A Fast Tool for Analysis and Optimization of Isotropic and Composite Stiffened Panels

Abstract

This paper presents an analytical formulation for the study of buckling and post-buckling of longitudinally isotropic and composite stiffened panels subjected to axial compression implemented in a minimum weight optimization procedure based on genetic algorithms. First, it is presented the derivation of closed-form solutions for the linearized buckling load in case of global and local buckling modes. Global buckling is studied referring to linear smeared theory and applying the method of Galerkin to solve governing equations. Local buckling is studied considering the portion of panel between two stiffeners which are modeled as torsion bars. The procedure is based on the Minimum Potential Energy Principle that is applied using the method of Ritz. It is then presented a semi-analytical procedure for the study of the nonlinear local post-buckling field based on the application of a variational approach which is solved using the method of Ritz. A minimum weight optimization procedure for an isotropic and a composite panel with constraints on buckling and post-buckling behavior is then discussed. The analytical formulation is coupled with genetic algorithms for constraint evaluations, leading to a computationally efficient procedure. Optimized configurations are verified using the finite element method. It is shown that the difference between analytical and numerical results is below 9% for the buckling loads, and below 3% for post-buckling stiffnesses.