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.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/23282 |
| Date | 28 June 2013 |
| Creators | Liu, Shaobin |
| Contributors | Aerospace and Ocean Engineering, Canfield, Robert A., Hajj, Muhammad R., Kapania, Rakesh K., Roy, Christopher J., Patil, Mayuresh J. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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