Parameterized Reduced Models for Efficient Optimization of Structural Dynamic Behavior

Abstract

Substructure synthesis is a method of model order reduction which is generally more efficient, computationally speaking, than analyzing the complete structural system. However, these methods are not necessarily well adapted for use within an optimization process since they do not preserve the fidelity of the reduced models when structural modifications within the reduced substructure are introduced. As a result, a costly model reduction must be performed at each iteration step. This paper presents a new method to improve standard reduction methods by taking into account a priori knowledge of the potential structural modifications. Indeed, this information proves to be salutary in creating a single enriched model reduction transformation that preserves the precision of the reduced substructure model throughout the optimization process. The proposed approach consists in extending the standard transformation matrix by a set of static residual vectors which are optimized with respect to the design variables to be modified. The proposed method can be used with a variety component mode synthesis approaches with any type of substructure natural modes: free-free, cantilever or hybrid modes. The proposed methodology is illustrated on the basis of a simulated test case taken from the aero-engine industry. Introduction The ever increasing demand for faster engineering analysis in the design process has resulted in a substantial amount of research and development on faster and more accurate approximate reanalysis method. The difficulty of any model reduction procedure lies in how to complete the representation basis in order to reduce truncation effects. Two main classes of methodologies can be found in the literature. The first class seeks to generate a set of Ritz vectors capable of representing with precision the structural behavior under a wide variety of structural modifications. For example, Balmes 1 10 studied the possibility of using a constant basis of Ritz vectors to create parametric families of reduced models whereas Bouazzouni A., et al 2 9 developed a method for optimally constructing additional vectors by using the dynamic behavior of the structure before modification combined with the a priori knowledge of the design variables. Both of these approaches have already been used effectively in an industrial context. The second class of reduction methods are based on a high order polynomial expansions of model responses about a nominal point in parameter space. This approach proves to be particularly interesting for small number of design variables and can be used for topological optimization. In this paper, we will extend the approach developed in 2 for use with substructure synthesis techniques. The latter represent a economic means for evaluating the structural behavior of complex mechanical assemblies and are known collectively as component mode synthesis methods. This approach represents a structure as an assembly of individually reduced substructures called superelements. For example, the Craig-Bampton (CB) method is one of many techniques of component mode synthesis used intensively in the aerospace industry 3 4 . However, these methods are not always well adapted to the industrial problem. This is especially true when parametric studies are to be performed with respect to design variables contained within individual superelements. The designer has the choice of either re-using the nominal model reduction transformation or performing a new superelement analysis for each modified component. The first option generally leads to inaccurate results while the latter is often impracticable due to cost considerations. We propose in this paper a new method to improve the standard superelement reduction methods by taking into account an a priori knowledge of the potentially modifiable design variables with the objective of constructing a unique reduction transformation matrix which will preserve Copyright  2002 The American Institute of Aeronautics and Astronautics Inc. All rights rserved. 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Con 22-25 April 2002, Denver, Colorado AIAA 2002-1392 Copyright © 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.