Vibration and buckling optimization of thin-walled functionally graded open-section beams

Abstract This study presents vibration and buckling optimization of thin-walled functionally graded (FG) beams with bi-symmetric I-shape and channel-section. Material properties are assumed to vary through-the-contour direction by a non-monotonic function. A piece-wise cubic Hermite interpolation is used to estimate the volume fractions of the constituent phases. Based on Vlasov’s thin-walled theory, the beam element with two-node fourteen degrees of freedom is developed. Differential evolution (DE) is employed as an optimizer to solve the optimization problems. N-point volume fraction through-the-contour direction is considered as the design variables. A dimensionless objective function is formulated on the grounds of the optimization of frequency criterion and buckling load. Results of the study are presented graphically. Optimal results are obtained to be significant for several specific design of thin-walled beams.