Authors :
John Chukwuma Ezeh; Collins Uchechukwu Anya; Pius Chibueze Anyadiegwu; Owus Mathias Ibearugbulem
Volume/Issue :
Volume 8 - 2023, Issue 10 - October
Google Scholar :
https://tinyurl.com/36nfcvrp
Scribd :
https://tinyurl.com/3sadc49y
DOI :
https://doi.org/10.5281/zenodo.10061326
Abstract :
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.
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.
