Continuum Sensitivity Method for Nonlinear Dynamic Aeroelasticity

• Main Author: Liu, Shaobin
• Other Authors: Aerospace and Ocean Engineering
• Format: Others
• Published: Virginia Tech 2013
• Subjects: Continuum Sensitivity; Shape Sensitivity; Aeroelasticity; Optimization; Fluid-structure interaction
• Online Access: http://hdl.handle.net/10919/23282

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