Genetic-Algorithm Optimization of Dynamic Efficiency in Bidirectional Porous Functionally Graded Beams

Abstract

This study develops an analytical–evolutionary framework for optimizing the dynamic efficiency of bidirectional porous functionally graded beams. Touratier’s higher-order shear deformation theory is coupled with a real-coded genetic algorithm. The material-gradation indices in the thickness and width directions, the porosity coefficient, and the cross-sectional aspect ratio are treated as four coupled design variables. Dynamic efficiency is defined as the first modal frequency per unit mass, J = f1/m (Hz/kg), with f1 evaluated at β1 = π/L for the simply supported finite beam. Uniform and non-uniform porosity laws are examined under three admissible design domains. After correcting and consistently implementing the modified rule of mixtures, the restricted-domain efficiencies are 117.819 and 96.766 Hz/kg for uniform and non-uniform porosity, respectively. Extending the material-gradation bounds increases them to 920.823 and 328.627 Hz/kg, while extension of the geometric domain gives 2302.058 and 821.568 Hz/kg. Thirty independent GA runs for each case yield 100% success under a 0.5% tolerance. Deterministic corner and one-at-a-time sampled checks confirm the observed boundary-directed trends within the investigated boxes. The results are mathematical optima for the stated objective and constraints, not production-ready designs.