Optimization of critical buckling load for variable stiffness composites using the lamination parameters as the field variables

Buckling is a critical design concern for thin-walled structures and fiber-reinforced composite materials because it occurs with much lower strains than in failure. In this study, an in-house code is developed to optimize the critical buckling load using the lamination parameters as a design variable that applies the curvature constraints on the lamination parameters directly for the first time during optimization. The variable stiffness design revealed an approximately 160% improvement in the buckling load with respect to the optimal constant stiffness. The improvement in the critical buckling load ratio is over 400% with respect to the quasi-isotropic case, which is consistent with previous findings (Wu et al., 2015). The critical buckling load is 27% less when two opposite edges are clamped and two opposite edges are free compared to the ideal simply supported out-of-plane displacement boundary conditions that were used in previous optimization studies (Wu et al., 2015, Hao et al. 2019, Wu et al. 2012, Setoodeh et al. 2009, IJsselmuiden et al. 2010). The objective function shall be the critical load ratio when the Neumann boundary condition is used, as the membrane reactions remain constant during optimization, in contrast when the Dirichlet type used. In addition, a widely accepted optimum fiber angle distribution, suggested in Gúrda et al. (2008), is implemented in a user-defined subroutine (UMAT) of Abaqus® to compare the buckling response of constant and variable stiffness of a plate.