Design Sensitivities of Components Using Nonlinear Reduced-Order Models and Complex Variables

Abstract

This work-in-progress paper explores the use of complex variables to define the design sensitivities of high-speed aircraft components modeled by nonlinear reduced-order models (NLROMs). Extreme conditions are expected to be seen by high-speed flight vehicles and it is anticipated that portions of the structure are likely to exhibit significant nonlinearity in their response. Accurate prediction of the path-dependent response requires direct time-integration of nonlinear models. Large finite element models of the structural components would require prohibitively large amounts of computer time to properly simulate. Methodologies have been proposed that use NLROMs to model the component level, dynamic response. The nonlinear ROMs are linear modal models that have been coupled through the addition of nonlinear modal stiffness terms. The nonlinearity in these models is sensitive to the connectivity of the components with the assembly. Recent work has investigated the use of complex variables to update NLROMs based on the boundary stiffness of the adjoining structure. This paper will explore complex methods to determine component design sensitivities to the thermal expansion and stiffness of the surrounding structure.