Optimization of porosity distribution of FGP beams considering buckling strength

In this paper, the porosity distribution of functionally graded porous (FGP) beams are optimized using the genetic algorithm to achieve the maximum ratio of the normalized buckling load to the beam's weight. The analytical forms for critical buckling loads of the FGP beams under different end conditions are determined analytically using principle virtual work based on the Euler and Timoshenko beam theories. The effects of Nano Graphene Platelets (NGPs) on the critical buckling load of the nanocomposite FGP beams are also taken into account. The sensitivity analyses show that porosity will reduce the buckling load-to-weight ratio of porous beams to conventional beams in some cases. Based on the optimization results, the optimum distribution of the porosity and NGPs' volume fraction are proposed for several porosity coefficients. The obtained results indicate that the optimum distribution for porosity has a symmetric sandwich-like shape while the optimum distribution for NGPs' volume fraction is uniform.