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Lower Bounds To Colunm And Plate Buckling Loads, Pen-Yuan Shih

Mechanical Engineering ETDs

The complexity inherent in the theory of elastic stability has resulted in the extensive use of approximate techniques for determining buckling loads. The Rayleigh quotient provides reasonable answers for a surprisingly broad category of problems. However, the quotient is an upper bound to the buckling load and for certain engineering structures, further it is difficult to estimate the error. A rigorous and conservative analysis requires that a lower bound be computed.

There are several techniques for finding lower bounds to eigenvalues but because of various complicating factors none is routinely used for elastic stability analyses. The purpose of this dissertation ...