Continuum Sensitivity Method for Nonlinear Dynamic Aeroelasticity

In this dissertation, a continuum sensitivity method is developed for efficient and accurate computation of design derivatives for nonlinear aeroelastic structures subject to transient aerodynamic loads. The continuum sensitivity equations (CSE) are a set of linear partial differential equations (PDEs) obtained by differentiating the original governing equations of the physical system. The linear CSEs may be solved by using the same numerical method used for the original analysis problem. The material (total) derivative, the local (partial) derivative, and their relationship is introduced for shape sensitivity analysis. The CSEs are often posed in terms of local derivatives (local form) for fluid applications and in terms of total derivatives (total form) for structural applications. The local form CSE avoids computing mesh sensitivity throughout the domain, as required by discrete analytic sensitivity methods. The application of local form CSEs to built-up structures is investigated. The difficulty of implementing local form CSEs for built-up structures due to the discontinuity of local sensitivity variables is pointed out and a special treatment is introduced. The application of the local form and the total form CSE methods to aeroelastic problems are compared. Their advantages and disadvantages are discussed, based on their derivations, efficiency, and accuracy. Under certain conditions, the total form continuum method is shown to be equivalent to the analytic discrete method, after discretization, for systems governed by a general second-order PDE. The advantage of the continuum sensitivity method is that less information of the source code of the analysis solver is required. Verification examples are solved for shape sensitivity of elastic, fluid and aeroelastic problems.