Abstract
This chapter presents specialized problem of large displacements but with strains restricted to be small. Small strain stress-strain relations are adequate; however, for accurate determination of the displacements, geometric non-linearity needs to be considered. The classic problem is that of structural stability and has many practical implications. The applications of such an analysis are clearly of considerable importance in aerospace and automotive engineering applications, design of telescopes, wind loading on cooling towers, box girder bridges with thin diaphragms, and other relatively slender structures. This chapter elucidates the aforementioned class of problems applied to beam, plate, and shell systems by examining the basic non-linear equilibrium equations. Such considerations also lead to the formulation of classical initial stability problems. These concepts are illustrated in detail by formulating the large deflection and initial stability problems for beams as well as flat plates. This chapter adopts a Lagrangian approach throughout in which displacements are referred to the original configuration.
Published Version
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