular plate considering shear deformation effect,” Glob. J. Civ. Eng., vol. 1, pp. 16-27, 2020.

K. Bhaskar, B. Kaushik, “Simple and exact series solutions for flexure of orthotropic rectangular plates with any combination of clamped and simply supported edges,” Compos. Struct., vol. 63, no. 1, pp. 63–68.

R. Li, P. Wang, Y. Tian, B. Wang, G. Li, “A unified analytic solution approach to static bending and free vibration problems of rectangular thin plates,” Sci. Rep., vol. 5, pp. 17-54, 2015.

K. P. Soldatos, “On certain refined theories for plate bending,” ASME J. Appl. Mech., vol. 55, pp. 994–995, 1988.

A. S. Sayyad, Y. M. Ghugal, “Bending and free vibration analysis of thick isotropic plates by using exponential shear deformation theory,” J. Appl. Comput. Mech., vol. 6, pp. 65-82, 2012.

F. C. Onyeka, T. E. Okeke, “Analysis of critical imposed load of plate using variational calculus,” J. Adv. Sci. Eng., vol. 4, no. 1, pp. 13–23, 2020.

A. S. Sayyad, “Comparison of various shear deformation theories for the free vibration of thick isotropic beams,” Int. J. Civ. Struct. Eng., vol. 2, no. 1, pp. 85-97, 2011.

F. C. Onyeka, D. Osegbowa, “Application of a new refined shear deformation theory for the analysis of thick rectangular plates,” Niger. Res. J. Eng. and Environ. Sci., vol. 5, no. 2, pp. 901-917, 2020.

A. S. Sayyad, B. M. Shinde, Y. M. Ghugal, “Bending, vibration and buckling of laminated composite plates using a simple four variable plate theory,” Lat. Am. J. Solids Struct., vol. 13, no. 3, 2016.

A. Mahi, E. A. Adda Bedia, A. Tounsi, “A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates,” Appl. Math. Model. Simul. Comput. Eng. Environ. Sys., vol. 39, no. 9, pp. 2489–2508, 2015.

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 J. Eng. Technol., vol. 6, no. 4, pp. 414-419, 2021.

A. S. Mantari, C. Oktem, G. Soares, “A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates,” Int. J. Solids Struct., vol. 49, pp. 43-53, 2012.

A. S. Sayyad, Y. M. Ghugal, “Buckling and free vibration analysis of orthotropic plates by using exponential shear deformation theory,” Lat. Am. J. Solids Struct., vol. 11, no. 8, 2014.

F. C. Onyeka, T. E. Okeke, "New refined shear deformation theory effect on non-linear analysis of a thick plate using energy method," Arid Zone J. Eng., Technol. Environ., vol. 17, no. 2, pp. 121-140, 2021.

I. I. Sayyad, S. B. Chikalthankar, V. M. Nandedkar, “Trigonometric shear deformation theory for thick plate analysis,” International Conference on Recent Trends in Engineering & Technology, 2013, Organized by SNJB's Late Sau. K. B. Jain College of Engineering, Chandwad.

F. C. Onyeka, D. Osegbowa, “Stress analysis of thick rectangular plate using higher order polynomial shear deformation theory,” FUTO J. Series – FUTOJNLS, vol. 6, no. 2, pp. 142-161, 2020.

Y. M. Ghugal, A. S. Sayyad, “Free vibration of thick isotropic plates using trigonometric shear deformation theory,” J. Solid Mech., vol. 3, no. 2, pp. 172-182, 2012.

A. M. Zenkour, “Exact mixed-classical solutions for the bending analysis of shear deformable rectangular plates,” Appl. Math. Model., vol. 27, no. 7, pp. 515-534, 2003.

N. G. Iyengar, “Structural stability of columns and plates,” 1988, New York: Ellis Horwood Ltd.

L. Fiedler, W. Lacarbonara, F. Vestroni, “A generalized higher-order theory for buckling of thick multi-layered composite plates with normal and transverse shear strains,” Compos. Struct., vol. 92, pp. 3011–3019, 2010.

D. O. Onwuka, O. M. Ibearugbulem, S. E. Iwuoha, J. I. Arimanwa, S. Sule, “Buckling analysis of biaxially compressed all-round simply supported (ssss) thin rectangular isotropic plates using the Galerkin’s method,” J. Civ. Eng. Urban., vol. 6, no. 1, pp. 48-53, 2016.

J. C Ezeh, I. C. Onyechere, O. M. Ibearugbulem, U. C. Anya, L. Anyaogu, “Buckling analysis of thick rectangular flat ssss plates using polynomial displacement functions,” Int. J. Sci. Eng. Res., vol. 9, no. 9, pp. 387-392, 2018.

O. M. Ibearugbulem, V. T. Ibeabuchi, K. O. Njoku, “Buckling analysis of SSSS stiffened rectangular isotropic plates using work principle approach,” Int. J. Innov. Res. Dev., vol. 3, no. 11, pp. 169-176, 2014.

C. C. Ike, “Kantorovich-Euler lagrange-galerkin’s method for bending analysis of thin plates,” Niger. J. Technol., vol. 36, no. 2, pp. 351-360, 2017.

F. C. Onyeka, “Effect of stress and load distribution analysis on an isotropic rectangular plate,” Arid Zone J. Eng. Technol. Environ., vol. 17, no. 1, pp. 9-26, 2021.

F. C. Onyeka, B. O. Mama, T. E. Okeke, “Exact three-dimensional stability analysis of plate using a direct variational energy method,” Civ. Eng. J., vol. 8, no. 1, pp. 60–80, 2022.

N. J. Pagano, “Exact solutions for bidirectional composites and sandwich plates,” J. Compos. Mater., vol. 4, pp. 20–34, 1970.

F. C. Onyeka, B. O. Mama, “Analytical study of bending characteristics of an elastic rectangular plate using direct variational energy approach with trigonometric function,” Emerg. Sci. J., vol. 5, no. 6, pp. 916-928, 2021.

F. C. Onyeka, F. O. Okafor, H. N. Onah, “Application of exact solution approach in the analysis of thick rectangular plate,” Int. J. Appl. Eng. Res., vol. 14, no. 8, pp. 2043-2057, 2019.

L. S, Gwarah, “Application of shear deformation theory in the analysis of thick rectangular plates using polynomial displacement functions,” PhD Thesis Presented to the School of Civil Engineering, Federal University of Technology, Owerri, Nigeria, 2019.

F. C. Onyeka, T. E. Okeke, “Statical bending analysis of thick rectangular plate using polynomial shear deformation theory,” J. Sci. Ind. Stud., vol. 15, no. 2, pp. 137-145, 2020.

O. M. Ibearugbulem, U. C. Onwuegbuchulem and C. N. Ibearugbulem, “Analytical three-dimensional bending analyses of simply supported thick rectangular plate,” Int. J. Eng. Adv. Res., vol. 3, no. 1, pp. 27-45, 2021.

O. M. Ibearugbulem, L. S. Gwarah, C. N. Ibearugbulem, “Use of polynomial shape function in shear deformation theory for thick plate analysis,” J. Eng., vol. no. 6, pp. 8-20, 2016.

J. C. Ezeh, I. C. Onyechere, O. M. Ibearugbulem, U. C. Anya, L. Anyaogu, “Buckling analysis of thick rectangular flat SSSS plates using polynomial displacement functions,” Int. J. Sci. Eng. Res., vol. 9, no. 9, pp. 387- 392, 2018.

O. M. Ibearugbulem, S. I. Ebirim, U. C. Anya, L. O. Ettu, “Application of alternative II theory to vibration and stability analysis of thick rectangular plates (isotropic and orthotropic),” Niger. J. Technol., vol. 39, no. 1, pp. 52 – 62, 2020.

H. O. Ozioko, O. M. Ibearugbulem, J. C. Ezeh, U. C. Anya, “Algorithm for exact solution of thick anisotropic plates,” Scholar J. Appl. Sci. Res., vol. 2, no. 4, pp. 11-25, 2019.

O. M. Ibearugbulem, I. C. Onyechere, J. C. Ezeh, U. C. Anya, “Determination of exact displacement functions for rectangular thick plate analysis,” FUTO J. Series (FUTOJNLS), vol. 5, no. 1, pp. 101–116, 2019.

J. C. Ezeh, O. M. Ibearugbulem, C. I. Onyechere, “Pure bending of thin rectangular flat plates using ordinary finite difference method,” Int. J. Emerg. Technol. Adv. Eng., vol. 3, no. 3, pp. 20-23, 2013.

Published
2022-07-31
How to Cite
Onyeka, F. C., Okeke, T. E., & Ikhazuagbe, O. (2022). Non-linear bending and stress analysis of a transversely loaded isotropic plates material using 3-D plate theory. Journal of Advances in Science and Engineering, 7(1), 1-8. https://doi.org/10.37121/jase.v7i1.190
Section
Research Articles