Optimization of beams for lateral buckling
optimizationofbe00burn.pdf (6.379Mb)Abstract
The treatise seeks to find the optimum shape of a thin
beam under the influence of lateral buckling. The specific
formulation is by means of the isoperimetric problem of the
calculus of variations. An energy method approach yields
the governing equations for the problem. An analytic
solution was not obtained due to the nonlinearity and
coupling conditions of the equations.
A variable height lateral buckling problem is formulated
as an alternate attempt to find the optimum design. Through
Bessel equation analysis numerous designs are obtained and
the resulting buckling loads are calculated. The largest
buckling load corresponds to a beam design which appears to
be very close to the optimum shape.
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