Dynamic Buckling Of Imperfection- Sensitive Elastic Structures Under Slowly- Varying Time Dependent Loading

ABSTRACT

The dynamic buckling loads of some imperfection-sensitive elastic structures subjected

to slowly varying time dependent loading are determined using perturbation procedures.

First, we consider an elastically imperfect column resting on a softening nonlinear elastic

foundation. The governing differential equation has two small parameters. We determine

the dynamic buckling load of this column subjected to the stipulated loading for three

different cases. The cases are when the small parameters are not related and when they are

related first linearly and next quadratically in some way.

This idea is next applied to an elastically imperfect spherical cap and the dynamic

buckling load of the cap subjected to a slowly varying time dependent loading is

determined. The result shows, among other things, that for the case of the cap, the

coupling term has no significant contribution to the initial post-buckling phenomenon.

By assuming, in the results, that the slowly varying loading function is numerically

unity, we obtain the associated step loading results for both the column and the spherical

cap. These latter results confirm existing results for columns under step loading and

establish new ones for the spherical cap.

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