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CU-Boulder ASEN 5519 - A Family of Uniform Strain Tetrahedral Elements

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AbstractExecutive SummaryReferencesA Least Squares Approach for Uniform Strain Triangular and Tetrahedral Finite ElementsEnhanced Uniform Strain Triangular and Tetrahedral Finite ElementsEnhanced Uniform Strain Triangular and Tetrahedral Finite Elements.A Transition Element for Uniform Strain Hexahedral and Tetrahedral Finite ElementsA Method for Connecting Dissimilar Finite Element Meshes in Two DimensionsA Method for Connecting Dissimilar Finite Element Meshes in Three DimensionsDistributionSANDIA REPORTSAND98–2!709Unlimited ReleasePrinted December 1998Tof Uniform Strain TetrahedralaMethodfor ConnectingiteElement Meshes.. .........,,. ,~.+”,?:1:,,.,....,:,.!.;:.?,,-....~.~~,,......... ... ..’,“>-.,,,+,,;:,,..;~.:,“:,,,.”$-m.,’.,.,. .’..$..:.;.,fC.R.Dohrmann,S. W. Key, M. W. Heinstein, J. Jung-Prepared bySandia NationaI LaboratoriesAlbuquerque, New Mexico $7185 and Livermore, California 94550Sandia is a multipragfam laboratory operated by Sandia Corporation,a LockheedMalrttnCompany,for the United States Department ofEnergy under (XWact DE-AC04-94AL85000.Approved ftx public release; further dissemination unlimited.(i!li!lSandia Nationallaboratories*i-6&Issued by San&a National Laboratories,operated for the United StatesDepartment of Energy by Sandia Corporation.NOTICE: This report was prepared as an account of work sponsored by anagency of the United States Government. Neither the United States Govern-ment nor any agency thereof, nor any of their employees, nor any of theircontractors, subcontract ors, or their employees, makes any warranty,express or implied, or assumes any legal liability or responsibility for theaccuracy, completeness, or usefulness of any information, apparatus, prod-uct, or process disclosed, or represents that its use would not infringe pri-vately owned rights. Reference herein to any specific commercial product,process, or service by trade name, trademark, manufacturer, or otherwise,does not necessarily constitute or imply its endorsement, recommendation,or favoring by the United States Government, any agency thereof, or any oftheir contractors or subcontractors. The views and opinions expressedherein do not necessarily state or reflect those of the United States Govern-ment, any agency thereof, or any of their contractors.Printed in the United States of America. This report has been reproduceddirectly from the best available copy.Available to DOE and DOE contractors fromOffice of Scientific and Technical InformationP.O.BOX 62Oak Ridge, TN 37831Prices available from(615) 576-8401, FTS 626-8401Available to the public fromNational Technical Information ServiceU.S. Department of Commerce5285 port Royal RdSpringfield, VA 22161NTIS price codesPrinted copy: A07Microfiche copy: AO1●●SAND98-2709Unlimited ReleasePrinted December 1998A Family of Uniform Strain Tetrahedral Elementsand a Method for Connecting DissimilarFinite Element MeshesC. R. DohrmannStructural Dynamics DepartmentS. W. Key, M. W. Heinstein, J. JungEngineering and Manufacturing Mechanics DepartmentSandia National LaboratoriesP.O. Box 5800Albuquerque, NM 87185-0439AbstractThis report documents a collection of papers on a family of uniform straintetrahedral finite elements and their connection to different element types.Also included in the report are two papers which address the general problemof connecting dissimilar meshes in two and three dimensions. Much of thework presented here was motivated by the development of the tetrahedralelement described in the report “A Suitable Low-Order, Eight-Node Tetra-hedral Finite Element For Solids,” by S. W. Key et al., SAND98-0756, March1998. Two basic issues addressed by the papers are: (1) the performance ofalternative tetrahedral elements with uniform strain and enhanced uniformstrain formulations, and (2) the proper connection of tetrahedral and otherelement types when two meshes are“tied” together to represent a singlecontinuous domain.Executive SummaryThe unavailability of a robust, automated, all-hexahedral mesher moti-vated recent investigations of a family of uniform strain tetrahedral elements[1-2]. These elements were shown to posses the same convergence and an-tilocking characteristics of the uniform strain hexahedron. A related studyof enhanced versions of these elements [3]was also carried out. It was shownthat significant improvements in accuracy are obtained for certain elementtypes by allowing more than a single state of uniform strain within eachelement.An important advantage of the tetrahedron over the hexahedron is itsability to more readily mesh complicated geometries. On the other hand,more tetrahedral elements are generally required to mesh a volume for aspecified element edge length. Taking these factors into consideration, atransition element was developed for meshes containing both hexahedral andtetrahedral elements [4]. This effort was motivated by the idea of meshinga geometry primarily with hexahedral elements. For regions of the meshthat cannot be completed with hexahedral elements, a direct transition totetrahedral elements could be made to complete the mesh. In this way, theadvantages of both element types could be brought to bear on the meshingproblem.The development of the transition element in Ref. 4 lead naturally to ageneral method for connecting dissimilar finite element meshes in two andthree dimension [5-6]. The method combines the concept of master and slavesurfaces with the uniform strain approach for finite elements. By modifyingthe boundaries of elements on the slave surface, corrections are made to ele-ment formulations such that first-order patch tests are passed. The methodcan be used to connect meshes which use different element types. In addition,master and slave surfaces can be designated independently of relative meshresolutions. It was shown that significant improvements in accuracy, espe-cially at the shared boundary, are obtained using the new approach comparedwith standard approaches used in existing finite element codes.The purpose of this report is to provide a single document for the workpresented in Refs. 2-6. The first two papers deal specifically with the devel-opment and performance of a family of uniform strain tetrahedral elements.The third paper shows how to properly connect tetrahedral elements to thefaces of hexahedral elements. The final two papers identify and explore the1implementation of the definitive requirement which must be satisfied whentwo separately


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CU-Boulder ASEN 5519 - A Family of Uniform Strain Tetrahedral Elements

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