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GOAL-ORIENTED ERROR ESTIMATION AND ADAPTIVITY FOR HIERARCHICAL MODELS OF THIN ELASTIC STRUCTURES

BILLADE, NILESH S
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1085691003

Abstract Details

2004, MS, University of Cincinnati, Engineering : Mechanical Engineering.
Dimensional reduction has been routinely used to simplify complex three-dimensional problems posed over thin domains to more manageable two-dimensional problems. Hierarchical models of thin bodies, which usually assume that the solution displays a polynomial behavior in the thickness direction, allow the analyst to obtain more accurate solution than classical plate and shell theories while retaining their lower-dimensional advantages. In the numerical approximation of hierarchical models of thin bodies, there are two separate contributions to the total error: (a) Modeling error is the error due to dimensional reduction, and (b) Discretization error is the error due to the numerical approximation. Traditionally, estimation of these errors has been performed in terms of abstract quantities like the global energy norm. The energy norm, however, does not give a clear representation of the error in the local features of the solution. This work focusses on extending the theory of a posteriori modeling error estimation to local quantities of interest that have physical meaning. In this work, modeling error estimates in local quantities of interest are first obtained for scalar elliptic boundary value problems posed over thin curvilinear geometries, like arches and shells, by ignoring the presence of the discretization error. Next, independent estimates are obtained for the modeling and discretization errors in quantities of interest for dimensionally reduced hierarchical models of thin elastic structures. This helps the practitioner estimate the relative magnitude and impact of these two errors to the total error. These local estimates are used to develop what are known as goal-oriented adaptive modeling strategies in which the two errors are controlled independently to effectively reduce the total error in the quantities of interest.
Dr. Kumar Vemaganti (Advisor)
133 p.
Engineering, Mechanical
dimensional reduction; modeling error; hierarchical modeling; error estimation; goal-oriented adaptivity;

Recommended Citations

Citations

  • BILLADE, N. S. (2004). GOAL-ORIENTED ERROR ESTIMATION AND ADAPTIVITY FOR HIERARCHICAL MODELS OF THIN ELASTIC STRUCTURES [Master's thesis, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1085691003

    APA Style (7th edition)

  • BILLADE, NILESH. GOAL-ORIENTED ERROR ESTIMATION AND ADAPTIVITY FOR HIERARCHICAL MODELS OF THIN ELASTIC STRUCTURES. 2004. University of Cincinnati, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1085691003.

    MLA Style (8th edition)

  • BILLADE, NILESH. "GOAL-ORIENTED ERROR ESTIMATION AND ADAPTIVITY FOR HIERARCHICAL MODELS OF THIN ELASTIC STRUCTURES." Master's thesis, University of Cincinnati, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1085691003

    Chicago Manual of Style (17th edition)

ucin1085691003
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© 2004, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.