Analytical derivatives technology for structural shape design

The ability to perform and evaluate the effect of shape changes on the stress and modal responses of components is an important ingredient in the “design” of aircraft engine components. The classical design of experiments (DOE)-based approach that is motivated from statistics (for physical experiments) is one of the possible approaches for the evaluation of the component response with respect to design parameters Myers, Montgomery. Response surface methodology, process and product optimization using design of experiments. John Wiley and Sons, NY (1995)]. As the underlying physical model used for the component response is deterministic and understood through a computer simulation model, one needs to re-think the use of the classical DOE techniques for this class of problems. In this paper, we explore an alternate sensitivity-analysis-based technique where a deterministic parametric response is constructed using exact derivatives of the complex finite-element (FE)-based computer models to design parameters. The method is based on a discrete sensitivity analysis formulation using semi-automatic differentiation (Griewank, SIAM (2000), ADIFOR, Automatic Differentiation of FORTRAN codes ) to compute the Taylor series or its Pade equivalent for finite-element-based responses. Shape design or optimization in the context of finite element modeling is challenging because the evaluation of the response for different shape requires the need for a meshing consistent with the new geometry. This paper examines the differences in the nature and performance (accuracy and efficiency) of the analytical derivatives approach against other existing approaches with validation on several benchmark structural applications. The use of analytical derivatives for parametric analysis is demonstrated to have accuracy benefits on certain classes of shape applications.