Discontinuous Petrov–Galerkin method with optimal test functions for thin-body problems in solid mechanics

Handle URI:
http://hdl.handle.net/10754/597992
Title:
Discontinuous Petrov–Galerkin method with optimal test functions for thin-body problems in solid mechanics
Authors:
Niemi, Antti H.; Bramwell, Jamie A.; Demkowicz, Leszek F.
Abstract:
We study the applicability of the discontinuous Petrov-Galerkin (DPG) variational framework for thin-body problems in structural mechanics. Our numerical approach is based on discontinuous piecewise polynomial finite element spaces for the trial functions and approximate, local computation of the corresponding 'optimal' test functions. In the Timoshenko beam problem, the proposed method is shown to provide the best approximation in an energy-type norm which is equivalent to the L2-norm for all the unknowns, uniformly with respect to the thickness parameter. The same formulation remains valid also for the asymptotic Euler-Bernoulli solution. As another one-dimensional model problem we consider the modelling of the so called basic edge effect in shell deformations. In particular, we derive a special norm for the test space which leads to a robust method in terms of the shell thickness. Finally, we demonstrate how a posteriori error estimator arising directly from the discontinuous variational framework can be utilized to generate an optimal hp-mesh for resolving the boundary layer. © 2010 Elsevier B.V.
Citation:
Niemi AH, Bramwell JA, Demkowicz LF (2011) Discontinuous Petrov–Galerkin method with optimal test functions for thin-body problems in solid mechanics. Computer Methods in Applied Mechanics and Engineering 200: 1291–1300. Available: http://dx.doi.org/10.1016/j.cma.2010.10.018.
Publisher:
Elsevier BV
Journal:
Computer Methods in Applied Mechanics and Engineering
Issue Date:
Feb-2011
DOI:
10.1016/j.cma.2010.10.018
Type:
Article
ISSN:
0045-7825
Sponsors:
This work was made possible with funding from King Abdullah University of Science and Technology (KAUST). We are grateful for this financial support.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorNiemi, Antti H.en
dc.contributor.authorBramwell, Jamie A.en
dc.contributor.authorDemkowicz, Leszek F.en
dc.date.accessioned2016-02-25T13:10:32Zen
dc.date.available2016-02-25T13:10:32Zen
dc.date.issued2011-02en
dc.identifier.citationNiemi AH, Bramwell JA, Demkowicz LF (2011) Discontinuous Petrov–Galerkin method with optimal test functions for thin-body problems in solid mechanics. Computer Methods in Applied Mechanics and Engineering 200: 1291–1300. Available: http://dx.doi.org/10.1016/j.cma.2010.10.018.en
dc.identifier.issn0045-7825en
dc.identifier.doi10.1016/j.cma.2010.10.018en
dc.identifier.urihttp://hdl.handle.net/10754/597992en
dc.description.abstractWe study the applicability of the discontinuous Petrov-Galerkin (DPG) variational framework for thin-body problems in structural mechanics. Our numerical approach is based on discontinuous piecewise polynomial finite element spaces for the trial functions and approximate, local computation of the corresponding 'optimal' test functions. In the Timoshenko beam problem, the proposed method is shown to provide the best approximation in an energy-type norm which is equivalent to the L2-norm for all the unknowns, uniformly with respect to the thickness parameter. The same formulation remains valid also for the asymptotic Euler-Bernoulli solution. As another one-dimensional model problem we consider the modelling of the so called basic edge effect in shell deformations. In particular, we derive a special norm for the test space which leads to a robust method in terms of the shell thickness. Finally, we demonstrate how a posteriori error estimator arising directly from the discontinuous variational framework can be utilized to generate an optimal hp-mesh for resolving the boundary layer. © 2010 Elsevier B.V.en
dc.description.sponsorshipThis work was made possible with funding from King Abdullah University of Science and Technology (KAUST). We are grateful for this financial support.en
dc.publisherElsevier BVen
dc.subjectDiscontinuous Petrov-Galerkinen
dc.subjectHp-Adaptivityen
dc.subjectThin structuresen
dc.titleDiscontinuous Petrov–Galerkin method with optimal test functions for thin-body problems in solid mechanicsen
dc.typeArticleen
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.contributor.institutionUniversity of Texas at Austin, Austin, United Statesen
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