A comparative study of metamodeling methods for the design optimization of variable stiffness composites

Automated fiber placement is a manufacturing technology that enables to build composite laminates with curvilinear fibers. To determine their optimum mechanical properties, finite element analysis is commonly used as a solver within an optimization framework. The analysis of laminates with curvilinear fibers coupled with the fiber path optimization requires a large number of function evaluations, each time-consuming. To reduce the time for analysis and thus for optimization, a metamodel is often proposed. This work examines a set of metamodeling techniques for the design optimization of composite laminates with variable stiffness. Three case studies are considered. The first two pertain to the fiber path design of a plate under uniform compression. The third concerns the optimization of a composite cylinder under pure bending. Four metamodeling methods, namely Polynomial Regression, Radial Basis Functions, Kriging and Support Vector Regression, are tested, and their performance is compared. Accuracy, robustness, and suitability for integration within an optimization framework are the appraisal criteria. The results show that the most accurate and robust models in exploring the design space are Kriging and Radial Basis Functions. The suitability of Kriging is the highest for a low number of design variables, whereas the best choice for a high number of variables is Radial Basis Functions.