38932650 abaqus example problems manual

ABAQUS Example Problems ManualABAQUS Example Problems Manual

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ADAMS is a registered United States trademark of Mechanical Dynamics, Inc.

ADAMS/Flex and ADAMS/View are trademarks of Mechanical Dynamics, Inc.

CATIA is a registered trademark of Dassault Systmes.

C-MOLD is a registered trademark of Advanced CAE Technology, Inc., doing business as C-MOLD.

Compaq Alpha is registered in the U.S. Patent and Trademark Office.

FE-SAFE is a trademark of Safe Technology, Ltd.

Fujitsu, UXP, and VPP are registered trademarks of Fujitsu Limited.

Hewlett-Packard, HP-GL, and HP-GL/2 are registered trademarks of Hewlett-Packard Co.

Hitachi is a registered trademark of Hitachi, Ltd.

IBM RS/6000 is a trademark of IBM.

Intel is a registered trademark of the Intel Corporation.

NEC is a trademark of the NEC Corporation.

PostScript is a registered trademark of Adobe Systems, Inc.

Silicon Graphics is a registered trademark of Silicon Graphics, Inc.

SUN is a registered trademark of Sun Microsystems, Inc.

TEX is a trademark of the American Mathematical Society.

UNIX and Motif are registered trademarks and X Window System is a trademark of The Open Groupin the U.S. and other countries.

Windows NT is a registered trademark of the Microsoft Corporation.

ABAQUS/CAE incorporates portions of the ACIS software by SPATIAL TECHNOLOGY INC. ACISis a registered trademark of SPATIAL TECHNOLOGY INC.

This release of ABAQUS on Windows NT includes the diff program obtained from the Free SoftwareFoundation. You may freely distribute the diff program and/or modify it under the terms of the GNULibrary General Public License as published by the Free Software Foundation, Inc., 59 Temple Place,Suite 330, Boston, MA 02111-1307 USA.

This release of ABAQUS/CAE includes lp_solve, a simplex-based code for linear and integerprogramming problems by Michel Berkelaar of Eindhoven University of Technology, Eindhoven, theNetherlands.

Python, copyright 1991-1995 by Stichting Mathematisch Centrum, Amsterdam, The Netherlands. AllRights Reserved. Permission to use, copy, modify, and distribute the Python software and itsdocumentation for any purpose and without fee is hereby granted, provided that the above copyrightnotice appear in all copies and that both that copyright notice and this permission notice appear insupporting documentation, and that the names of Stichting Mathematisch Centrum or CWI or

ADAMS is a registered United States trademark of Mechanical Dynamics, Inc.

ADAMS/Flex and ADAMS/View are trademarks of Mechanical Dynamics, Inc.

CATIA is a registered trademark of Dassault Systmes.

C-MOLD is a registered trademark of Advanced CAE Technology, Inc., doing business as C-MOLD.

Compaq Alpha is registered in the U.S. Patent and Trademark Office.

FE-SAFE is a trademark of Safe Technology, Ltd.

Fujitsu, UXP, and VPP are registered trademarks of Fujitsu Limited.

Hewlett-Packard, HP-GL, and HP-GL/2 are registered trademarks of Hewlett-Packard Co.

Hitachi is a registered trademark of Hitachi, Ltd.

IBM RS/6000 is a trademark of IBM.

Intel is a registered trademark of the Intel Corporation.

NEC is a trademark of the NEC Corporation.

PostScript is a registered trademark of Adobe Systems, Inc.

Silicon Graphics is a registered trademark of Silicon Graphics, Inc.

SUN is a registered trademark of Sun Microsystems, Inc.

TEX is a trademark of the American Mathematical Society.

UNIX and Motif are registered trademarks and X Window System is a trademark of The Open Groupin the U.S. and other countries.

Windows NT is a registered trademark of the Microsoft Corporation.

ABAQUS/CAE incorporates portions of the ACIS software by SPATIAL TECHNOLOGY INC. ACISis a registered trademark of SPATIAL TECHNOLOGY INC.

This release of ABAQUS on Windows NT includes the diff program obtained from the Free SoftwareFoundation. You may freely distribute the diff program and/or modify it under the terms of the GNULibrary General Public License as published by the Free Software Foundation, Inc., 59 Temple Place,Suite 330, Boston, MA 02111-1307 USA.

This release of ABAQUS/CAE includes lp_solve, a simplex-based code for linear and integerprogramming problems by Michel Berkelaar of Eindhoven University of Technology, Eindhoven, theNetherlands.

Python, copyright 1991-1995 by Stichting Mathematisch Centrum, Amsterdam, The Netherlands. AllRights Reserved. Permission to use, copy, modify, and distribute the Python software and itsdocumentation for any purpose and without fee is hereby granted, provided that the above copyrightnotice appear in all copies and that both that copyright notice and this permission notice appear insupporting documentation, and that the names of Stichting Mathematisch Centrum or CWI or

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Corporation for National Research Initiatives or CNRI not be used in advertising or publicitypertaining to distribution of the software without specific, written prior permission.

All other brand or product names are trademarks or registered trademarks of their respectivecompanies or organizations.

Corporation for National Research Initiatives or CNRI not be used in advertising or publicitypertaining to distribution of the software without specific, written prior permission.

All other brand or product names are trademarks or registered trademarks of their respectivecompanies or organizations.

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General conversion factors (to five significant digits)Quantity U.S. unit SI equivalent

Length 1 in 0.025400 m1 ft 0.30480 m1 mile 1609.3 m

Area 1 in2 0.64516 10-3 m21 ft2 0.092903 m21 acre 4046.9 m2

Volume 1 in3 0.016387 10-3 m31 ft3 0.028317 m31 US gallon 3.7854 10-3 m3

Conversion factors for stress analysisQuantity U.S. unit SI equivalent

Density 1 slug/ft3 = 1 lbf s2/ft4 515.38 kg/m31 lbf s2/in4 10.687 106 kg/m3

Energy 1 ft lbf 1.3558 J (N m)Force 1 lbf 4.4482 N (kg m/s2)Mass 1 slug = 1 lbf s2/ft 14.594 kg (N s2/m)

1 lbf s2/in 175.13 kgPower 1 ft lbf/s 1.3558 W (N m/s)Pressure, Stress 1 psi (lbf/in2) 6894.8 Pa (N/m2)

Conversion factors for heat transfer analysisQuantity U.S. unit SI equivalent

Conductivity 1 Btu/ft hr F 1.7307 W/m C1 Btu/in hr F 20.769 W/m C

Density 1 lbm/in3 27680. kg/m3Energy 1 Btu 1055.1 JHeat flux density 1 Btu/in2 hr 454.26 W/m2Power 1 Btu/hr 0.29307 WSpecific heat 1 Btu/lbm F 4186.8 J/kg CTemperature 1 F 5/9 C

Temp F 9/5 Temp C + 329/5 Temp K - 459.67

Important constantsConstant U.S. unit SI unit

Absolute zero -459.67 F -273.15 CAcceleration of gravity 32.174 ft/s2 9.8066 m/s2Atmospheric pressure 14.694 psi 0.10132 106 PaStefan-Boltzmannconstant

0.1714 10-8 Btu/hr ft2

R45.669 10-8 W/m2 K4

where R = F + 459.67 where K = C + 273.15

Approximate properties of mild steel at room temperatureQuantity U.S. unit SI unit

Conductivity 28.9 Btu/ft hr F 50 W/m C2.4 Btu/in hr F

Density 15.13 slug/ft3 (lbf s2/ft4) 7800 kg/m30.730 10-3 lbf s2/in4

General conversion factors (to five significant digits)Quantity U.S. unit SI equivalent

Length 1 in 0.025400 m1 ft 0.30480 m1 mile 1609.3 m

Area 1 in2 0.64516 10-3 m21 ft2 0.092903 m21 acre 4046.9 m2

Volume 1 in3 0.016387 10-3 m31 ft3 0.028317 m31 US gallon 3.7854 10-3 m3

Conversion factors for stress analysisQuantity U.S. unit SI equivalent

Density 1 slug/ft3 = 1 lbf s2/ft4 515.38 kg/m31 lbf s2/in4 10.687 106 kg/m3

Energy 1 ft lbf 1.3558 J (N m)Force 1 lbf 4.4482 N (kg m/s2)Mass 1 slug = 1 lbf s2/ft 14.594 kg (N s2/m)

1 lbf s2/in 175.13 kgPower 1 ft lbf/s 1.3558 W (N m/s)Pressure, Stress 1 psi (lbf/in2) 6894.8 Pa (N/m2)

Conversion factors for heat transfer analysisQuantity U.S. unit SI equivalent

Conductivity 1 Btu/ft hr F 1.7307 W/m C1 Btu/in hr F 20.769 W/m C

Density 1 lbm/in3 27680. kg/m3Energy 1 Btu 1055.1 JHeat flux density 1 Btu/in2 hr 454.26 W/m2Power 1 Btu/hr 0.29307 WSpecific heat 1 Btu/lbm F 4186.8 J/kg CTemperature 1 F 5/9 C

Temp F 9/5 Temp C + 329/5 Temp K - 459.67

Important constantsConstant U.S. unit SI unit

Absolute zero -459.67 F -273.15 CAcceleration of gravity 32.174 ft/s2 9.8066 m/s2Atmospheric pressure 14.694 psi 0.10132 106 PaStefan-Boltzmannconstant

0.1714 10-8 Btu/hr ft2

R45.669 10-8 W/m2 K4

where R = F + 459.67 where K = C + 273.15

Approximate properties of mild steel at room temperatureQuantity U.S. unit SI unit

Conductivity 28.9 Btu/ft hr F 50 W/m C2.4 Btu/in hr F

Density 15.13 slug/ft3 (lbf s2/ft4) 7800 kg/m30.730 10-3 lbf s2/in4

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0.282 lbm/in3Elastic modulus 30 106 psi 207 109 PaSpecific heat 0.11 Btu/lbm F 460 J/kg CYield stress 30 103 psi 207 106 Pa

0.282 lbm/in3Elastic modulus 30 106 psi 207 109 PaSpecific heat 0.11 Btu/lbm F 460 J/kg CYield stress 30 103 psi 207 106 Pa

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UNITED STATESHibbitt, Karlsson & Sorensen, Inc. Hibbitt, Karlsson & Sorensen (Michigan),

Inc.1080 Main Street 14500 Sheldon Road, Suite 160Pawtucket, RI 02860-4847 Plymouth, MI 48170-2408Tel: 401 727 4200 Tel: 734 451 0217Fax: 401 727 4208 Fax: 734 451 0458E-mail: [email protected],[email protected]

E-mail: [email protected]

http://www.abaqus.comHibbitt, Karlsson & Sorensen (West),Inc.

ABAQUS Solutions Northeast, LLC

39221 Paseo Padre Parkway, Suite F Summit Office Park, West BuildingFremont, CA 94538-1611 300 Centerville Road, Suite 209WTel: 510 794 5891 Warwick, RI 02886-0201Fax: 510 794 1194 Tel: 401 739 3637E-mail: [email protected] Fax: 401 739 3302

E-mail: [email protected] Engineering, Inc.1440 Innovation PlaceWest Lafayette, IN 47906-1000Tel: 765 497 1373Fax: 765 497 4444E-mail: [email protected] AUSTRALIAKB Engineering S. R. L. Compumod Pty. Ltd.Florida 274, Of. 37 Level 13, 309 Pitt Street(1005) Buenos Aires, Argentina Sydney 2000Tel: +54 11 4393 8444 P.O. Box A807Fax: +54 11 4326 2424 Sydney South 1235E-mail: [email protected] Tel: 02 9283 2577

Fax: 02 9283 2585E-mail: [email protected]://www.compumod.com.au

AUSTRIA BENELUXVOEST-ALPINE STAHL LINZ GmbH ABAQUS Benelux BVDepartment WFE Huizermaatweg 576Postfach 3 1276 LN HuizenA-4031 Linz The NetherlandsTel: 0732 6585 9919 Tel: +31 35 52 58 424Fax: 0732 6980 4338 Fax: +31 35 52 44 257E-mail: [email protected] E-mail: [email protected] CZECH REPUBLIC AND SLOVAK

REPUBLICAdvanced Finite Element Services ASATTEDepartment of Engineering Mechanics Technick 4, 166 07 Praha 6Tsinghua University Czech RepublicBeijing 100084, P. R. China Tel: 420 2 24352654Tel: 010 62783986 Fax: 420 2 33322482

UNITED STATESHibbitt, Karlsson & Sorensen, Inc. Hibbitt, Karlsson & Sorensen (Michigan),

Inc.1080 Main Street 14500 Sheldon Road, Suite 160Pawtucket, RI 02860-4847 Plymouth, MI 48170-2408Tel: 401 727 4200 Tel: 734 451 0217Fax: 401 727 4208 Fax: 734 451 0458E-mail: [email protected],[email protected]


http://www.abaqus.comHibbitt, Karlsson & Sorensen (West),Inc.

ABAQUS Solutions Northeast, LLC

39221 Paseo Padre Parkway, Suite F Summit Office Park, West BuildingFremont, CA 94538-1611 300 Centerville Road, Suite 209WTel: 510 794 5891 Warwick, RI 02886-0201Fax: 510 794 1194 Tel: 401 739 3637E-mail: [email protected] Fax: 401 739 3302

E-mail: [email protected] Engineering, Inc.1440 Innovation PlaceWest Lafayette, IN 47906-1000Tel: 765 497 1373Fax: 765 497 4444E-mail: [email protected] AUSTRALIAKB Engineering S. R. L. Compumod Pty. Ltd.Florida 274, Of. 37 Level 13, 309 Pitt Street(1005) Buenos Aires, Argentina Sydney 2000Tel: +54 11 4393 8444 P.O. Box A807Fax: +54 11 4326 2424 Sydney South 1235E-mail: [email protected] Tel: 02 9283 2577

Fax: 02 9283 2585E-mail: [email protected]://www.compumod.com.au

AUSTRIA BENELUXVOEST-ALPINE STAHL LINZ GmbH ABAQUS Benelux BVDepartment WFE Huizermaatweg 576Postfach 3 1276 LN HuizenA-4031 Linz The NetherlandsTel: 0732 6585 9919 Tel: +31 35 52 58 424Fax: 0732 6980 4338 Fax: +31 35 52 44 257E-mail: [email protected] E-mail: [email protected] CZECH REPUBLIC AND SLOVAK

REPUBLICAdvanced Finite Element Services ASATTEDepartment of Engineering Mechanics Technick 4, 166 07 Praha 6Tsinghua University Czech RepublicBeijing 100084, P. R. China Tel: 420 2 24352654Tel: 010 62783986 Fax: 420 2 33322482

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Fax: 010 62771163 E-mail: [email protected]: [email protected] GERMANYABAQUS Software, s.a.r.l. ABACOM Software GmbH7, rue de la Patte d'Oie Theaterstrae 30-3278000 Versailles D-52062 AachenTel: 01 39 24 15 40 Tel: 0241 474010Fax: 01 39 24 15 45 Fax: 0241 4090963E-mail: [email protected] E-mail: [email protected] JAPANHibbitt, Karlsson & Sorensen Italia,s.r.l.

Hibbitt, Karlsson & Sorensen, Inc.

Viale Certosa, 1 3rd Floor, Akasaka Nihon Building20149 Milano 5-24, Akasaka 9-chomeTel: 02 39211211 Minato-kuFax: 02 39211210 Tokyo, 107-0052E-mail: [email protected] Tel: 03 5474 5817

Fax: 03 5474 5818E-mail: [email protected]

KOREA MALAYSIAHibbitt, Karlsson & Sorensen Korea, Inc. Compumod Sdn BhdSuite 306, Sambo Building #33.03 Menara Lion13-2 Yoido-Dong, Youngdeungpo-ku 165 Jalan AmpangSeoul, 150-010 50450 Kuala LumpurTel: 02 785 6707/8 Tel: 3 466 2122Fax: 02 785 6709 Fax: 3 466 2123E-mail: [email protected] E-mail: [email protected] ZEALAND POLANDMatrix Applied Computing Ltd. BudSoft Sp. z o.o.P.O. Box 56-316, Auckland 61-807 PoznaCourier: Unit 2-5, 72 Dominion Road,Mt Eden,

Sw. Marcin 58/64

Auckland Tel: 61 852 31 19Tel: +64 9 623 1223 Fax: 61 852 31 19Fax: +64 9 623 1134 E-mail: [email protected]: [email protected] SOUTH AFRICACompumod (Singapore) Pte Ltd Finite Element Analysis Services (Pty) Ltd.#17-05 Asia Chambers Suite 20-303C, The Waverley20 McCallum Street Wyecroft RoadSingapore 069046 Mowbray 7700Tel: 223 2996 Tel: 021 448 7608Fax: 226 0336 Fax: 021 448 7679E-mail:[email protected]


SPAIN SWEDENPrincipia Ingenieros Consultores, S.A. FEM-Tech ABVelzquez, 94 Pilgatan 828006 Madrid SE-721 30 Vsters

Fax: 010 62771163 E-mail: [email protected]: [email protected] GERMANYABAQUS Software, s.a.r.l. ABACOM Software GmbH7, rue de la Patte d'Oie Theaterstrae 30-3278000 Versailles D-52062 AachenTel: 01 39 24 15 40 Tel: 0241 474010Fax: 01 39 24 15 45 Fax: 0241 4090963E-mail: [email protected] E-mail: [email protected] JAPANHibbitt, Karlsson & Sorensen Italia,s.r.l.

Hibbitt, Karlsson & Sorensen, Inc.

Viale Certosa, 1 3rd Floor, Akasaka Nihon Building20149 Milano 5-24, Akasaka 9-chomeTel: 02 39211211 Minato-kuFax: 02 39211210 Tokyo, 107-0052E-mail: [email protected] Tel: 03 5474 5817

Fax: 03 5474 5818E-mail: [email protected]

KOREA MALAYSIAHibbitt, Karlsson & Sorensen Korea, Inc. Compumod Sdn BhdSuite 306, Sambo Building #33.03 Menara Lion13-2 Yoido-Dong, Youngdeungpo-ku 165 Jalan AmpangSeoul, 150-010 50450 Kuala LumpurTel: 02 785 6707/8 Tel: 3 466 2122Fax: 02 785 6709 Fax: 3 466 2123E-mail: [email protected] E-mail: [email protected] ZEALAND POLANDMatrix Applied Computing Ltd. BudSoft Sp. z o.o.P.O. Box 56-316, Auckland 61-807 PoznaCourier: Unit 2-5, 72 Dominion Road,Mt Eden,

Sw. Marcin 58/64

Auckland Tel: 61 852 31 19Tel: +64 9 623 1223 Fax: 61 852 31 19Fax: +64 9 623 1134 E-mail: [email protected]: [email protected] SOUTH AFRICACompumod (Singapore) Pte Ltd Finite Element Analysis Services (Pty) Ltd.#17-05 Asia Chambers Suite 20-303C, The Waverley20 McCallum Street Wyecroft RoadSingapore 069046 Mowbray 7700Tel: 223 2996 Tel: 021 448 7608Fax: 226 0336 Fax: 021 448 7679E-mail:[email protected]


SPAIN SWEDENPrincipia Ingenieros Consultores, S.A. FEM-Tech ABVelzquez, 94 Pilgatan 828006 Madrid SE-721 30 Vsters

0-7

Tel: 91 209 1482 Tel: 021 12 64 10Fax: 91 575 1026 Fax: 021 18 12 44E-mail: [email protected] E-mail: [email protected] UNITED KINGDOMAPIC Hibbitt, Karlsson & Sorensen (UK) Ltd.7th Fl., 131 Sung Chiang Road The Genesis CentreTaipei, 10428 Science Park South, BirchwoodTel: 02 25083066 Warrington, Cheshire WA3 7BHFax: 02 25077185 Tel: 01925 810166E-mail: [email protected] Fax: 01925 810178


Tel: 91 209 1482 Tel: 021 12 64 10Fax: 91 575 1026 Fax: 021 18 12 44E-mail: [email protected] E-mail: [email protected] UNITED KINGDOMAPIC Hibbitt, Karlsson & Sorensen (UK) Ltd.7th Fl., 131 Sung Chiang Road The Genesis CentreTaipei, 10428 Science Park South, BirchwoodTel: 02 25083066 Warrington, Cheshire WA3 7BHFax: 02 25077185 Tel: 01925 810166E-mail: [email protected] Fax: 01925 810178


0-8

This section lists various resources that are available for help with using ABAQUS, includingtechnical and systems support, training seminars, and documentation.

SupportHKS offers both technical (engineering) support and systems support for ABAQUS. Technical andsystems support are provided through the nearest local support office. You can contact our offices bytelephone, fax, electronic mail, or regular mail. Information on how to contact each office is listed inthe front of each ABAQUS manual. Support information is also available by visiting the ABAQUSHome Page on the World Wide Web (details are given below). When contacting your local supportoffice, please specify whether you would like technical support (you have encountered problemsperforming an ABAQUS analysis) or systems support (ABAQUS will not install correctly, licensingdoes not work correctly, or other hardware-related issues have arisen).

We welcome any suggestions for improvements to the support program or documentation. We willensure that any enhancement requests you make are considered for future releases. If you wish to file acomplaint about the service or products provided by HKS, refer to the ABAQUS Home Page.

Technical supportHKS technical support engineers can assist in clarifying ABAQUS features and checking errors bygiving both general information on using ABAQUS and information on its application to specificanalyses. If you have concerns about an analysis, we suggest that you contact us at an early stage, sinceit is usually easier to solve problems at the beginning of a project rather than trying to correct ananalysis at the end.

Please have the following information ready before calling the technical support hotline, and include itin any written contacts:

The version of ABAQUS that are you using.

The version numbers for ABAQUS/Standard and ABAQUS/Explicit are given at the top of thedata (.dat) file.

The version numbers for ABAQUS/CAE and ABAQUS/Viewer can be found by selectingHelp->On version from the main menu bar.

The version number for ABAQUS/CAT is given at the top of the input (.inp) file as well asthe data file.

The version numbers for ABAQUS/ADAMS and ABAQUS/C-MOLD are output to thescreen.

The version number for ABAQUS/Safe is given under the ABAQUS logo in the mainwindow.

The type of computer on which you are running ABAQUS.

This section lists various resources that are available for help with using ABAQUS, includingtechnical and systems support, training seminars, and documentation.

SupportHKS offers both technical (engineering) support and systems support for ABAQUS. Technical andsystems support are provided through the nearest local support office. You can contact our offices bytelephone, fax, electronic mail, or regular mail. Information on how to contact each office is listed inthe front of each ABAQUS manual. Support information is also available by visiting the ABAQUSHome Page on the World Wide Web (details are given below). When contacting your local supportoffice, please specify whether you would like technical support (you have encountered problemsperforming an ABAQUS analysis) or systems support (ABAQUS will not install correctly, licensingdoes not work correctly, or other hardware-related issues have arisen).

We welcome any suggestions for improvements to the support program or documentation. We willensure that any enhancement requests you make are considered for future releases. If you wish to file acomplaint about the service or products provided by HKS, refer to the ABAQUS Home Page.

Technical supportHKS technical support engineers can assist in clarifying ABAQUS features and checking errors bygiving both general information on using ABAQUS and information on its application to specificanalyses. If you have concerns about an analysis, we suggest that you contact us at an early stage, sinceit is usually easier to solve problems at the beginning of a project rather than trying to correct ananalysis at the end.

Please have the following information ready before calling the technical support hotline, and include itin any written contacts:

The version of ABAQUS that are you using.

The version numbers for ABAQUS/Standard and ABAQUS/Explicit are given at the top of thedata (.dat) file.

The version numbers for ABAQUS/CAE and ABAQUS/Viewer can be found by selectingHelp->On version from the main menu bar.

The version number for ABAQUS/CAT is given at the top of the input (.inp) file as well asthe data file.

The version numbers for ABAQUS/ADAMS and ABAQUS/C-MOLD are output to thescreen.

The version number for ABAQUS/Safe is given under the ABAQUS logo in the mainwindow.

The type of computer on which you are running ABAQUS.

0-9

The symptoms of any problems, including the exact error messages, if any.

Workarounds or tests that you have already tried.

When calling for support about a specific problem, any available ABAQUS output files may be helpfulin answering questions that the support engineer may ask you.

The support engineer will try to diagnose your problem from the model description and a descriptionof the difficulties you are having. Frequently, the support engineer will need model sketches, whichcan be faxed to HKS or sent in the mail. Plots of the final results or the results near the point that theanalysis terminated may also be needed to understand what may have caused the problem.

If the support engineer cannot diagnose your problem from this information, you may be asked to sendthe input data. The data can be sent by means of e-mail, tape, or disk. Please check the ABAQUSHome Page at www.abaqus.com for the media formats that are currently accepted.

All support calls are logged into a database, which enables us to monitor the progress of a particularproblem and to check that we are resolving support issues efficiently. If you would like to know the lognumber of your particular call for future reference, please ask the support engineer. If you are calling todiscuss an existing support problem and you know the log number, please mention it so that we canconsult the database to see what the latest action has been and, thus, avoid duplication of effort. Inaddition, please give the receptionist the support engineer's name (or include it at the top of any e-mailcorrespondence).

Systems supportHKS systems support engineers can help you resolve issues related to the installation and running ofABAQUS, including licensing difficulties, that are not covered by technical support.

You should install ABAQUS by carefully following the instructions in the ABAQUS Site Guide. Ifyou encounter problems with the installation or licensing, first review the instructions in the ABAQUSSite Guide to ensure that they have been followed correctly. If this does not resolve the problems, lookon the ABAQUS Home Page under Technical Support for information about known installationproblems. If this does not address your situation, please contact your local support office. Sendwhatever information is available to define the problem: error messages from an aborted analysis or adetailed explanation of the problems encountered. Whenever possible, please send the output from theabaqus info=env and abaqus info=sys commands.

ABAQUS Web serverFor users connected to the Internet, many questions can be answered by visiting the ABAQUS HomePage on the World Wide Web at

http://www.abaqus.comThe information available on the ABAQUS Home Page includes:

Frequently asked questions

ABAQUS systems information and machine requirements

The symptoms of any problems, including the exact error messages, if any.

Workarounds or tests that you have already tried.

When calling for support about a specific problem, any available ABAQUS output files may be helpfulin answering questions that the support engineer may ask you.

The support engineer will try to diagnose your problem from the model description and a descriptionof the difficulties you are having. Frequently, the support engineer will need model sketches, whichcan be faxed to HKS or sent in the mail. Plots of the final results or the results near the point that theanalysis terminated may also be needed to understand what may have caused the problem.

If the support engineer cannot diagnose your problem from this information, you may be asked to sendthe input data. The data can be sent by means of e-mail, tape, or disk. Please check the ABAQUSHome Page at www.abaqus.com for the media formats that are currently accepted.

All support calls are logged into a database, which enables us to monitor the progress of a particularproblem and to check that we are resolving support issues efficiently. If you would like to know the lognumber of your particular call for future reference, please ask the support engineer. If you are calling todiscuss an existing support problem and you know the log number, please mention it so that we canconsult the database to see what the latest action has been and, thus, avoid duplication of effort. Inaddition, please give the receptionist the support engineer's name (or include it at the top of any e-mailcorrespondence).

Systems supportHKS systems support engineers can help you resolve issues related to the installation and running ofABAQUS, including licensing difficulties, that are not covered by technical support.

You should install ABAQUS by carefully following the instructions in the ABAQUS Site Guide. Ifyou encounter problems with the installation or licensing, first review the instructions in the ABAQUSSite Guide to ensure that they have been followed correctly. If this does not resolve the problems, lookon the ABAQUS Home Page under Technical Support for information about known installationproblems. If this does not address your situation, please contact your local support office. Sendwhatever information is available to define the problem: error messages from an aborted analysis or adetailed explanation of the problems encountered. Whenever possible, please send the output from theabaqus info=env and abaqus info=sys commands.

ABAQUS Web serverFor users connected to the Internet, many questions can be answered by visiting the ABAQUS HomePage on the World Wide Web at

http://www.abaqus.comThe information available on the ABAQUS Home Page includes:

Frequently asked questions

ABAQUS systems information and machine requirements

0-10

Benchmark timing documents

Error status reports

ABAQUS documentation price list

Training seminar schedule

Newsletters

Anonymous ftp siteFor users connected to the Internet, HKS maintains useful documents on an anonymous ftp account onthe computer ftp.abaqus.com. Simply ftp to ftp.abaqus.com. Login as user anonymous, and type youre-mail address as your password. Directions will come up automatically upon login.

Writing to technical supportAddress of HKS Headquarters:Hibbitt, Karlsson & Sorensen, Inc.1080 Main StreetPawtucket, RI 02860-4847, USAAttention: Technical Support

Addresses for other offices and representatives are listed in the front of each manual.

Support for academic institutionsUnder the terms of the Academic License Agreement we do not provide support to users at academicinstitutions unless the institution has also purchased technical support. Please see the ABAQUS HomePage, or contact us for more information.

TrainingAll HKS offices offer regularly scheduled public training classes.

The Introduction to ABAQUS/Standard and ABAQUS/Explicit seminar covers basic usage andnonlinear applications, such as large deformation, plasticity, contact, and dynamics. Workshopsprovide as much practical experience with ABAQUS as possible.

The Introduction to ABAQUS/CAE seminar discusses modeling, managing simulations, and viewingresults with ABAQUS/CAE. "Hands-on" workshops are complemented by lectures.

Advanced seminars cover topics of interest to customers with experience using ABAQUS, such asengine analysis, metal forming, fracture mechanics, and heat transfer.

We also provide training seminars at customer sites. On-site training seminars can be one or more daysin duration, depending on customer requirements. The training topics can include a combination ofmaterial from our introductory and advanced seminars. Workshops allow customers to exerciseABAQUS on their own computers.

Benchmark timing documents

Error status reports

ABAQUS documentation price list

Training seminar schedule

Newsletters

Anonymous ftp siteFor users connected to the Internet, HKS maintains useful documents on an anonymous ftp account onthe computer ftp.abaqus.com. Simply ftp to ftp.abaqus.com. Login as user anonymous, and type youre-mail address as your password. Directions will come up automatically upon login.

Writing to technical supportAddress of HKS Headquarters:Hibbitt, Karlsson & Sorensen, Inc.1080 Main StreetPawtucket, RI 02860-4847, USAAttention: Technical Support

Addresses for other offices and representatives are listed in the front of each manual.

Support for academic institutionsUnder the terms of the Academic License Agreement we do not provide support to users at academicinstitutions unless the institution has also purchased technical support. Please see the ABAQUS HomePage, or contact us for more information.

TrainingAll HKS offices offer regularly scheduled public training classes.

The Introduction to ABAQUS/Standard and ABAQUS/Explicit seminar covers basic usage andnonlinear applications, such as large deformation, plasticity, contact, and dynamics. Workshopsprovide as much practical experience with ABAQUS as possible.

The Introduction to ABAQUS/CAE seminar discusses modeling, managing simulations, and viewingresults with ABAQUS/CAE. "Hands-on" workshops are complemented by lectures.

Advanced seminars cover topics of interest to customers with experience using ABAQUS, such asengine analysis, metal forming, fracture mechanics, and heat transfer.

We also provide training seminars at customer sites. On-site training seminars can be one or more daysin duration, depending on customer requirements. The training topics can include a combination ofmaterial from our introductory and advanced seminars. Workshops allow customers to exerciseABAQUS on their own computers.

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For a schedule of seminars see the ABAQUS Home Page, or call HKS or your local HKSrepresentative.

DocumentationThe following documentation and publications are available from HKS, unless otherwise specified, inprinted form and through our online documentation server. For more information on accessing theonline books, refer to the discussion of execution procedures in the user's manuals.

In addition to the documentation listed below, HKS publishes two newsletters on a regular schedule:ABAQUS/News and ABAQUS/Answers. ABAQUS/News includes topical information about programreleases, training seminars, etc. ABAQUS/Answers includes technical articles on particular topicsrelated to ABAQUS usage. These newsletters are distributed at no cost to users who wish to subscribe.Please contact your local ABAQUS support office if you wish to be added to the mailing list for thesepublications. They are also archived in the Reference Shelf on the ABAQUS Home Page.

Training Manuals

Getting Started with ABAQUS/Standard: This document is a self-paced tutorial designed tohelp new users become familiar with using ABAQUS/Standard for static and dynamic stressanalysis simulations. It contains a number of fully worked examples that provide practicalguidelines for performing structural analyses with ABAQUS.

Getting Started with ABAQUS/Explicit: This document is a self-paced tutorial designed to helpnew users become familiar with using ABAQUS/Explicit. It begins with the basics of modeling inABAQUS, so no prior knowledge of ABAQUS is required. A number of fully worked examplesprovide practical guidelines for performing explicit dynamic analyses, such as drop tests and metalforming simulations, with ABAQUS/Explicit.

Lecture Notes: These notes are available on many topics to which ABAQUS is applied. They areused in the technical seminars that HKS presents to help users improve their understanding andusage of ABAQUS (see the "Training" section above for more information about these seminars).While not intended as stand-alone tutorial material, they are sufficiently comprehensive that theycan usually be used in that mode. The list of available lecture notes is included in theDocumentation Price List.

User's Manuals

ABAQUS/Standard User's Manual: This volume contains a complete description of theelements, material models, procedures, input specifications, etc. It is the basic reference documentfor ABAQUS/Standard.

ABAQUS/Explicit User's Manual: This volume contains a complete description of the elements,material models, procedures, input specifications, etc. It is the basic reference document forABAQUS/Explicit.

For a schedule of seminars see the ABAQUS Home Page, or call HKS or your local HKSrepresentative.

DocumentationThe following documentation and publications are available from HKS, unless otherwise specified, inprinted form and through our online documentation server. For more information on accessing theonline books, refer to the discussion of execution procedures in the user's manuals.

In addition to the documentation listed below, HKS publishes two newsletters on a regular schedule:ABAQUS/News and ABAQUS/Answers. ABAQUS/News includes topical information about programreleases, training seminars, etc. ABAQUS/Answers includes technical articles on particular topicsrelated to ABAQUS usage. These newsletters are distributed at no cost to users who wish to subscribe.Please contact your local ABAQUS support office if you wish to be added to the mailing list for thesepublications. They are also archived in the Reference Shelf on the ABAQUS Home Page.

Training Manuals

Getting Started with ABAQUS/Standard: This document is a self-paced tutorial designed tohelp new users become familiar with using ABAQUS/Standard for static and dynamic stressanalysis simulations. It contains a number of fully worked examples that provide practicalguidelines for performing structural analyses with ABAQUS.

Getting Started with ABAQUS/Explicit: This document is a self-paced tutorial designed to helpnew users become familiar with using ABAQUS/Explicit. It begins with the basics of modeling inABAQUS, so no prior knowledge of ABAQUS is required. A number of fully worked examplesprovide practical guidelines for performing explicit dynamic analyses, such as drop tests and metalforming simulations, with ABAQUS/Explicit.

Lecture Notes: These notes are available on many topics to which ABAQUS is applied. They areused in the technical seminars that HKS presents to help users improve their understanding andusage of ABAQUS (see the "Training" section above for more information about these seminars).While not intended as stand-alone tutorial material, they are sufficiently comprehensive that theycan usually be used in that mode. The list of available lecture notes is included in theDocumentation Price List.

User's Manuals

ABAQUS/Standard User's Manual: This volume contains a complete description of theelements, material models, procedures, input specifications, etc. It is the basic reference documentfor ABAQUS/Standard.

ABAQUS/Explicit User's Manual: This volume contains a complete description of the elements,material models, procedures, input specifications, etc. It is the basic reference document forABAQUS/Explicit.

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ABAQUS/CAE User's Manual: This reference document for ABAQUS/CAE includes threecomprehensive tutorials as well as detailed descriptions of how to use ABAQUS/CAE for modelgeneration, analysis, and results evaluation.

ABAQUS/Viewer User's Manual: This basic reference document for ABAQUS/Viewer includesan introductory tutorial as well as a complete description of how to use ABAQUS/Viewer todisplay your model and results.

ABAQUS/ADAMS User's Manual: This document describes how to install and how to useABAQUS/ADAMS, an interface program that creates ABAQUS models of ADAMS componentsand converts the ABAQUS results into an ADAMS modal neutral file that can be used by theADAMS/Flex program. It is the basic reference document for the ABAQUS/ADAMS program.

ABAQUS/CAT User's Manual: This document describes how to install and how to useABAQUS/CAT, an interface program that creates an ABAQUS input file from a CATIA modeland postprocesses the analysis results in CATIA. It is the basic reference document for theABAQUS/CAT program.

ABAQUS/C-MOLD User's Manual: This document describes how to install and how to useABAQUS/C-MOLD, an interface program that translates finite element mesh, material property,and initial stress data from a C-MOLD analysis to an ABAQUS input file.

ABAQUS/Safe User's Manual: This document describes how to install and how to useABAQUS/Safe, an interface program that calculates fatigue lives and fatigue strength reservefactors from finite element models. It is the basic reference document for the ABAQUS/Safeprogram. The theoretical background to fatigue analysis is contained in the Modern Metal FatigueAnalysis manual (available only in print).

Using ABAQUS Online Documentation: This online manual contains instructions on using theABAQUS online documentation server to read the manuals that are available online.

ABAQUS Release Notes: This document contains brief descriptions of the new features availablein the latest release of the ABAQUS product line.

ABAQUS Site Guide: This document describes how to install ABAQUS and how to configurethe installation for particular circumstances. Some of this information, of most relevance to users,is also provided in the user's manuals.

Examples Manuals

ABAQUS Example Problems Manual: This volume contains more than 75 detailed examplesdesigned to illustrate the approaches and decisions needed to perform meaningful linear andnonlinear analysis. Typical cases are large motion of an elastic-plastic pipe hitting a rigid wall;inelastic buckling collapse of a thin-walled elbow; explosive loading of an elastic, viscoplastic thinring; consolidation under a footing; buckling of a composite shell with a hole; and deep drawing ofa metal sheet. It is generally useful to look for relevant examples in this manual and to reviewthem when embarking on a new class of problem.

ABAQUS/CAE User's Manual: This reference document for ABAQUS/CAE includes threecomprehensive tutorials as well as detailed descriptions of how to use ABAQUS/CAE for modelgeneration, analysis, and results evaluation.

ABAQUS/Viewer User's Manual: This basic reference document for ABAQUS/Viewer includesan introductory tutorial as well as a complete description of how to use ABAQUS/Viewer todisplay your model and results.

ABAQUS/ADAMS User's Manual: This document describes how to install and how to useABAQUS/ADAMS, an interface program that creates ABAQUS models of ADAMS componentsand converts the ABAQUS results into an ADAMS modal neutral file that can be used by theADAMS/Flex program. It is the basic reference document for the ABAQUS/ADAMS program.

ABAQUS/CAT User's Manual: This document describes how to install and how to useABAQUS/CAT, an interface program that creates an ABAQUS input file from a CATIA modeland postprocesses the analysis results in CATIA. It is the basic reference document for theABAQUS/CAT program.

ABAQUS/C-MOLD User's Manual: This document describes how to install and how to useABAQUS/C-MOLD, an interface program that translates finite element mesh, material property,and initial stress data from a C-MOLD analysis to an ABAQUS input file.

ABAQUS/Safe User's Manual: This document describes how to install and how to useABAQUS/Safe, an interface program that calculates fatigue lives and fatigue strength reservefactors from finite element models. It is the basic reference document for the ABAQUS/Safeprogram. The theoretical background to fatigue analysis is contained in the Modern Metal FatigueAnalysis manual (available only in print).

Using ABAQUS Online Documentation: This online manual contains instructions on using theABAQUS online documentation server to read the manuals that are available online.

ABAQUS Release Notes: This document contains brief descriptions of the new features availablein the latest release of the ABAQUS product line.

ABAQUS Site Guide: This document describes how to install ABAQUS and how to configurethe installation for particular circumstances. Some of this information, of most relevance to users,is also provided in the user's manuals.

Examples Manuals

ABAQUS Example Problems Manual: This volume contains more than 75 detailed examplesdesigned to illustrate the approaches and decisions needed to perform meaningful linear andnonlinear analysis. Typical cases are large motion of an elastic-plastic pipe hitting a rigid wall;inelastic buckling collapse of a thin-walled elbow; explosive loading of an elastic, viscoplastic thinring; consolidation under a footing; buckling of a composite shell with a hole; and deep drawing ofa metal sheet. It is generally useful to look for relevant examples in this manual and to reviewthem when embarking on a new class of problem.

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ABAQUS Benchmarks Manual: This volume (available online and, if requested, in print)contains over 200 benchmark problems and standard analyses used to evaluate the performance ofABAQUS; the tests are multiple element tests of simple geometries or simplified versions of realproblems. The NAFEMS benchmark problems are included in this manual.

ABAQUS Verification Manual: This online-only volume contains more than 5000 basic testcases, providing verification of each individual program feature (procedures, output options,MPCs, etc.) against exact calculations and other published results. It may be useful to run theseproblems when learning to use a new capability. In addition, the supplied input data files providegood starting points to check the behavior of elements, materials, etc.

Reference Manuals

ABAQUS Keywords Manual: This volume contains a complete description of all the inputoptions that are available in ABAQUS/Standard and ABAQUS/Explicit.

ABAQUS Theory Manual: This volume (available online and, if requested, in print) containsdetailed, precise discussions of all theoretical aspects of ABAQUS. It is written to be understoodby users with an engineering background.

ABAQUS Command Language Manual: This online manual provides a description of theABAQUS Command Language and a command reference that lists the syntax of each command.The manual describes how commands can be used to create and analyze ABAQUS/CAE models,to view the results of the analysis, and to automate repetitive tasks. It also contains information onusing the ABAQUS Command Language or C++ as an application programming interface (API).

ABAQUS Input Files: This online manual contains all the input files that are included with theABAQUS release and referred to in the ABAQUS Example Problems Manual, the ABAQUSBenchmarks Manual, and the ABAQUS Verification Manual. They are listed in the order in whichthey appear in the manuals, under the title of the problem that refers to them. The input filereferences in the manuals hyperlink directly to this book.

Quality Assurance Plan: This document describes HKS's QA procedures. It is a controlleddocument, provided to customers who subscribe to either HKS's Nuclear QA Program or theQuality Monitoring Service.

IntroductionThis is the Example Problems Manual for ABAQUS. It contains many solved examples that illustratethe use of the program for common types of problems. Some of the problems are quite difficult andrequire combinations of the capabilities in the code.

The problems have been chosen to serve two purposes: to verify the capabilities in ABAQUS byexercising the code on nontrivial cases and to provide guidance to users who must work on a class ofproblems with which they are relatively unfamiliar. In each worked example the discussion in themanual states why the example is included and leads the reader through the standard approach to an

ABAQUS Benchmarks Manual: This volume (available online and, if requested, in print)contains over 200 benchmark problems and standard analyses used to evaluate the performance ofABAQUS; the tests are multiple element tests of simple geometries or simplified versions of realproblems. The NAFEMS benchmark problems are included in this manual.

ABAQUS Verification Manual: This online-only volume contains more than 5000 basic testcases, providing verification of each individual program feature (procedures, output options,MPCs, etc.) against exact calculations and other published results. It may be useful to run theseproblems when learning to use a new capability. In addition, the supplied input data files providegood starting points to check the behavior of elements, materials, etc.

Reference Manuals

ABAQUS Keywords Manual: This volume contains a complete description of all the inputoptions that are available in ABAQUS/Standard and ABAQUS/Explicit.

ABAQUS Theory Manual: This volume (available online and, if requested, in print) containsdetailed, precise discussions of all theoretical aspects of ABAQUS. It is written to be understoodby users with an engineering background.

ABAQUS Command Language Manual: This online manual provides a description of theABAQUS Command Language and a command reference that lists the syntax of each command.The manual describes how commands can be used to create and analyze ABAQUS/CAE models,to view the results of the analysis, and to automate repetitive tasks. It also contains information onusing the ABAQUS Command Language or C++ as an application programming interface (API).

ABAQUS Input Files: This online manual contains all the input files that are included with theABAQUS release and referred to in the ABAQUS Example Problems Manual, the ABAQUSBenchmarks Manual, and the ABAQUS Verification Manual. They are listed in the order in whichthey appear in the manuals, under the title of the problem that refers to them. The input filereferences in the manuals hyperlink directly to this book.

Quality Assurance Plan: This document describes HKS's QA procedures. It is a controlleddocument, provided to customers who subscribe to either HKS's Nuclear QA Program or theQuality Monitoring Service.

IntroductionThis is the Example Problems Manual for ABAQUS. It contains many solved examples that illustratethe use of the program for common types of problems. Some of the problems are quite difficult andrequire combinations of the capabilities in the code.

The problems have been chosen to serve two purposes: to verify the capabilities in ABAQUS byexercising the code on nontrivial cases and to provide guidance to users who must work on a class ofproblems with which they are relatively unfamiliar. In each worked example the discussion in themanual states why the example is included and leads the reader through the standard approach to an

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analysis: element and mesh selection, material model, and a discussion of the results. Input data filesare provided for all of these cases. Many of these problems are worked with different element types,mesh densities, and other variations. This results in a relatively large number of input data files forsome of the problems. Only a few of the input files are listed in the printed manual. The selection hasbeen made to provide the most guidance to the user.

All input files, both the ones that are listed in the printed manual and the ones that are referenced, areincluded with the ABAQUS release. The ABAQUS/Fetch utility is used to extract these input filesfrom the compressed archive files provided with the ABAQUS release. For example, to fetch input fileboltpipeflange_3d_cyclsym.inp, type

abaqus fetch job=boltpipeflange_3d_cyclsym.inpParametric study script (.psf) and user subroutine (.f) files can be fetched in the same manner. Allfiles for a particular problem can be obtained by leaving off the file extension. The ABAQUS/Fetchexecution procedure is explained in detail in `Èxecution procedure for ABAQUS/Fetch,'' Section 3.2.9of the ABAQUS/Standard User's Manual and the ABAQUS/Explicit User's Manual.

It is sometimes useful to search the input files. The findkeyword utility is used to locate input filesthat contain user-specified input. This utility is defined in `Èxecution procedure for querying thekeyword/problem database,'' Section 3.2.8 of the ABAQUS/Standard User's Manual and theABAQUS/Explicit User's Manual.

In addition, all the input files included with the ABAQUS release can be accessed through theABAQUS Input Files electronic book. This book is part of the ABAQUS online documentationcollection and, as such, is fully searchable (with the exception of numeric strings andABAQUS-specific terms). When reading the online version of the ABAQUS Benchmarks Manual, theABAQUS Example Problems Manual, or the ABAQUS Verification Manual, the user can click on aninput file name; the ABAQUS Input Files book will open to that file in a separate window.

To reproduce the graphical representation of the solution reported in some of the examples, the outputfrequency used in the input files may need to be increased. For example, in ``Linear analysis of theIndian Point reactor feedwater line,'' Section 2.2.2, the figures that appear in the manual can beobtained only if the solution is written to the results file every increment; that is, if the input files arechanged to read

*NODE FILE, ..., FREQUENCY=1instead of FREQUENCY=100 as appears now.

In addition to the Example Problems Manual, there are two other manuals that contain workedproblems. The ABAQUS Benchmarks Manual contains benchmark problems (including the NAFEMSsuite of test problems) and standard analyses used to evaluate the performance of ABAQUS. The testsin this manual are multiple element tests of simple geometries or simplified versions of real problems.The ABAQUS Verification Manual contains a large number of examples that are intended aselementary verification of the basic modeling capabilities.

The verification of ABAQUS consists of running the problems in the ABAQUS Example ProblemsManual, the ABAQUS Benchmarks Manual, and the ABAQUS Verification Manual. Before a version

analysis: element and mesh selection, material model, and a discussion of the results. Input data filesare provided for all of these cases. Many of these problems are worked with different element types,mesh densities, and other variations. This results in a relatively large number of input data files forsome of the problems. Only a few of the input files are listed in the printed manual. The selection hasbeen made to provide the most guidance to the user.

All input files, both the ones that are listed in the printed manual and the ones that are referenced, areincluded with the ABAQUS release. The ABAQUS/Fetch utility is used to extract these input filesfrom the compressed archive files provided with the ABAQUS release. For example, to fetch input fileboltpipeflange_3d_cyclsym.inp, type

abaqus fetch job=boltpipeflange_3d_cyclsym.inpParametric study script (.psf) and user subroutine (.f) files can be fetched in the same manner. Allfiles for a particular problem can be obtained by leaving off the file extension. The ABAQUS/Fetchexecution procedure is explained in detail in `Èxecution procedure for ABAQUS/Fetch,'' Section 3.2.9of the ABAQUS/Standard User's Manual and the ABAQUS/Explicit User's Manual.

It is sometimes useful to search the input files. The findkeyword utility is used to locate input filesthat contain user-specified input. This utility is defined in `Èxecution procedure for querying thekeyword/problem database,'' Section 3.2.8 of the ABAQUS/Standard User's Manual and theABAQUS/Explicit User's Manual.

In addition, all the input files included with the ABAQUS release can be accessed through theABAQUS Input Files electronic book. This book is part of the ABAQUS online documentationcollection and, as such, is fully searchable (with the exception of numeric strings andABAQUS-specific terms). When reading the online version of the ABAQUS Benchmarks Manual, theABAQUS Example Problems Manual, or the ABAQUS Verification Manual, the user can click on aninput file name; the ABAQUS Input Files book will open to that file in a separate window.

To reproduce the graphical representation of the solution reported in some of the examples, the outputfrequency used in the input files may need to be increased. For example, in ``Linear analysis of theIndian Point reactor feedwater line,'' Section 2.2.2, the figures that appear in the manual can beobtained only if the solution is written to the results file every increment; that is, if the input files arechanged to read

*NODE FILE, ..., FREQUENCY=1instead of FREQUENCY=100 as appears now.

In addition to the Example Problems Manual, there are two other manuals that contain workedproblems. The ABAQUS Benchmarks Manual contains benchmark problems (including the NAFEMSsuite of test problems) and standard analyses used to evaluate the performance of ABAQUS. The testsin this manual are multiple element tests of simple geometries or simplified versions of real problems.The ABAQUS Verification Manual contains a large number of examples that are intended aselementary verification of the basic modeling capabilities.

The verification of ABAQUS consists of running the problems in the ABAQUS Example ProblemsManual, the ABAQUS Benchmarks Manual, and the ABAQUS Verification Manual. Before a version

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of ABAQUS is released, it must run all verification, benchmark, and example problems correctly.of ABAQUS is released, it must run all verification, benchmark, and example problems correctly.

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1. Static Stress/Displacement Analyses1.1 Static and quasi-static stress analyses

1.1.1 Axisymmetric analysis of bolted pipe flange connectionsProduct: ABAQUS/Standard

A bolted pipe flange connection is a common and important part of many piping systems. Suchconnections are typically composed of hubs of pipes, pipe flanges with bolt holes, sets of bolts andnuts, and a gasket. These components interact with each other in the tightening process and whenoperation loads such as internal pressure and temperature are applied. Experimental and numericalstudies on different types of interaction among these components are frequently reported. The studiesinclude analysis of the bolt-up procedure that yields uniform bolt stress (Bibel and Ezell, 1992),contact analysis of screw threads (Fukuoka, 1992; Chaaban and Muzzo, 1991), and full stress analysisof the entire pipe joint assembly (Sawa et al., 1991). To establish an optimal design, a full stressanalysis determines factors such as the contact stresses that govern the sealing performance, therelationship between bolt force and internal pressure, the effective gasket seating width, and thebending moment produced in the bolts. This example shows how to perform such a design analysis byusing an economical axisymmetric model and how to assess the accuracy of the axisymmetric solutionby comparing the results to those obtained from a simulation using a three-dimensional segmentmodel. In addition, several three-dimensional models that use multiple levels of superelements areanalyzed to demonstrate the use of superelements with a large number of retained degrees of freedom.

Geometry and modelThe bolted joint assembly being analyzed is depicted in Figure 1.1.1-1. The geometry and dimensionsof the various parts are taken from Sawa et al. (1991), modified slightly to simplify the modeling. Theinner wall radius of both the hub and the gasket is 25 mm. The outer wall radii of the pipe flange andthe gasket are 82.5 mm and 52.5 mm, respectively. The thickness of the gasket is 2.5 mm. The pipeflange has eight bolt holes that are equally spaced in the pitch circle of radius 65 mm. The radius of thebolt hole is modified in this analysis to be the same as that of the bolt: 8 mm. The bolt head (bearingsurface) is assumed to be circular, and its radius is 12 mm.

The Young's modulus is 206 GPa and the Poisson's ratio is 0.3 for both the bolt and the pipehub/flange. The gasket is modeled with either solid continuum or gasket elements. When continuumelements are used, the gasket's Young's modulus, E, equals 68.7 GPa and its Poisson's ratio, , equals0.3.

When gasket elements are used, a linear gasket pressure/closure relationship is used with the effective"normal stiffness," Sn, equal to the material Young's modulus divided by the thickness so that Sn =27.48 GPa/mm. Similarly a linear shear stress/shear motion relationship is used with an effective shearstiffness, St, equal to the material shear modulus divided by the thickness so that St = 10.57 GPa/mm.The membrane behavior is specified with a Young's modulus of 68.7 GPa and a Poisson's ratio of 0.3.Sticking contact conditions are assumed in all contact areas: between the bearing surface and theflange and between the gasket and the hub. Contact between the bolt shank and the bolt hole is

1. Static Stress/Displacement Analyses1.1 Static and quasi-static stress analyses

1.1.1 Axisymmetric analysis of bolted pipe flange connectionsProduct: ABAQUS/Standard

A bolted pipe flange connection is a common and important part of many piping systems. Suchconnections are typically composed of hubs of pipes, pipe flanges with bolt holes, sets of bolts andnuts, and a gasket. These components interact with each other in the tightening process and whenoperation loads such as internal pressure and temperature are applied. Experimental and numericalstudies on different types of interaction among these components are frequently reported. The studiesinclude analysis of the bolt-up procedure that yields uniform bolt stress (Bibel and Ezell, 1992),contact analysis of screw threads (Fukuoka, 1992; Chaaban and Muzzo, 1991), and full stress analysisof the entire pipe joint assembly (Sawa et al., 1991). To establish an optimal design, a full stressanalysis determines factors such as the contact stresses that govern the sealing performance, therelationship between bolt force and internal pressure, the effective gasket seating width, and thebending moment produced in the bolts. This example shows how to perform such a design analysis byusing an economical axisymmetric model and how to assess the accuracy of the axisymmetric solutionby comparing the results to those obtained from a simulation using a three-dimensional segmentmodel. In addition, several three-dimensional models that use multiple levels of superelements areanalyzed to demonstrate the use of superelements with a large number of retained degrees of freedom.

Geometry and modelThe bolted joint assembly being analyzed is depicted in Figure 1.1.1-1. The geometry and dimensionsof the various parts are taken from Sawa et al. (1991), modified slightly to simplify the modeling. Theinner wall radius of both the hub and the gasket is 25 mm. The outer wall radii of the pipe flange andthe gasket are 82.5 mm and 52.5 mm, respectively. The thickness of the gasket is 2.5 mm. The pipeflange has eight bolt holes that are equally spaced in the pitch circle of radius 65 mm. The radius of thebolt hole is modified in this analysis to be the same as that of the bolt: 8 mm. The bolt head (bearingsurface) is assumed to be circular, and its radius is 12 mm.

The Young's modulus is 206 GPa and the Poisson's ratio is 0.3 for both the bolt and the pipehub/flange. The gasket is modeled with either solid continuum or gasket elements. When continuumelements are used, the gasket's Young's modulus, E, equals 68.7 GPa and its Poisson's ratio, , equals0.3.

When gasket elements are used, a linear gasket pressure/closure relationship is used with the effective"normal stiffness," Sn, equal to the material Young's modulus divided by the thickness so that Sn =27.48 GPa/mm. Similarly a linear shear stress/shear motion relationship is used with an effective shearstiffness, St, equal to the material shear modulus divided by the thickness so that St = 10.57 GPa/mm.The membrane behavior is specified with a Young's modulus of 68.7 GPa and a Poisson's ratio of 0.3.Sticking contact conditions are assumed in all contact areas: between the bearing surface and theflange and between the gasket and the hub. Contact between the bolt shank and the bolt hole is

Static Stress/Displacement Analyses

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ignored.

The finite element idealizations of the symmetric half of the pipe joint are shown in Figure 1.1.1-2 andFigure 1.1.1-3, corresponding to the axisymmetric and three-dimensional analyses, respectively. Themesh used for the axisymmetric analysis consists of a mesh for the pipe hub/flange and gasket and aseparate mesh for the bolts. In Figure 1.1.1-2the top figure shows the mesh of the pipe hub and flange,with the bolt hole area shown in a lighter shade; and the bottom figure shows the overall mesh with thegasket and the bolt in place.

For the axisymmetric model second-order elements with reduced integration, CAX8R, are usedthroughout the mesh of the pipe hub/flange. The gasket is modeled with either CAX8R solidcontinuum elements or GKAX6 gasket elements. Contact between the gasket and the pipe hub/flangeis modeled with contact pairs between surfaces defined on the faces of elements in the contact regionor between such element-based surfaces and node-based surfaces. In an axisymmetric analysis thebolts and the perforated flange must be modeled properly. The bolts are modeled as plane stresselements since they do not carry hoop stress. Second-order plane stress elements with reducedintegration, CPS8R, are employed for this purpose. The contact surface definitions, which areassociated with the faces of the elements, account for the plane stress condition automatically. Toaccount for all eight bolts used in the joint, the combined cross-sectional areas of the shank and thehead of the bolts must be calculated and redistributed to the bolt mesh appropriately using the areaattributes for the solid elements. The contact area is adjusted automatically.

Figure 1.1.1-4 illustrates the cross-sectional views of the bolt head and the shank. Each plane stresselement represents a volume that extends out of the x-y plane. For example, element A represents avolume calculated as (HA) (AreaA). Likewise, element B represents a volume calculated as (HB ) (AreaB ). The sectional area in the x-z plane pertaining to a given element can be calculated as

Area = 2

Z X2X1

[(R2 x2)12 ]dx = [x(R2 x2)

12 +R2 arcsin (

x

jRj )]X2X1

;

where R is the bolt head radius, Rbolthead , or the shank radius, Rshank (depending on the elementlocation), and X1 and X2 are x-coordinates of the left and right side of the given element,respectively.

If the sectional areas are divided by the respective element widths, WA and WB , we obtainrepresentative element thicknesses. Multiplying each element thickness by eight (the number of boltsin the model) produces the thickness values that are found in the *SOLID SECTION options.

Sectional areas that are associated with bolt head elements located on the model's contact surfaces areused to calculate the surface areas of the nodes used in defining the node-based surfaces of the model.Referring again to Figure 1.1.1-4, nodal contact areas for a single bolt are calculated as follows:

A1 =AC4

; A9 =AF4

;

ignored.

The finite element idealizations of the symmetric half of the pipe joint are shown in Figure 1.1.1-2 andFigure 1.1.1-3, corresponding to the axisymmetric and three-dimensional analyses, respectively. Themesh used for the axisymmetric analysis consists of a mesh for the pipe hub/flange and gasket and aseparate mesh for the bolts. In Figure 1.1.1-2the top figure shows the mesh of the pipe hub and flange,with the bolt hole area shown in a lighter shade; and the bottom figure shows the overall mesh with thegasket and the bolt in place.

For the axisymmetric model second-order elements with reduced integration, CAX8R, are usedthroughout the mesh of the pipe hub/flange. The gasket is modeled with either CAX8R solidcontinuum elements or GKAX6 gasket elements. Contact between the gasket and the pipe hub/flangeis modeled with contact pairs between surfaces defined on the faces of elements in the contact regionor between such element-based surfaces and node-based surfaces. In an axisymmetric analysis thebolts and the perforated flange must be modeled properly. The bolts are modeled as plane stresselements since they do not carry hoop stress. Second-order plane stress elements with reducedintegration, CPS8R, are employed for this purpose. The contact surface definitions, which areassociated with the faces of the elements, account for the plane stress condition automatically. Toaccount for all eight bolts used in the joint, the combined cross-sectional areas of the shank and thehead of the bolts must be calculated and redistributed to the bolt mesh appropriately using the areaattributes for the solid elements. The contact area is adjusted automatically.

Figure 1.1.1-4 illustrates the cross-sectional views of the bolt head and the shank. Each plane stresselement represents a volume that extends out of the x-y plane. For example, element A represents avolume calculated as (HA) (AreaA). Likewise, element B represents a volume calculated as (HB ) (AreaB ). The sectional area in the x-z plane pertaining to a given element can be calculated as

Area = 2

Z X2X1

[(R2 x2)12 ]dx = [x(R2 x2)

12 +R2 arcsin (

x

jRj )]X2X1

;

where R is the bolt head radius, Rbolthead , or the shank radius, Rshank (depending on the elementlocation), and X1 and X2 are x-coordinates of the left and right side of the given element,respectively.

If the sectional areas are divided by the respective element widths, WA and WB , we obtainrepresentative element thicknesses. Multiplying each element thickness by eight (the number of boltsin the model) produces the thickness values that are found in the *SOLID SECTION options.

Sectional areas that are associated with bolt head elements located on the model's contact surfaces areused to calculate the surface areas of the nodes used in defining the node-based surfaces of the model.Referring again to Figure 1.1.1-4, nodal contact areas for a single bolt are calculated as follows:

A1 =AC4

; A9 =AF4

;


1-18

A2 =AC2

; A4 =AD2

; A6 =AE2

; A8 =AF2

;

A3 = (AC +AD )=4; A5 = (AD +AE )=4; A7 = (AE +AF )=4;

where A1 through A9 are contact areas that are associated with contact nodes 1-9 and Ac through AFare sectional areas that are associated with bolt head elements C-F . Multiplying the above areas byeight (the number of bolts in the model) provides the nodal contact areas found under the *SURFACEINTERACTION options.

A common way of handling the presence of the bolt holes in the pipe flange in axisymmetric analysesis to smear the material properties used in the bolt hole area of the mesh and to use inhomogeneousmaterial properties that correspond to a weaker material in this region. General guidelines fordetermining the effective material properties for perforated flat plates are found in ASME Section VIIIDiv 2 Article 4-9. For the type of structure under study, which is not a flat plate, a common approachto determining the effective material properties is to calculate the elasticity moduli reduction factor,which is the ratio of the ligament area in the pitch circle to the annular area of the pitch circle. In thismodel the annular area of the pitch circle is given by AA = 6534.51 mm2, and the total area of the boltholes is given by AH = 882 = 1608.5 mm2. Hence, the reduction factor is simply 1AH=AA =0.754. The effective in-plane moduli of elasticity, E10 and E20 , are obtained by multiplying therespective moduli, E1 and E2, by this factor. We assume material isotropy in the r-z plane; thus,E10 = E20 = E0: The modulus in the hoop direction, E30 , should be very small and is chosen suchthat E0=E30 = 106. The in-plane shear modulus is then calculated based on the effective elasticitymodulus: G012 = E0=2(1 + ): The shear moduli in the hoop direction are also calculated similarly butwith set to zero (they are not used in an axisymmetric model). Hence, we have E10 = E20 = 155292MPa, E30 = 0.155292 MPa, G012 = 59728 MPa, and G013 = G023 = 0.07765 MPa. These elasticitymoduli are specified using *ELASTIC, TYPE=ENGINEERING CONSTANTS for the bolt hole part ofthe mesh.

The mesh for the three-dimensional analysis without superelements, shown in Figure 1.1.1-3,represents a 22.5 segment of the pipe joint and employs second-order brick elements with reducedintegration, C3D20R, for the pipe hub/flange and bolts. The gasket is modeled with C3D20R elementsor GK3D18 elements. The top figure shows the mesh of the pipe hub and flange, and the bottom figureshows both the gasket and bolt (in the lighter color). Contact is modeled by the interaction of contactsurfaces defined by grouping specific faces of the elements in the contacting regions. Forthree-dimensional contact where both the master and slave surfaces are deformable, the SMALLSLIDING parameter must be used on the *CONTACT PAIR option to indicate that small relativesliding occurs between contacting surfaces. No special adjustments need be made for the materialproperties used in the three-dimensional model because all parts are modeled appropriately.

Four different meshes that use superelements to model the flange are tested. A first-level superelementis created for the entire 22.5 segment of the flange shown in Figure 1.1.1-3, while the gasket and thebolt are meshed as before. The nodes on the flange in contact with the bolt cap form a node-basedsurface, while the nodes on the flange in contact with the gasket form another node-based surface.

A2 =AC2

; A4 =AD2

; A6 =AE2

; A8 =AF2

;

A3 = (AC +AD )=4; A5 = (AD +AE )=4; A7 = (AE +AF )=4;

where A1 through A9 are contact areas that are associated with contact nodes 1-9 and Ac through AFare sectional areas that are associated with bolt head elements C-F . Multiplying the above areas byeight (the number of bolts in the model) provides the nodal contact areas found under the *SURFACEINTERACTION options.

A common way of handling the presence of the bolt holes in the pipe flange in axisymmetric analysesis to smear the material properties used in the bolt hole area of the mesh and to use inhomogeneousmaterial properties that correspond to a weaker material in this region. General guidelines fordetermining the effective material properties for perforated flat plates are found in ASME Section VIIIDiv 2 Article 4-9. For the type of structure under study, which is not a flat plate, a common approachto determining the effective material properties is to calculate the elasticity moduli reduction factor,which is the ratio of the ligament area in the pitch circle to the annular area of the pitch circle. In thismodel the annular area of the pitch circle is given by AA = 6534.51 mm2, and the total area of the boltholes is given by AH = 882 = 1608.5 mm2. Hence, the reduction factor is simply 1AH=AA =0.754. The effective in-plane moduli of elasticity, E10 and E20 , are obtained by multiplying therespective moduli, E1 and E2, by this factor. We assume material isotropy in the r-z plane; thus,E10 = E20 = E0: The modulus in the hoop direction, E30 , should be very small and is chosen suchthat E0=E30 = 106. The in-plane shear modulus is then calculated based on the effective elasticitymodulus: G012 = E0=2(1 + ): The shear moduli in the hoop direction are also calculated similarly butwith set to zero (they are not used in an axisymmetric model). Hence, we have E10 = E20 = 155292MPa, E30 = 0.155292 MPa, G012 = 59728 MPa, and G013 = G023 = 0.07765 MPa. These elasticitymoduli are specified using *ELASTIC, TYPE=ENGINEERING CONSTANTS for the bolt hole part ofthe mesh.

The mesh for the three-dimensional analysis without superelements, shown in Figure 1.1.1-3,represents a 22.5 segment of the pipe joint and employs second-order brick elements with reducedintegration, C3D20R, for the pipe hub/flange and bolts. The gasket is modeled with C3D20R elementsor GK3D18 elements. The top figure shows the mesh of the pipe hub and flange, and the bottom figureshows both the gasket and bolt (in the lighter color). Contact is modeled by the interaction of contactsurfaces defined by grouping specific faces of the elements in the contacting regions. Forthree-dimensional contact where both the master and slave surfaces are deformable, the SMALLSLIDING parameter must be used on the *CONTACT PAIR option to indicate that small relativesliding occurs between contacting surfaces. No special adjustments need be made for the materialproperties used in the three-dimensional model because all parts are modeled appropriately.

Four different meshes that use superelements to model the flange are tested. A first-level superelementis created for the entire 22.5 segment of the flange shown in Figure 1.1.1-3, while the gasket and thebolt are meshed as before. The nodes on the flange in contact with the bolt cap form a node-basedsurface, while the nodes on the flange in contact with the gasket form another node-based surface.


1-19

These node-based surfaces will form contact pairs with the master surfaces on the bolt cap and on thegasket, which are defined with *SURFACE as before. The retained degrees of freedom on thesuperelement include all three degrees of freedom for the nodes in these node-based surfaces as well asfor the nodes on the 0 and 22.5 faces of the flange. Appropriate boundary conditions are specified atthe superelement usage level.

A second-level superelement of 45 is created by reflecting the first-level superelement with respect tothe 22.5 plane. The nodes on the 22.5 face belonging to the reflected superelement are constrained inall three degrees of freedom to the corresponding nodes on the 22.5 face belonging to the originalfirst-level superelement. The half-bolt and the gasket sector corresponding to the reflectedsuperelement are also constructed by reflection. The retained degrees of freedom include all threedegrees of freedom of all contact nodes sets and of the nodes on the 0 and 45 faces of the flange.MPC-type CYCLSYM is used to impose cyclic symmetric boundary conditions on these two faces.

A third-level superelement of 90 is created by reflecting the original 45 second-level superelementwith respect to the 45 plane and by connecting it to the original 45 superelement. The remaining partof the gasket and the bolts corresponding to the 45 - 90 sector of the model is created by reflectionand appropriate constraints. In this case it is not necessary to retain any degrees of freedom on the 0and 90 faces of the flange because this 90 superelement will not be connected to other superelementsand appropriate boundary conditions can be specified at the superelement creation level.

The final model is set up by mirroring the 90 mesh with respect to the symmetry plane of the gasketperpendicular to the y-axis. Thus, an otherwise large analysis ( 750,000 unknowns) when nosuperelements are used can be solved conveniently ( 80,000 unknowns) by using the third-levelsuperelement twice. The sparse solver is used because it significantly reduces the run time for thismodel.

Loading and boundary conditionsThe only boundary conditions are symmetry boundary conditions. In the axisymmetric model uz = 0 isapplied to the symmetry plane of the gasket and to the bottom of the bolts. In the three-dimensionalmodel uy = 0 is applied to the symmetry plane of the gasket as well as to the bottom of the bolt. The =0 and =22.5 planes are also symmetry planes. On the =22.5 plane, symmetry boundaryconditions are enforced by invoking suitable nodal transformations and applying boundary conditionsto local directions in this symmetry plane. These transformations are implemented using the*TRANSFORM option. On both the symmetry planes, the symmetry boundary conditions uz = 0 areimposed everywhere except for the dependent nodes associated with the C BIQUAD MPC and nodeson one side of the contact surface. The second exception is made to avoid overconstraining problems,which arise if there is a boundary condition in the same direction as a Lagrange multiplier constraintassociated with the *FRICTION, ROUGH option.

In the models where superelements are used, the boundary conditions are specified depending on whatsuperelement is used. For the first-level 22.5 superelement the boundary conditions and constraintequations were the same as for the three-dimensional model shown in Figure 1.1.1-3. For the 45second-level superelement the symmetry boundary conditions are enforced on the =45 plane withthe constraint equation uz + ux = 0. A transform could have been used as well. For the 90 third-level

These node-based surfaces will form contact pairs with the master surfaces on the bolt cap and on thegasket, which are defined with *SURFACE as before. The retained degrees of freedom on thesuperelement include all three degrees of freedom for the nodes in these node-based surfaces as well asfor the nodes on the 0 and 22.5 faces of the flange. Appropriate boundary conditions are specified atthe superelement usage level.

A second-level superelement of 45 is created by reflecting the first-level superelement with respect tothe 22.5 plane. The nodes on the 22.5 face belonging to the reflected superelement are constrained inall three degrees of freedom to the corresponding nodes on the 22.5 face belonging to the originalfirst-level superelement. The half-bolt and the gasket sector corresponding to the reflectedsuperelement are also constructed by reflection. The retained degrees of freedom include all threedegrees of freedom of all contact nodes sets and of the nodes on the 0 and 45 faces of the flange.MPC-type CYCLSYM is used to impose cyclic symmetric boundary conditions on these two faces.

A third-level superelement of 90 is created by reflecting the original 45 second-level superelementwith respect to the 45 plane and by connecting it to the original 45 superelement. The remaining partof the gasket and the bolts corresponding to the 45 - 90 sector of the model is created by reflectionand appropriate constraints. In this case it is not necessary to retain any degrees of freedom on the 0and 90 faces of the flange because this 90 superelement will not be connected to other superelementsand appropriate boundary conditions can be specified at the superelement creation level.

The final model is set up by mirroring the 90 mesh with respect to the symmetry plane of the gasketperpendicular to the y-axis. Thus, an otherwise large analysis ( 750,000 unknowns) when nosuperelements are used can be solved conveniently ( 80,000 unknowns) by using the third-levelsuperelement twice. The sparse solver is used because it significantly reduces the run time for thismodel.

Loading and boundary conditionsThe only boundary conditions are symmetry boundary conditions. In the axisymmetric model uz = 0 isapplied to the symmetry plane of the gasket and to the bottom of the bolts. In the three-dimensionalmodel uy = 0 is applied to the symmetry plane of the gasket as well as to the bottom of the bolt. The =0 and =22.5 planes are also symmetry planes. On the =22.5 plane, symmetry boundaryconditions are enforced by invoking suitable nodal transformations and applying boundary conditionsto local directions in this symmetry plane. These transformations are implemented using the*TRANSFORM option. On both the symmetry planes, the symmetry boundary conditions uz = 0 areimposed everywhere except for the dependent nodes associated with the C BIQUAD MPC and nodeson one side of the contact surface. The second exception is made to avoid overconstraining problems,which arise if there is a boundary condition in the same direction as a Lagrange multiplier constraintassociated with the *FRICTION, ROUGH option.

In the models where superelements are used, the boundary conditions are specified depending on whatsuperelement is used. For the first-level 22.5 superelement the boundary conditions and constraintequations were the same as for the three-dimensional model shown in Figure 1.1.1-3. For the 45second-level superelement the symmetry boundary conditions are enforced on the =45 plane withthe constraint equation uz + ux = 0. A transform could have been used as well. For the 90 third-level


1-20

superelement the face =90 is constrained with the boundary condition ux = 0.

A clamping force of 15 kN is applied to each bolt by using the *PRE-TENSION SECTION option. Thepre-tension section is identified by means of the *SURFACE option. The pre-tension is thenprescribed by applying a concentrated load to the pre-tension node. In the axisymmetric analysis theactual load applied is 120 kN since there are eight bolts. In the three-dimensional model with nosuperelements the actual load applied is 7.5 kN since only half of a bolt is modeled. In the modelsusing superelements all half-bolts are loaded with a 7.5 kN force. For all of the models the pre-tensionsection is specified about half-way down the bolt shank.

Sticking contact conditions are assumed in all surface interactions in all analyses and are simulatedwith the *FRICTION, ROUGH and *SURFACE BEHAVIOR, NO SEPARATION options.

Results and discussionAll analyses are performed as small-displacement analyses.

Figure 1.1.1-5 shows a top view of the normal stress distributions in the gasket at the interface betweenthe gasket and the pipe hub/flange predicted by the axisymmetric (bottom) and three-dimensional (top)analyses when solid continuum elements are used to model the gasket. The figure shows that thecompressive normal stress is highest at the outer edge of the gasket, decreases radially inward, andchanges from compression to tension at a radius of about 35 mm, which is consistent with findingsreported by Sawa et al. (1991). The close agreement in the overall solution between axisymmetric andthree-dimensional analyses is quite apparent, indicating that, for such problems, axisymmetric analysisoffers a simple yet reasonably accurate alternative to three-dimensional analysis.

Figure 1.1.1-6 shows a top view of the normal stress distributions in the gasket at the interface betweenthe gasket and the pipe hub/flange predicted by the axisymmetric (bottom) and three-dimensional (top)analyses when gasket elements are used to model the gasket. Close agreement in the overall solutionbetween the axisymmetric and three-dimensional analyses is also seen in this case. The gasket startscarrying compressive load at a radius of about 40 mm, a difference of 5 mm with the previous result.This difference is the result of the gasket elements being unable to carry tensile loads in their thicknessdirection. This solution is physically more realistic since, in most cases, gaskets separate from theirneighboring parts when subjected to tensile loading. Removing the *SURFACE BEHAVIOR, NOSEPARATION option from the gasket/flange contact surface definition in the input files that model thegasket with continuum elements yields good agreement with the results obtained in Figure 1.1.1-6(since, in that case, the solid continuum elements in the gasket cannot carry tensile loading in thegasket thickness direction).

The models in this example can be modified to study other factors, such as the effective seating widthof the gasket or the sealing performance of the gasket under operating loads. The gasket elements offerthe advantage of allowing very complex behavior to be defined in the gasket thickness direction.Gasket elements can also use any of the small-strain material models provided in ABAQUS includinguser-defined material models. Figure 1.1.1-7shows a comparison of the normal stress distributions inthe gasket at the interface between the gasket and the pipe hub/flange predicted by the axisymmetric(bottom) and three-dimensional (top) analyses when isotropic material properties are prescribed forgasket elements. The results in Figure 1.1.1-7compare well with the results in Figure 1.1.1-5 from

superelement the face =90 is constrained with the boundary condition ux = 0.

A clamping force of 15 kN is applied to each bolt by using the *PRE-TENSION SECTION option. Thepre-tension section is identified by means of the *SURFACE option. The pre-tension is thenprescribed by applying a concentrated load to the pre-tension node. In the axisymmetric analysis theactual load applied is 120 kN since there are eight bolts. In the three-dimensional model with nosuperelements the actual load applied is 7.5 kN since only half of a bolt is modeled. In the modelsusing superelements all half-bolts are loaded with a 7.5 kN force. For all of the models the pre-tensionsection is specified about half-way down the bolt shank.

Sticking contact conditions are assumed in all surface interactions in all analyses and are simulatedwith the *FRICTION, ROUGH and *SURFACE BEHAVIOR, NO SEPARATION options.

Results and discussionAll analyses are performed as small-displacement analyses.

Figure 1.1.1-5 shows a top view of the normal stress distributions in the gasket at the interface betweenthe gasket and the pipe hub/flange predicted by the axisymmetric (bottom) and three-dimensional (top)analyses when solid continuum elements are used to model the gasket. The figure shows that thecompressive normal stress is highest at the outer edge of the gasket, decreases radially inward, andchanges from compression to tension at a radius of about 35 mm, which is consistent with findingsreported by Sawa et al. (1991). The close agreement in the overall solution between axisymmetric andthree-dimensional analyses is quite apparent, indicating that, for such problems, axisymmetric analysisoffers a simple yet reasonably accurate alternative to three-dimensional analysis.

Figure 1.1.1-6 shows a top view of the normal stress distributions in the gasket at the interface betweenthe gasket and the pipe hub/flange predicted by the axisymmetric (bottom) and three-dimensional (top)analyses when gasket elements are used to model the gasket. Close agreement in the overall solutionbetween the axisymmetric and three-dimensional analyses is also seen in this case. The gasket startscarrying compressive load at a radius of about 40 mm, a difference of 5 mm with the previous result.This difference is the result of the gasket elements being unable to carry tensile loads in their thicknessdirection. This solution is physically more realistic since, in most cases, gaskets separate from theirneighboring parts when subjected to tensile loading. Removing the *SURFACE BEHAVIOR, NOSEPARATION option from the gasket/flange contact surface definition in the input files that model thegasket with continuum elements yields good agreement with the results obtaine

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