Optimal design of thin-walled functionally graded beams for buckling problems

This paper presents a modeling as well as a numerical approach for geometric and material optimization of thin-walled functionally graded I-shaped cross-section beam focusing on lateral and flexural-torsional buckling problems. Material properties are assumed to be varied through the shell thickness by a non-monotonic function in which volume fractions of constituent phases have been estimated according to a piecewise cubic interpolation. Governing buckling equations, also a finite element method based on Vlasov's thin-walled theory are developed. Genetic algorithm (GA) is utilized as an optimal tool that preserving the computational efficiency of the overall analysis. N-point volume fraction through-the-thickness direction, as well as width-to-thickness, span-to-height ratios are simultaneously considered as design variables. The obtained critical buckling parameters are verified via several benchmark problems. Optimum results are found to be beneficial for a specific design of thin-walled functionally graded beams.