The Effect of Coordinate and Boundary Conditions on Displacement and Strain of Thin Rectangular Plate with Large Deflection

Authors : John Chukwuma Ezeh; Collins Uchechukwu Anya; Pius Chibueze Anyadiegwu; Owus Mathias Ibearugbulem

Volume/Issue : Volume 8 - 2023, Issue 10 - October

DOI : https://doi.org/10.5281/zenodo.10061326

The objective of this research is to investigate the impact of coordinate and boundary conditions on the displacement and strain properties of a thin rectangular plate subjected to substantial deflection. The formulas for nonlinear displacement and nonlinear strain were found by utilising the Von-Karman strain-displacement equation. The Von-Karman equations were mathematically integrated with regard to the variables x and y, resulting in the determination of the nonlinear displacement in both the x and y directions. The nonlinear displacements were further differentiated with respect to both the x and y coordinates, leading to the derivation of the nonlinear strain-displacement equations. The researchers in the study conducted by Ibearugbulem et al. (2020) employed the total potential energy functional of a thin rectangular plate in their investigation of pure bending. The functional was minimised with respect to displacement, resulting in the derivation of a governing equation and two compatibility equations. The aforementioned equations were subsequently solved in order to obtain the in-plane displacements as a function of deflection. The energy functional was further minimised to determine the coefficient of deflection and produce the various formulas employed in the analysis of plates exhibiting considerable bending. The utilisation of polynomial displacement functions was employed in the analysis of pure bending. The load characteristics that were established were compared to those obtained by Levy and Ibearugbulem, revealing a maximum discrepancy of 21.53% and 18.9% respectively. This supports the current methodology. The nonlinear displacement and strain values for thin rectangular plates of SSSS and CCCC were obtained in two distinct coordinate systems. The initial set of coordinates is characterised by the values (0.5, 0.5, 0.5), whereas the subsequent set of coordinates is defined by the values (0.25, 0.25, 0.5). A comparison was made between the findings obtained from the SSSS and CCCC plates.

Keywords : Von-Karman; Nonlinear Kinematic; Coordinate and Boundary Conditions.

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31 - December - 2023 