Robert Millard Jones

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The purpose of this book is to introduce graduate students and practicing engineers to the basic concepts of stability of structural elements and when they buckle. Bars, plates, and circular cylindrical shells are used as relatively simple examples to illustrate the fundamental concepts. Bars will be shown to carry, or sustain, just about the buckling load once buckling has occurred. Plates are seen to carry much more than the buckling load. Finally, some very common shells under some loading conditions carry much less than the buckling load after buckling occurs. Such comparison of the load-deformation behavior, including the postbuckling behavior, of these common structural elements yields a rationale for determining the practical usefulness of a calculated buckling load. Indeed, such comparisions reveal why buckling of structural elements can be the primary concern in many structural applications. A minimum prerequisite for addressing the material in this book is an advanced mechanics of materials course in which elasticity, plates, and shells are introduced. More extensive coverage of these three topics in separate courses is desirable, but not essential. In addition, exposure to energy methods in applied mechanics would be helpful, but the motivated student can fill in the gaps in the author's presentation of energy concepts by self study. Of course, the more background that a reader has in these subjects, the more mature will be the structural mechanics base and the more overall perspective will be relied upon and gained. The primary approach to the solution of buckling problems in this book involves the calculus of variations. Leonhard Euler invented and developed the calculus of variations in the 1700s to study bar deflection and buckling problems! Thus, use of the calculus of variations in this book seems to be a natural, historic manner in which to approach the buckling problem even now. For those readers who do not wish to pursue the derivation of the governing differential equations and associated boundary conditions by use of the calculus of variations, it is possible to study only the individual buckling problems in each applications section. Thus, this book is useful both to those who want to know where the equations and results come from (and how to derive them) and to those who want to know only how to use the equations and results.