Sensitivity-based scaling for approximating structural response

Abstract

This article presents a sensitivity-based linearly varying scale factor used to reconcile results from simple and refined models for analysis of the same structure. The improved accuracy of the linear scale factor compared to a constant scale factor, as well as the commonly used tangent approximation, is demonstrated. A wing-box structure is used as an example, with displacements, stresses, and frequencies correlated. The linear scale factor could permit the use of a simplified model in an optimization procedure during preliminary design to approximate the response given by a refined model over a considerable range of design changes. HE design optimization of an engineering system typi- cally requires hundreds of analyses of that system. The use of approximation s to the objective function and con- straints during portions of the design process is quite com- mon,1 because of the high computational cost of these detailed analyses. Such design approximations can be divided into two classes. First there are local, derivative-based approximations such as the linear approximation based on a Taylor-series expansion about a design point. These approximations are typically based on an accurate model to obtain the system response and its derivatives. Second, there are global ap- proximations that try to capture the behavior of the objective function or constraints over the entire design domain. Such approximations can be based on a response surface which is constructed on the basis of many analyses.2 However, global approximations are often based on a simplified theory, a coarser model, or both.3 Such global approximations are referred to here as simple-model approximations. Local approximations are typically very accurate near the design point where they are generated, but since they are based on an extrapolation procedure their accuracy can deteriorate catastrophically at a distance. Simple-model approximations are intended to cap- ture the physics of the problem at some lower, but acceptable level of accuracy over the entire design domain. Therefore, at a particular design point the simple-model approximations are generally less accurate than local approximations, but on the other hand, they typically do not experience the cata-