On the use of reduced integration in combination with discontinuous Galerkin discretization: application to volumetric and shear locking problems

Abstract In the present work, the discontinuous Galerkin (DG) method is applied to linear elasticity for two-dimensional and three-dimensional settings. A locking-free element formulation based on reduced integration and physically-based hourglass stabilization (Q1SP) is coupled for the first time w...

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Main Authors: Hamid Reza Bayat, Stephan Wulfinghoff, Steffen Kastian, Stefanie Reese
Format: Article
Language:English
Published: SpringerOpen 2018-05-01
Series:Advanced Modeling and Simulation in Engineering Sciences
Subjects:
Online Access:http://link.springer.com/article/10.1186/s40323-018-0103-x
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spelling doaj-e969cce3348a4be09c5470cd59b7ff392020-11-25T02:16:44ZengSpringerOpenAdvanced Modeling and Simulation in Engineering Sciences2213-74672018-05-015111610.1186/s40323-018-0103-xOn the use of reduced integration in combination with discontinuous Galerkin discretization: application to volumetric and shear locking problemsHamid Reza Bayat0Stephan Wulfinghoff1Steffen Kastian2Stefanie Reese3Institute of Applied Mechanics, RWTH Aachen UniversityInstitute of Applied Mechanics, RWTH Aachen UniversityInstitute of Applied Mechanics, RWTH Aachen UniversityInstitute of Applied Mechanics, RWTH Aachen UniversityAbstract In the present work, the discontinuous Galerkin (DG) method is applied to linear elasticity for two-dimensional and three-dimensional settings. A locking-free element formulation based on reduced integration and physically-based hourglass stabilization (Q1SP) is coupled for the first time with the DG framework. The incomplete interior penalty Galerkin method is chosen, being one example of different variations of DG methods. Several 2D and 3D typical benchmark problems of linear elasticity are investigated. A selection of numerical integration schemes for the boundary terms is presented, namely reduced and mixed integration schemes. The treatment of the surface terms by means of different rules of integration shows a significant influence on the performance of the resulting DG method in combination with the standard Q1 element. This intelligent treatment of the surface part leads to a DG variant with very good convergence properties.http://link.springer.com/article/10.1186/s40323-018-0103-xDiscontinuous GalerkinReduced integrationIncompressibilityLinear elasticity
collection DOAJ
language English
format Article
sources DOAJ
author Hamid Reza Bayat
Stephan Wulfinghoff
Steffen Kastian
Stefanie Reese
spellingShingle Hamid Reza Bayat
Stephan Wulfinghoff
Steffen Kastian
Stefanie Reese
On the use of reduced integration in combination with discontinuous Galerkin discretization: application to volumetric and shear locking problems
Advanced Modeling and Simulation in Engineering Sciences
Discontinuous Galerkin
Reduced integration
Incompressibility
Linear elasticity
author_facet Hamid Reza Bayat
Stephan Wulfinghoff
Steffen Kastian
Stefanie Reese
author_sort Hamid Reza Bayat
title On the use of reduced integration in combination with discontinuous Galerkin discretization: application to volumetric and shear locking problems
title_short On the use of reduced integration in combination with discontinuous Galerkin discretization: application to volumetric and shear locking problems
title_full On the use of reduced integration in combination with discontinuous Galerkin discretization: application to volumetric and shear locking problems
title_fullStr On the use of reduced integration in combination with discontinuous Galerkin discretization: application to volumetric and shear locking problems
title_full_unstemmed On the use of reduced integration in combination with discontinuous Galerkin discretization: application to volumetric and shear locking problems
title_sort on the use of reduced integration in combination with discontinuous galerkin discretization: application to volumetric and shear locking problems
publisher SpringerOpen
series Advanced Modeling and Simulation in Engineering Sciences
issn 2213-7467
publishDate 2018-05-01
description Abstract In the present work, the discontinuous Galerkin (DG) method is applied to linear elasticity for two-dimensional and three-dimensional settings. A locking-free element formulation based on reduced integration and physically-based hourglass stabilization (Q1SP) is coupled for the first time with the DG framework. The incomplete interior penalty Galerkin method is chosen, being one example of different variations of DG methods. Several 2D and 3D typical benchmark problems of linear elasticity are investigated. A selection of numerical integration schemes for the boundary terms is presented, namely reduced and mixed integration schemes. The treatment of the surface terms by means of different rules of integration shows a significant influence on the performance of the resulting DG method in combination with the standard Q1 element. This intelligent treatment of the surface part leads to a DG variant with very good convergence properties.
topic Discontinuous Galerkin
Reduced integration
Incompressibility
Linear elasticity
url http://link.springer.com/article/10.1186/s40323-018-0103-x
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AT steffenkastian ontheuseofreducedintegrationincombinationwithdiscontinuousgalerkindiscretizationapplicationtovolumetricandshearlockingproblems
AT stefaniereese ontheuseofreducedintegrationincombinationwithdiscontinuousgalerkindiscretizationapplicationtovolumetricandshearlockingproblems
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