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On the Analysis of a Pre – Statically Loaded Nonlinear Cubic Structure Pressurized by an Explicitly Time Dependent Slowly Varying Load

This investigation is concerned with the determination of the dynamic buckling load of a Pre – Statically loaded imperfect elastic cubic model structure that is later struck by a dynamically slowly varying explicitly time - dependent load which is infinitely differentiable and has right hand derivatives of all orders at the initial time. Our initial pre–occupation is the determination of a uniformly valid asymptotic expression of the maximum displacement by means of multi–timing regular perturbation procedures. This is finally followed by a determination of the dynamic buckling load of the structure. The result shows, among other things, that the dynamic buckling load depends on the first derivative of the load function evaluated at the initial time. Besides, the dynamic buckling load is related to the static buckling load and this relationship is independent of the imperfection parameter. The result is, in the final analysis, particularized to cases of a step load with or without a pre–load. All results are asymptotic in nature and so, are valid as the small parameters approach zero.

Nonlinear, Slowly Varying, Infinitely Differentiable, Explicitly Time Dependent, Pre – Statically Loaded

Gerald Ozoigbo, Anthony Ette, Joy Chukwuchekwa, Williams Osuji, Itoro Udo-Akpan. (2022). On the Analysis of a Pre – Statically Loaded Nonlinear Cubic Structure Pressurized by an Explicitly Time Dependent Slowly Varying Load. American Journal of Mechanics and Applications, 10(1), 1-15.

Copyright © 2022 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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