Analysis of critical imposed load of plate using variational calculus

Keywords: CCFS plate, Critical lateral imposed load, Elastic yielding point, Shear deformation plate theory

Abstract

This work studied the critical load analysis of rectangular plates, carrying uniformly distributed loads utilizing direct variational energy calculus. The aim of this study is to establish the techniques for calculating the critical lateral imposed loads of the plate before deflection attains the specified maximum threshold, qiw as well as its corresponding critical lateral imposed load before the plate reaches an elastic yield point. The formulated potential energy by the static elastic theory of the plate was minimized to get the shear deformation and coefficient of deflection. The plates under consideration are clamped at the first and second edges, free of support at the third edge and simply supported at the fourth edge (CCFS). From the numerical analysis obtained, it is found that the critical lateral imposed loads (qiw and qip) increase as the thickness (t) of plate increases, and decrease as the length to width ratio increases. This suggests that as the thickness increases, the allowable deflection improves the safety of the plate, whereas an increase in the span (length) of the plate increases the failure tendency of the plate structure.

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Author Biographies

Festus C. Onyeka, Edo University Iyamho, Edo State, Nigeria

Dr. F. C. Onyeka, Department of Civil Engineering, Edo University Iyamho, Edo State, Nigeria

Thompson E. Okeke, University of Nigeria, Nsukka

Department of Civil Engineering, University of Nigeria, Nsukka, Enugu State, Nigeria

References

R. Li, P. Wang, Y. Tian, B. Wang, and G. Li. "A unified analytic solution approach to static bending and free vibration problems of rectangular thin plates," Sci. Rep., vol. 5, 17054, 2015, doi: 10.1038/srep17054

F. C. Onyeka, “Direct analysis of critical lateral load in a thick rectangular plate using refined plate theory,” Int. J. Civ. Eng. Technol., vol. 10, no. 5, pp. 492-505, 2019.

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

A. S. Mantari, C. Oktem, and 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.

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

G. R. Kirchhoff, “About the balance and the movement of an elastic disk,” J. Pure Appl. Maths, vol. 40, pp. 51-88, 1850.

G. R. Kirchhoff, “About the vibrations of a circular elastic disc,” Ann. Phys. Chem., vol. 81, pp. 258-264, 1850.

Y. M. Ghugal, and A. S. Sayyad, “Free vibration of thick isotropic plates using trigonometric shear deformation theory,” J. Solid Mech., vol. 3, no. 2, pp. 172-182, 2011.

A. S. Sayyad, and Y. M. Ghugal, “Bending and free vibration analysis of thick isotropic plates by using exponential shear deformation theory,” Appl. Comput. Mech., vol. 6, 2, pp. 65–82, 2012.

A. S. Sayyad, and Y. M. Ghugal, “Buckling analysis of thick isotropic plates by using exponential shear deformation theory,” Appl. Comput. Mech., vol. 6, no. 2, pp. 185–192, 2012.

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

A. Mahi, E-A. Bedia, and A. Tausi, “A new hyperbolic shear deformation theory for bending and free vibration analysis of an isotropic functionally graded, sandwich, laminated composite plate,” Appl. Math. Model., vol. 25, 2489-2508, 2015.

O. M. Ibearugbulem, and F. C. Onyeka, “Moment and stress analysis solutions of clamped rectangular thick plate,” Eur. J. Eng. Res. Sci., vol. 5, no. 4, pp. 531-534, 2020.

F. C. Onyeka, and O. M. Ibearugbulem, “Load analysis and bending solutions of rectangular thick plate,” Int. J. Emerg. Technol., vol. 11, no. 3, pp. 1103–1110, 2020.

Published
2021-01-02
How to Cite
Onyeka, F. C., & Okeke, T. E. (2021). Analysis of critical imposed load of plate using variational calculus. Journal of Advances in Science and Engineering, 4(1), 13-23. https://doi.org/10.37121/jase.v4i1.125
Section
Research Articles