Convergence Study of Local Continuum Sensitivity Method Using Spatial Gradient Reconstruction

Abstract

Gradient-based optimization for large-scale, multidisciplinary design problems requires accurate and efficient sensitivity analysis to compute design derivatives. The local continuum shape sensitivity method with spatial gradient reconstruction is a nonintrusive design sensitivity analysis method that was previously published for linear and nonlinear structural analysis. The numerical behavior, accuracy, and convergence for this method are studied using benchmark problems. The benchmark problems include finite element analysis of an axial bar and finite element analysis of a rectangular membrane using unstructured grids. The results are used to establish general guidelines for conducting mesh refinement and selecting the parameters associated with spatial gradient reconstruction calculations. Lastly, design derivatives are calculated for the potential flow solution around a Joukowsky airfoil. The analytic design derivative solutions are used to calculate the true errors associated with the local continuum design derivative results.