Non-Classical Problems in the Theory of Elastic Stability

Abstract

When a structure is put under an increasing compressive load, it becomes unstable and buckling occurs. Buckling is a particularly significant concern in designing shell structures such as aircraft, automobiles, ships, or bridges. This book discusses stability analysis and buckling problems and offers practical tools for dealing with uncertainties that exist in real systems. The techniques are based on two complementary theories which are developed in the text. First, the probabilistic theory of stability is presented, with particular emphasis on reliability. Both theoretical and computational issues are discussed. Secondly, the authors present the alternative to probability based on the notion of 'anti-optimization', a theory that is valid when the necessary information for probabilistic analysis is absent, that is, when only scant data are available. Design engineers, researchers, and graduate students in aerospace, mechanical, marine, and civil engineering who are concerned with issues of structural integrity will find this book a useful reference source.

Critical Buckling of Drill Strings in Cylindrical Cavities of Inclined Bore-Holes

“…It is mentioned above that the stated problem is singularly perturbed and so its solutions, as a rule, have the shapes of boundary effects concentrated in small vicinity of the DS end. The problems of this type are known as non-classical ones [22]. That is why one would expect that they are not sensitive to enlargement of the DS length.…”

Buckling of the initial imperfect rectangular thin plate with variable thickness

“…The simplest approach to the problem is a direct discussion of t he energy criterion of elastic stability by means of the second variation of the potential energy. The energy method permits us to determine the buckling load of imperfect plates with variable thickness, as illustrated in [2]. Here, we consider the small thickness variation, and as a first approximation, only the terms up to the first order of thickness variation parameter are retained.…”

“…In the case of large deflection, the strain -displacement increments relations are of the forms [1], [2] : In the isotropic case, expression (2.8) is the total potential energy with:…”

“…The energy variation is performed at the fundamental pre-buckling state ( [2]). Rejecting the fourth variation of the potential energy from expression (2.8) , one obtains: (2.9) where the bilinear term Pn [uo, u] If the rectangular plate is simply supported around the periphery and edges are immovable in the plane of plate, then the boundary conditions are:…”

“…Recently, the problem of the influence of the thickness variation and the initial curvature on the buckling load has been researched by several authors, such as Timoshenko [1], Elishakoff et al [2], Zhiming [3], Yeh et al [4], Mateus et al [5], Nguyen and Tran [6], Ciancio [7].…”