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An extended finite element method wi...

Dolbow, John Everett.

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An extended finite element method with discontinuous enrichment for applied mechanics.

Record Type:	Electronic resources : Monograph/item
Title/Author:	An extended finite element method with discontinuous enrichment for applied mechanics./
Author:	Dolbow, John Everett.
Description:	198 p.
Notes:	Source: Dissertation Abstracts International, Volume: 60-12, Section: B, page: 6189.
Contained By:	Dissertation Abstracts International60-12B.
Subject:	Applied Mechanics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9953271
ISBN:	0599565705

An extended finite element method with discontinuous enrichment for applied mechanics.
Dolbow, John Everett.

An extended finite element method with discontinuous enrichment for applied mechanics. - 198 p.

Source: Dissertation Abstracts International, Volume: 60-12, Section: B, page: 6189.

Thesis (Ph.D.)--Northwestern University, 1999.

The modeling of a discontinuous field with a standard finite element approximation presents unique challenges. The construction of an approximating space which is discontinuous across a given line or surface places strict restrictions on the finite element mesh. The simulation of an evolution of the discontinuity is in turn burdened by the requirement to remesh at each stage of the calculation. This work approaches the problem by locally enriching the standard element-based approximation with discontinuous functions. The enriched basis is formed from a union of the set of nodal shape functions with a set of products of nodal shape functions and enrichment functions. The construction of the approximating space in this fashion places the formulation in the class of partition of unity methods. By aligning the discontinuities in the enrichment functions with a specified geometry, a discontinuous field is represented independently of the finite element mesh. This capability is shown to significantly extend the standard method for a number of applications in applied mechanics.

ISBN: 0599565705Subjects--Topical Terms:

1018410
Applied Mechanics.

An extended finite element method with discontinuous enrichment for applied mechanics.
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100 1 $a Dolbow, John Everett. $3 1943177
245 1 0 $a An extended finite element method with discontinuous enrichment for applied mechanics.
300 $a 198 p.
500 $a Source: Dissertation Abstracts International, Volume: 60-12, Section: B, page: 6189.
500 $a Adviser: Ted Belytschko.
502 $a Thesis (Ph.D.)--Northwestern University, 1999.
520 $a The modeling of a discontinuous field with a standard finite element approximation presents unique challenges. The construction of an approximating space which is discontinuous across a given line or surface places strict restrictions on the finite element mesh. The simulation of an evolution of the discontinuity is in turn burdened by the requirement to remesh at each stage of the calculation. This work approaches the problem by locally enriching the standard element-based approximation with discontinuous functions. The enriched basis is formed from a union of the set of nodal shape functions with a set of products of nodal shape functions and enrichment functions. The construction of the approximating space in this fashion places the formulation in the class of partition of unity methods. By aligning the discontinuities in the enrichment functions with a specified geometry, a discontinuous field is represented independently of the finite element mesh. This capability is shown to significantly extend the standard method for a number of applications in applied mechanics.
520 $a The additional incorporation of near-tip functions allows for a natural application of the enriched approximation to fracture mechanics. The capability to accurately calculate stress intensity factors for a mesh which does not conform to the crack geometry is a distinct advantage of the method. In addition to two-dimensional linear elastic fracture, the extension of the method to the modeling of mixed-mode fracture in Mindlin-Reissner plates is examined. To this end, a domain form of the interaction integral is developed for the extraction of moment and shear force intensity factors. The application of discontinuous enrichment to model interfaces with nonlinear constitutive laws is also developed. In conjunction with a well developed iterative technique, several different constitutive laws are considered on the discontinuous interface, including frictional contact on the crack faces. The simulation of crack growth in this context is straightforward, as the enrichment functions alone model the crack geometry such that no remeshing is necessary. The simulated crack paths are shown to correlate well with experimental data, and consistent results are obtained with the method throughout.
590 $a School code: 0163.
650 4 $a Applied Mechanics. $3 1018410
650 4 $a Engineering, Civil. $3 783781
650 4 $a Mathematics. $3 515831
690 $a 0346
690 $a 0543
690 $a 0405
710 2 0 $a Northwestern University. $3 1018161
773 0 $t Dissertation Abstracts International $g 60-12B.
790 1 0 $a Belytschko, Ted, $e advisor
790 $a 0163
791 $a Ph.D.
792 $a 1999
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9953271