Optimization of beams for lateral buckling
Burns, Robert Louis
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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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