Optimization of Stiffened Panels Using Element Free Galerkin Method and Kriging Model

A framework is developed for structural optimization using Element Free Galerkin (EFG) method, kriging method and Genetic Algorithm (GA). The element free Galerkin method is used to evaluate the objective function at the sample points used for developing the surrogate model for estimating the function value in design optimization. Kriging method is used to develop a surrogate model and a genetic algorithm is used as a global optimizer. The framework is tested for a plate with curvilinear stiffeners. The efficiency and the accuracy of the framework is compared with two other approaches: 1) MD.PATRAN®, MD.NASTRAN® and VisualDOC® as implemented in EBF3PanelOpt, a Computational Design Environment being developed at Virginia Tech to optimally design panels with curvilinear stiffeners, and 2) kriging, MD.PATRAN® and MD.NASTRAN® (using EBF3PanelOpt) and genetic algorithm. All approaches use optimization methods on both the shape and size design variables. The optimization scheme is a two-step optimization approach by dividing the design variable into size and shape variables. First the buckling parameter is maximized over the shape design variable and then mass is minimized over the size variable with constraint on buckling. The comparison between three approaches shows the efficiency and accuracy of the developed framework. It was shown that by using meshfree method, the curvilinearly stiffener geometry and nodes are regenerated for each design point analysis while plate geometry and mesh can be kept unchanged during optimization which results in significant reduction in CPU time.