Holdings: The hierarchical finite cell method for problems in structural mechanics

The hierarchical finite cell method for problems in structural mechanics:

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Bibliographic Details
Main Author:	Joulaian, Meysam (Author)
Format:	Thesis Book
Language:	German
Published:	Düsseldorf VDI Verlag [2017]
Edition:	Als Manuskript gedruckt
Series:	Fortschritt-Berichte VDI. Reihe 18, Mechanik, Bruchmechanik Nr. 348
Subjects:	Finite-Elemente-Methode Strukturmechanik Hochschulschrift
Online Access:	Inhaltsverzeichnis
Physical Description:	X, 152 Seiten Illustrationen
ISBN:	9783183348183

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MARC


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adam_text	C ONTENTS N O TA TIO N V III A B STRACT IX Z USAM M ENTFASSUNG X 1 IN TROD U CTION 1 1.1 M OTIVATION.................................................................................................................... 1 1.2 SCOPE AND OUTLINE OF THIS W O R K .................................................................................. 4 2 F IN ITE CELL M ETH O D FOR PROBLEM S IN SOLID MECHANICS 5 2.1 THE STRONG AND WEAK FORM OF THE GOVERNING EQUATIONS............................................. 5 2.2 THE FINITE ELEMENT METHOD ........................................................................................ 7 2.3 MESH GENERATION AND THE FINITE CELL M ETHOD............................................................... 10 2.4 NUMERICAL CHALLENGES OF THE FINITE CELL M ETH O D ........................................................ 14 2.4.1 FAST ALGORITHMS TO INTRODUCE THE INDICATOR FU N C T IO N ................................... 14 2.4.2 IMPOSITION OF BOUNDARY CONDITIONS............................................................... 15 2.4.2.1 NEUMANN BOUNDARY C O N D ITIO N S .................................................. 15 2A 2.2 DIRICHLET BOUNDARY CONDITIONS ..................................................... 15 2.4.3 NUMERICAL INTEGRATION OF CUT C E L L S ............................................................... 16 2.4.4 MATERIAL INTERFACES AND WEAK DISCONTINUITIES ............................................... 16 2.4.5 EFFICIENT ITERATIVE SO LV E RS .............................................................................. 16 2.5 SOME APPLICATIONS OF THE F C M .................................................................................. 17 2.5.1 ELASTOSTATIC ANALYSIS OF A ONE-DIMENSIONAL R O D ............................................ 17 2.5.2 PERFORATED P LA TE .................................................................................................. 22 2.5.3 POROUS D O M A IN .................................................................................................. 25 3 N UM ERICAL INTEGRATION ALGORITHM S FOR TH E FC M 27 3.1 NUMERICAL INTEGRATION OF UNBROKEN C E L L S ......................................................................28 3.2 PERFORMANCE OF GAUSSIAN QUADRATURE RULES IN FACING DISCONTINUITIES .......................... 30 3.3 COMPOSED INTEGRATION..................................................................................................... 30 3.3.1 COMPOSED INTEGRATION BASED ON CONFORMING LOCAL M ESHES ............................. 32 3.3.2 COMPOSED INTEGRATION BASED ON UNIFORM SUB-CELL DIVISION ............................. 33 3.3.3 COMPOSED INTEGRATION BASED ON SPACETREES ...................................................... 35 3.3.4 RESOLUTION OF THE INTEGRATION M E S H ...................................................................36 3.3.5 COMPOSED INTEGRATION WITH AN /^-REFINEMENT PROCEDURE ................................ 38 3.4 MOMENT FITTING M E TH O D .................................................................................................. 38 3.4.1 STEP 1: SELECTION OF THE BASIS FUNCTIONS ..........................................................39 3.4.2 STEP 2: SETTING UP THE POSITION OF THE QUADRATURE P O IN T S ................................ 40 3.4.3 STEP 3: COMPUTATION OF THE RIGHT-HAND S I D E ................................................... 41 3.4.3.1 COMPUTING THE RIGHT-HAND SIDE ON B-REP M O D E L S ....................... 42 3.4.3.2 COMPUTING THE RIGHT-HAND SIDE ON VOXEL M O D E L S ....................... 44 3.4.3.3 COMPUTING THE RIGHT-HAND SIDE ON IMPLICITLY DESCRIBED GEOME TRIES ...............................................................................................45 3.4.4 STEP 4 SOLVING THE EQUATION S Y S TE M ................................................................ 45 3.4.5 RECOVERY OF THE GAUSS QUADRATURE R U LE .............................................................45 3.5 PERFORMANCE OF THE SUGGESTED NUMERICAL INTEGRATION SC H E M E S....................................47 3.5.1 CELL CUT BY A PLANAR SURFACE................................................................................47 3.5.2 CELL CUT BY SEVERAL PLANAR SU RFA C E S................................................................... 49 3.5.3 CELL CUT BY A CURVED S U R F A C E .............................................................................50 3.5.4 CELL CUT BY SEVERAL CURVED SURFACES ................................................................... 55 3.5.5 NUMERICAL INTEGRATION ON VOXEL M O D E L S ..........................................................57 3.6 PERFORMANCE OF THE NUMERICAL INTEGRATION METHODS IN THE F C M ..................................62 3.6.1 PERFORATED P LA TE ...................................................................................................62 3.6.2 SPHERE UNDER HYDROSTATIC STRESS S TA TE ................................................................ 64 3.6.3 POROUS DOMAIN UNDER P RE S S U RE ......................................................................... 69 4 LOCAL ENRICHM ENT O F TH E F C M 72 4.1 FCM FOR PROBLEMS WITH MATERIAL INTERFACES.................................................................... 72 4.2 LOCAL REFINEMENT AND ADAPTIVITY ................................................................................... 75 4.3 DESCRIBING MATERIAL INTERFACES USING THE LEVEL SET FU N CTIO N .......................................... 78 4.3.1 SMOOTH LEVEL SET FU N C TIO N S................................................................................ 79 4.3.2 NON-SMOOTH LEVEL SET FUNCTIONS..........................................................................82 4.4 LOCAL ENRICHMENT WITH THE AID OF THE PU M ETH O D ..........................................................85 4.4.1 ENRICHMENT FUNCTION FOR PROBLEMS WITH MATERIAL IN TE RFA C E S .......................... 86 4.4.1.1 STABLE X F E M /G F E M ...................................................................... 86 4.4.1.2 BLENDED ENRICH M EN T..........................................................................88 4.5 LOCAL ENRICHMENT WITH THE AID OF THE HP-D M E TH O D .......................................................90 4.6 SELECTION OF PROPER ENRICHMENT S T R A TE G Y ...................................................................... 92 4.7 NUMERICAL EXAMPLES ...................................................................................................... 93 4.7.1 ELASTOSTATIC ANALYSIS OF A BI-MATERIAL ONE-DIMENSIONAL RO D ...............................93 4.7.2 BI-MATERIAL PERFORATED PLATE WITH CURVED H O LE S ................................................ 97 4.7.3 INTERPLAY BETWEEN THE FICTITIOUS DOMAIN AND THE ENRICHMENT Z O N E ............. 101 4.7.4 3D CUBE WITH CYLINDRICAL INCLUSION ................................................................. 105 4.7.5 HETEROGENEOUS MATERIAL ................................................................................. 108 5 T HE SP ECTRAL CELL M ETH O D 111 5.1 TEMPORAL DISCRETIZATION AND LUMPED MASS MATRIX .....................................................112 5.2 SPECTRAL CELL METHOD AND MASS LUMPING IN CUT C E L L S ..................................................117 5.2.1 ROW-SUM TECHNIQUE FOR CUT C E L L S .....................................................................117 5.2.2 MASS SCALING TECHNIQUE.................................................................................... 118 5.2.3 DIAGONAL SCALING TECHNIQUE.............................................................................. 118 5.3 NUMERICAL EXAMPLES .................................................................................................... 119 5.3.1 LAMB WAVES IN A 2D P L A T E .............................................................................. 119 5.3.2 LAMB WAVES IN A PERFORATED PLATE ...............................................................123 5.3.3 LAMB WAVES IN A 2D POROUS P L A T E .................................................................125 5.3.4 WAVE PROPAGATION IN A SANDWICH P L A T E ...........................................................130 6 SUM M ARY AND O UTLOOK 133 A G AUSSIAN QUADRATURE RULES 136 A .L GAUSS-LEGENDRE QUADRATURE.......................................................................................... 136 A.2 GAUSS-LEGENDRE-LOBATTO Q U A D RA TU RE .......................................................................... 137 B P OLYN OM IAL INTEGRANDS 138 C C HEN-B ABUSKA P OIN TS 139 B IBLIOGRAPHY 140
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spelling	Joulaian, Meysam Verfasser (DE-588)1133576958 aut The hierarchical finite cell method for problems in structural mechanics Meysam Joulaian, M. SC., Hamburg The hierarchical finite cell method Als Manuskript gedruckt Düsseldorf VDI Verlag [2017] © 2017 X, 152 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Fortschritt-Berichte VDI. Reihe 18, Mechanik, Bruchmechanik Nr. 348 Dissertation Technische Universität Hamburg-Harburg 2016 Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Strukturmechanik (DE-588)4126904-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Finite-Elemente-Methode (DE-588)4017233-8 s Strukturmechanik (DE-588)4126904-4 s DE-604 Fortschritt-Berichte VDI. Reihe 18, Mechanik, Bruchmechanik Nr. 348 (DE-604)BV001902156 348 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029753735&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Joulaian, Meysam The hierarchical finite cell method for problems in structural mechanics Fortschritt-Berichte VDI. Reihe 18, Mechanik, Bruchmechanik Finite-Elemente-Methode (DE-588)4017233-8 gnd Strukturmechanik (DE-588)4126904-4 gnd
subject_GND	(DE-588)4017233-8 (DE-588)4126904-4 (DE-588)4113937-9
title	The hierarchical finite cell method for problems in structural mechanics
title_alt	The hierarchical finite cell method
title_auth	The hierarchical finite cell method for problems in structural mechanics
title_exact_search	The hierarchical finite cell method for problems in structural mechanics
title_full	The hierarchical finite cell method for problems in structural mechanics Meysam Joulaian, M. SC., Hamburg
title_fullStr	The hierarchical finite cell method for problems in structural mechanics Meysam Joulaian, M. SC., Hamburg
title_full_unstemmed	The hierarchical finite cell method for problems in structural mechanics Meysam Joulaian, M. SC., Hamburg
title_short	The hierarchical finite cell method for problems in structural mechanics
title_sort	the hierarchical finite cell method for problems in structural mechanics
topic	Finite-Elemente-Methode (DE-588)4017233-8 gnd Strukturmechanik (DE-588)4126904-4 gnd
topic_facet	Finite-Elemente-Methode Strukturmechanik Hochschulschrift
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volume_link	(DE-604)BV001902156
work_keys_str_mv	AT joulaianmeysam thehierarchicalfinitecellmethodforproblemsinstructuralmechanics AT joulaianmeysam thehierarchicalfinitecellmethod

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