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Modeling of wave phenomena in hetero...

Romkes, Albert.

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Modeling of wave phenomena in heterogeneous elastic solids.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Modeling of wave phenomena in heterogeneous elastic solids./
Author:	Romkes, Albert.
Description:	227 p.
Notes:	Source: Dissertation Abstracts International, Volume: 64-12, Section: B, page: 6153.
Contained By:	Dissertation Abstracts International64-12B.
Subject:	Applied Mechanics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3116173
ISBN:	0496636097

Modeling of wave phenomena in heterogeneous elastic solids.
Romkes, Albert.

Modeling of wave phenomena in heterogeneous elastic solids. - 227 p.

Source: Dissertation Abstracts International, Volume: 64-12, Section: B, page: 6153.

Thesis (Ph.D.)--The University of Texas at Austin, 2003.

This dissertation addresses the analysis of the classical problem in continuum mechanics of wave propagation through heterogeneous elastic media. The class of waves that are considered are stress waves propagating through linearly elastic media with highly oscillatory material properties.

ISBN: 0496636097Subjects--Topical Terms:

1018410
Applied Mechanics.

Modeling of wave phenomena in heterogeneous elastic solids.
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035 $a (UnM)AAI3116173
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100 1 $a Romkes, Albert. $3 1925993
245 1 0 $a Modeling of wave phenomena in heterogeneous elastic solids.
300 $a 227 p.
500 $a Source: Dissertation Abstracts International, Volume: 64-12, Section: B, page: 6153.
500 $a Supervisor: J. Tinsley Oden.
502 $a Thesis (Ph.D.)--The University of Texas at Austin, 2003.
520 $a This dissertation addresses the analysis of the classical problem in continuum mechanics of wave propagation through heterogeneous elastic media. The class of waves that are considered are stress waves propagating through linearly elastic media with highly oscillatory material properties.
520 $a This work provides an approach which resolves a classical open problem: the accurate characterization of interfacial stresses in highly heterogeneous media through which stress waves propagate. This is accomplished using an extension of the theory and methodology of adaptive modeling to complex sesquilinear forms.
520 $a A general abstract notion of residual based a posteriori error analysis is presented, which makes possible the development of a mathematical framework for the mathematical modeling and numerical analysis of this elastodynamic problem.
520 $a The notion of hierarchical modeling is first applied to the derivation of computable and reliable estimates of the modeling error in a specific quantity of interest: the average stress on a subdomain in the elastic body. The estimate is subsequently employed in a goal-oriented adaptive modeling algorithm that is introduced for solving wave propagation in heterogeneous media. To control the error due to geometric dispersion, the algorithm solves the wave problem in the complex frequency domain by iteratively adapting the mathematical material model until the error estimate meets a preset tolerance. The algorithm is applicable to elastic materials with arbitrary microstructure and does not require geometric periodicity. A number of one-dimensional steady-state and transient examples are investigated, which demonstrate the application of an adaptive modeling algorithm and the reliability and accuracy of the error estimate.
520 $a A new Discontinuous Galerkin Method (DGM) is presented to numerically solve the wave equation in the frequency domain. Well-posedness and convergence of the formulation is proved for the case of a Reaction-Diffusion type model problem. One- and two-dimensional numerical verifications are shown.
520 $a The general abstract framework of a posteriori error analysis is then again applied, but now to the new DGM formulation of the wave equation to derive an estimate of the numerical approximation error in the quantity of interest. An hp-adaptive algorithm for numerical error control is introduced and numerical results are presented for one-dimensional steady state applications.
590 $a School code: 0227.
650 4 $a Applied Mechanics. $3 1018410
650 4 $a Physics, Acoustics. $3 1019086
650 4 $a Engineering, Mechanical. $3 783786
690 $a 0346
690 $a 0986
690 $a 0548
710 2 0 $a The University of Texas at Austin. $3 718984
773 0 $t Dissertation Abstracts International $g 64-12B.
790 1 0 $a Oden, J. Tinsley, $e advisor
790 $a 0227
791 $a Ph.D.
792 $a 2003
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3116173