Solution of Semi-Inverse Buckling Problems Yields a Flexural Rigidity as a Rational Function

Novel closed-form solutions for buckling of inhomogeneous columns are reported in this study, utilizing the integral formulation of the problem. Whereas previous closed-form solutions were confined solely to polynomial mode shapes, here the rational functions are postulated as candidate mode shapes. Inhomogeneous column's flexural rigidities are derived as to have the column with specified buckling modes.