Shape Determination Problems of Structures by the Inverse Variational Principle : 2nd Report, Buckling and Vibration Problems

概要

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The purpose of this research is to study the problem of determining optimal shapes of structures from a unified point of view by using the inverse variational principle. In this report, optimal structural designs for the buckling and vibration problems are treated by this principle. In the former problem a change in the potential energy during the buckling is considered as an energy functional to be made stationary, and in the latter the sum of the strain and kinetic energies is so considered. It is shown that consideration of the variations of these functionals with respect to shape and displacement leads to the conventional method which maximizes Rayleigh's quotients. As examples, this principle is applied to bars discretized into finite elements to obtain their optimal shapes for which the buckling loads or the fundamental frequencies are maximum among all shapes with the same volume.
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