Closed-form solution for optimization of buckling column

The optimization problem for a column, loaded by compression forces is studied in this article. direction of the applied coincides until buckling moment with axis column. critical values are equal among all competitive designs columns. dimensional analysis eases mathematical technique problem. introduces two dimensionless factors, one total material volume and stiffness With method analysis, solution nonlinear algebraic equations Lagrange multiplier will be superfluous. closed-form solutions Sturm-Liouville mixed types boundary conditions derived. expressed terms higher transcendental functions. principal results hypergeometric elliptic functions, single- bimodal regimes, exact bounds masses optimal isoperimetric inequality was formulated as strict sign, because could not attained any finite seting design parameter. additional restriction on minimal area cross-section regularizes leads to definite attainable shape