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From:
Herbert E. Lindberg, “Little Book of Dynamic Buckling”, LCE Science/Software, September 2003
PREFACE:
A graduate program in mechanics (often part of aero/astronautical, civil or mechanical engineering) generally includes a short series on elastic stability of structures. Within the confines of available time, focus is on stability under static loading, with dynamic loading from earthquakes, aerodynamics, impact and so on touched on only briefly except for students with thesis topics in these areas. This short book is intended as a brief introduction to dynamic buckling that can be covered in the limited time available in a broad graduate program. It is small and inexpensive enough that the student can own his or her own copy, rather than simply taking notes during lectures extracted by the teacher from the several full-size texts available on this topic, including one by the present author.
The book introduces concepts of dynamic buckling in the simplest possible context for each phenomenon. The phenomena treated all fall under the definition of dynamic stability of structures under time-varying parametric loading. The goal is met by treating simple bars under axial loads, rings under lateral pulse loads, and cylindrical shells under radial and axial loads. The present document includes only a general introduction and then comprehensive presentation of theory and experimental data for bars under static and impact loads. Sections on rings and shells will be made available as orders are received.
In all cases motion is precipitated by inevitable imperfections in structural shape. Sometimes these appear as a simple parameter, as in the eccentricity of impact. In most cases, however, the imperfections are unknown functions of surface coordinates. In later chapters, two methods are introduced to describe shape imperfections: random coefficients of modal shapes (probabilistic analysis) and worst-case imperfection shapes found by convex modeling (uncertain shapes described by convex sets). Both types of imperfections are used and compared in closed-form solutions for these structures, and also form the basis for introducing initial shapes into finite element calculations of more general structures the student is likely to encounter in engineering practice.
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