POSTBUCKLING BEHAVIOUR OF ISOTROPIC THIN RECTANGULAR PLATES WITH ONE FREE EDGE

ADAH E. I., ONWUKA D. O., IBEARUGBULEM O. M., Ubi, S. E., NWIGWE E. E.

Abstract


This work aims to evaluate the individual stiffness of six plates’ boundary conditions with one free edge to obtain the
specific mathematical models for predicting the postbuckling loads of the six plates’ boundary conditions under
consideration. The shape profiles of each of the six plates were differentiated and substituted into the individual
stiffness integrals to obtain the numerical values of the individual stiffness. The individual stiffness values were then
substituted into the total bending and membrane stiffness expressions and evaluated. The resulting total and membrane
stiffness expressions were thereafter substituted into the general postbuckling equation and evaluated to obtain
specific mathematical models for the six plate types to predict the postbuckling loads of each plate. The newly
formulated mathematical models were validated by carrying out numerical predictions of the postbuckling loads of
each plate. The critical load obtained was compared with those in the literature and was found adequate. Additionally,
the results showed a gradual increase in the strength of plate beyond the initial yield point which is in line with the
behavior of plates. Based on these observations it was concluded that the newly formulated mathematical models for
predicting the postbuckling strength of thin isotropic rectangular plates considered here were adequate and that the
models will provide an easy means of analyzing thin plates for postbuckling loads.


Keywords


Postbuckling Load, Mathematical Models, Polynomial Shape Functions, Rectangular Plates, Free Edge, Boundary Conditions

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