Structural sensitivity analysis via reduced-order analytical model

Abstract

In dynamic analyses of flexible structures, it is often required to reduce the order of analytical finite element models to achieve reliable and efficient eigensolutions as well as many other engineering applications which require the order of an analytical model to be reduced, such as optimal designs of feedback control of aerospace structures. However, when a structural finite element model is reduced for such applications, the effect of design variable changes, which is localized in the original full-order mass and stiffness matrices, generally becomes spread in the reduced-order mass and stiffness matrices. This makes the sensitivity analysis, which is required in almost all modern structural designs, very difficult to achieve. In this paper, a technique is developed which reduces the order of original analytical finite element model, yet enables design sensitivity analysis to be performed efficiently by suitable selection of master and slave coordinates. Also, a method for calculating eigenvalue and eigenvector derivatives via the reduced-order analytical model is presented and applied to structural design practice to predict the changes of eigenvalues and eigenvectors given structural modifications as well as to tailor the eigenvalues and eigenvectors by identifying the structural modifications required. A realistic structural model is used to demonstrate the concept developed and results are compared with those from the analysis of original full analytical model. Possible integration of the proposed techniques into commercial finite element analysis softwares is discussed.