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Optimization of dynamic response using a monolithic-time formulation

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Abstract

The design of systems for dynamic response may involve constraints that need to be satisfied over an entire time interval or objective functions evaluated over the interval. Efficiently performing the constrained optimization is challenging, since the typical response is implicitly linked to the design variables through a numerical integration of the governing differential equations. Evaluating constraints is costly, as is the determination of sensitivities to variations in the design variables. In this paper, we investigate the application of a temporal spectral element method to the optimization of transient and time-periodic responses of fundamental engineering systems. Through the spectral discretization, the response is computed globally, thereby enabling a more explicit connection between the response and design variables and facilitating the efficient computation of response sensitivities. Furthermore, the response is captured in a higher order manner to increase analysis accuracy. Two applications of the coupling of dynamic response optimization with the temporal spectral element method are demonstrated. The first application, a one-degree-of-freedom, linear, impact absorber, is selected from the auto industry, and tests the ability of the method to treat transient constraints over a large-time interval. The second application, a related mass-spring-damper system, shows how the method can be used to obtain work and amplitude optimal time-periodic control force subject to constraints over a periodic time interval.

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Authors and Affiliations

  1. Air Force Research Laboratory, Air Vehicles Directorate, Wright-Patterson Air Force Base, Building 146, 2210 Eighth Street, Dayton, Ohio, 45433, USA

    Mohammad H. Kurdi & Philip S. Beran

Authors
  1. Mohammad H. Kurdi
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  2. Philip S. Beran
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Correspondence to Mohammad H. Kurdi.

Additional information

This research was performed while the first author held a National Research Council Research Associateship Award at the Air Force Research Laboratory.

An early version of this paper was presented at the 46th AIAA Aerospace Sciences Meeting and Exhibit, Jan 7–10, 2008, Reno, Nevada.

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Kurdi, M.H., Beran, P.S. Optimization of dynamic response using a monolithic-time formulation. Struct Multidisc Optim 39, 83–104 (2009). https://doi.org/10.1007/s00158-008-0316-6

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  • DOI: https://doi.org/10.1007/s00158-008-0316-6

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