A refined semi-analytic design sensitivity based on mode decomposition and Neumann series

Abstract

SUMMARYAmong various sensitivity evaluation techniques, semi-analytical method (SAM) is quite popular since this method is more advantageous than analytical method (AM) and global finite difference method (GFD). However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified for individual elements. Such errors result from the pseudo load vector calculated by differentiation using the finite difference scheme. In the present study, an iterative refined semianalytical method (IRSAM) combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes and the error of SAM caused by numerical difference scheme is alleviated by using a Von Neumann series approximation considering the higher order terms for the sensitivity derivatives. In eigenvalue problems, the tendency of eigenvalue sensitivity is similar to that of displacement sensitivity in static problems. Eigenvector is decomposed into rigid body mode and pure deformation mode. The present iterative SAM guarantees that the eigenvalue and eigenvector sensitivities converge to the reliable values for the wide range of perturbed size of the design variables. Accuracy and reliability of the shape design sensitivities in static problems and eigenvalue problems by the proposed method are assessed through the various numerical examples.

A new biased estimation method based on Neumann series for solving ill-posed problems

“…The selection of the regularization matrix K is the first important issue in the proposed method, which will be discussed in the next section. Using Neumann series, [25][26][27][28] equation ( 6) can be expanded as…”

Reduced order model of three-dimensional Euler equations using proper orthogonal decomposition basis

“…Additional details regarding the structural analysis and its validation can be found in Cho and Kim [12]. Fig.…”

“…The Euler solver with unstructured grids and the stress hybrid four-node shell element originally developed by Aminpour [11,12] were used in the aerodynamics/structure coupling analysis. Additional details regarding the structural analysis and its validation can be found in Cho and Kim [12].…”