Sangam: A Confluence of Knowledge Streams

Development and Applications of Finite Elements in Time Domain

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dc.contributor Aerospace and Ocean Engineering
dc.contributor Kapania, Rakesh K.
dc.contributor Cliff, Eugene M.
dc.contributor Johnson, Eric R.
dc.contributor Nikolaidis, Efstratios
dc.contributor Singh, Mahendra P.
dc.creator Park, Sungho
dc.date 2014-03-14T20:22:29Z
dc.date 2014-03-14T20:22:29Z
dc.date 1996-12-04
dc.date 1998-07-20
dc.date 1996-12-04
dc.date 1996-12-04
dc.date.accessioned 2023-02-28T16:56:46Z
dc.date.available 2023-02-28T16:56:46Z
dc.identifier etd-74913142975720
dc.identifier http://hdl.handle.net/10919/30693
dc.identifier http://scholar.lib.vt.edu/theses/available/etd-74913142975720/
dc.identifier.uri http://localhost:8080/xmlui/handle/CUHPOERS/264459
dc.description A bilinear formulation is used for developing the time finite element method (TFM) to obtain transient responses of both linear, nonlinear, damped and undamped systems. Also the formulation, used in the h-, p- and hp-versions, is extended and found to be readily amenable to multi-degree-of-freedom systems. The resulting linear and nonlinear algebraic equations for the transient response are differentiated to obtain the sensitivity of the response with respect to various design parameters. The present developments were tested on a series of linear and nonlinear examples and were found to yield, when compared with other methods, excellent results for both the transient response and its sensitivity to system parameters. Mostly, the results were obtained using the Legendre polynomials as basis functions, though, in some cases other orthogonal polynomials namely, Hermite, Chebyshev, and integrated Legendre polynomials were also employed (but to no great advantage). A key advantage of TFM, and the one often overlooked in its past applications, is the ease in which the sensitivity of the transient response with respect to various design parameters can be obtained. Since a considerable effort is spent in determining the sensitivity of the response with respect to system parameters in many algorithms for parametric identification, an identification procedure based on the TFM is developed and tested for a number of nonlinear single-and two-degree-of-freedom system problems. An advantage of the TFM is the easy calculation of the sensitivity of the transient response with respect to various design parameters, a key requirement for gradient-based parameter identification schemes. The method is simple, since one obtains the sensitivity of the response to system parameters by differentiating the algebraic equations, not original differential equations. These sensitivities are used in Levenberg-Marquardt iterative direct method to identify parameters for nonlinear single- and two-degree-of-freedom systems. The measured response was simulated by integrating the example nonlinear systems using the given values of the system parameters. To study the influence of the measurement noise on parameter identification, random noise is added to the simulated response. The accuracy and the efficiency of the present method is compared to a previously available approach that employs a multistep method to integrate nonlinear differential equations. It is seen, for the same accuracy, the present approach requires fewer data points. Finally, the TFM for optimal control problems based on Hamiltonian weak formulation is proposed by adopting the p- and hp-versions as a finite element discretization process. The p-version can be used to improve the accuracy of the solution by adding more unknowns to each element without refining the mesh. The usage of hierarchical type of shape functions can lead to a significant saving in computational effort for a given accuracy. A set of Legendre polynomials are chosen as higher order shape functions and applied to two simple minimization problems for optimal control. The proposed formulation provides very accurate results for these problems.
dc.description Ph. D.
dc.format application/pdf
dc.publisher Virginia Tech
dc.relation etd.pdf
dc.relation spark.pdf
dc.rights In Copyright
dc.rights http://rightsstatements.org/vocab/InC/1.0/
dc.subject optimal control
dc.subject time finite element
dc.subject sensitivity
dc.subject parametric identification
dc.title Development and Applications of Finite Elements in Time Domain
dc.type Dissertation


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