Mode Tracking Scheme Among Remeshed Models for Structural Optimization

Abstract

Mode tracking is required in the structural optimization when the frequencies of certain specified modes must be maintained within a suitable range. A simple tracking method employing the mode number is invalid or misleading when local modes appear or disappear during mesh updating. In this work, a mode tracking scheme combining the nearest neighbor method (NNM) with the modal assurance criterion (MAC) is proposed. Several NNM algorithms are compared, and the k-dimensional tree (kd-tree) NNM is used to transform eigenvectors (mode shapes) from different scales to identical one. A threshold determination method is implemented for the MAC to assess the similarities in all the calculated modes. On the basis of the mode tracking scheme, specified modes can be tracked between different finite element method (FEM) models which have different meshes and optimized shapes. The effectiveness is verified through an example of shape optimization using an electric motor structure.