Example Problems Manual
ABAQUS
EXAMPLE PROBLEMS MANUAL
The information in this document is subject to change without notice and should not be construed as a commitment by ABAQUS, Inc. ABAQUS, Inc., assumes no responsibility for any errors that may appear in this document.
The software described in this document is furnished under license and may be used or copied only in accordance with the terms of such license. No part of this document may be reproduced in any form or distributed in any way without prior written agreement with ABAQUS, Inc. ©ABAQUS, Inc., 2003.
Printed in U.S.A. All Rights Reserved.
ABAQUS is a registered trademark of ABAQUS, Inc. The following are trademarks of ABAQUS, Inc.: ABAQUS/Aqua; ABAQUS/CAE; ABAQUS/Design; ABAQUS/Explicit; ABAQUS/Foundation; ABAQUS/Standard; ABAQUS/Viewer; ABAQUS Interface for MOLDFLOW; ABAQUS Interface for MSC.ADAMS; and the ABAQUS, Inc., logo.
This release of ABAQUS may contain capabilities licensed under U.S. Patents 5,920,491 and 6,044,210. ABAQUS, Inc., may also have other patents or pending patent applications, trademarks, copyrights, or other intellectual property rights covering subject matter in this document. The furnishing of this document does not give you any license to the patents, trademarks, copyrights, or other intellectual property rights except as expressly provided in any written license agreement from ABAQUS, Inc.
ADAMS/Flex, ADAMS/View, MSC.ADAMS, and MSC.Patran are trademarks or registered trademarks of MSC.Software Corporation or its subsidiaries in the United States and/or other countries.
Autodesk Inventor is a trademark and Autodesk Mechanical Desktop is a registered trademark of Autodesk Inc. CADKEY is a registered trademark of CADKEY Corporation.
CATIA is a registered trademark of Dassault Systémes.
Compaq Alpha is registered in the U.S. Patent and Trademark Office. DIGITAL Visual FORTRAN is a trademark of Compaq.
Elysium is a pending trademark of Elysium Co., Ltd. and Elysium Inc.
FEMAP, I-DEAS, Parasolid, Solid Edge, and Unigraphics are registered trademarks of Electronic Data Systems Corporation or its subsidiaries in the United States and in other countries.
FE-SAFE is a trademark of Safe Technology, Ltd.
FLEXlm is a registered trademark of GLOBEtrotter Software, Inc.
Hewlett-Packard, HP-GL, HP-GL/2, and HP-UX are registered trademarks of Hewlett-Packard Co. IBM RS6000 is a trademark of IBM.
Intel is a registered trademark of the Intel Corporation.
MOLDFLOW, MOLDFLOW PLASTICS INSIGHT, and MPI are trademarks or registered trademarks of Moldflow Corporation and its worldwide subsidiaries. NASTRAN is a registered trademark of the National Aeronautics and Space Administration.
PostScript is a registered trademark of Adobe Systems, Inc.
Pro/ENGINEER is a registered trademark of Parametric Technology Corporation or its subsidiaries in the U.S. and in other countries. Silicon Graphics and OpenGL are registered trademarks of Silicon Graphics, Inc.
SolidDesigner is a trademark of CoCreate Software Inc. SolidWorks is a registered trademark of SolidWorks Corporation. SUN is a registered trademark of Sun Microsystems, Inc.
UNIX and Motif are registered trademarks and X Window System is a trademark of The Open Group in the U.S. and other countries. Windows and Microsoft Visual C++ are registered trademarks of the Microsoft Corporation.
ABAQUS/CAE incorporates portions of the ACIS software by SPATIAL TECHNOLOGY INC. ACIS is a registered trademark of SPATIAL TECHNOLOGY INC. This release of ABAQUS includes the gzip program obtained from the Free Software Foundation. This release of ABAQUS on Windows includes the diff program obtained from the Free Software Foundation. You may freely distribute the gzip and diff programs and/or modify them under the terms of the GNU Library 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 integer programming problems by Michel Berkelaar of Eindhoven University of Technology, Eindhoven, the Netherlands.
Python, copyright 1991–1995 by Stichting Mathematisch Centrum, Amsterdam, The Netherlands. All Rights Reserved. Permission to use, copy, modify, and distribute the Python software and its documentation for any purpose and without fee is hereby granted, provided that the above copyright notice appear in all copies and that both that copyright notice and this permission notice appear in supporting documentation, and that the names of Stichting Mathematisch Centrum or CWI or Corporation for National Research Initiatives or CNRI not be used in advertising or publicity pertaining to distribution of the software without specific, written prior permission.
This software is provided with Restricted Rights for procurements governed by DFARS Part 227.4. Use, duplication, or disclosure by the U.S. Government or any of its agencies is subject to restrictions as set forth in subparagraphs (c)(1)(ii) of the Rights in Technical Data and Computer Software clause,
DFARS 252.227–7013 (October 1988).
ABAQUS, Inc.
ABAQUS, Inc. ABAQUS Europe BV
1080 Main Street Gaetano Martinolaan 95
Pawtucket, RI 02860-4847 P. O. Box 1637
Tel: +1 401 727 4200 6201 BP Maastricht
Fax: +1 401 727 4208 The Netherlands
E-mail: [email protected] Tel: +31 43 356 6906
http://www.abaqus.com Fax: +31 43 356 6908
E-mail: [email protected] Sales, Support, and Services
UNITED STATES
ABAQUS Central, Inc. ABAQUS East, LLC
1440 Innovation Place 300 Centerville Road, Suite 209W
West Lafayette, IN 47906-1000 Warwick, RI 02886-0201
Tel: +1 765 497 1373 Tel: +1 401 739 3637
Fax: +1 765 497 4444 Fax: +1 401 739 3302
E-mail: [email protected] E-mail: [email protected]
ABAQUS Erie, Inc. ABAQUS Great Lakes, Inc.
3601 Green Road, Suite 316 14500 Sheldon Road, Suite 160
Beachwood, OH 44122 Plymouth, MI 48170-2408
Tel: +1 216 378 1070 Tel: +1 734 451 0217
Fax: +1 216 378 1072 Fax: +1 734 451 0458
E-mail: [email protected] E-mail: [email protected]
ABAQUS South, Inc. ABAQUS West, Inc.
3700 Forums Drive, Suite 101 39221 Paseo Padre Parkway, Suite F
Flower Mound, TX 75028 Fremont, CA 94538-1611
Tel: +1 214 513 1600 Tel: +1 510 794 5891
Fax: +1 214 513 1700 Fax: +1 510 794 1194
E-mail: [email protected] E-mail: [email protected]
ARGENTINA AUSTRALIA
KB Engineering S. R. L. Worley Advanced Analysis
Florida 274 - Oficina 35 Level 17, 300 Flinders Street
1005 Buenos Aires Melbourne, Vic 3000
Argentina Tel: +61 3 9280 2834
Tel: +54 11 4326 9176/7542 Fax: +61 3 9205 0573
Fax: +54 11 4326 2424 E-mail: [email protected]
AUSTRIA BENELUX
ABAQUS Austria GmbH ABAQUS Benelux BV
Zinckgasse 20-22/2/13 Huizermaatweg 576
A-1150 Vienna 1276 LN Huizen
Austria The Netherlands
Tel: +43 1 929 16 25-0 Tel: +31 35 52 58 424
Fax: +43 1 929 16 25-20 Fax: +31 35 52 44 257
E-mail: [email protected] E-mail: [email protected]
CHINA CZECH REPUBLIC
ABAQUS China Synerma s. r. o.
Beijing Representative Office Huntirov 58
Room 716, Tower B, COFCO Plaza 468 22 Skuhrov
No. 8, Jiangguomennei Dajie Czech Republic
Dong Cheng District Tel: +420 2 603 145 769
Beijing, 100005 Fax: +420 2 603 181 944
P. R. China E-mail: [email protected]
Tel: +86 01 85110566/85110567 Fax: +86 01 85110568
E-mail: [email protected]
FRANCE GERMANY (Aachen)
ABAQUS France SAS ABAQUS Deutschland GmbH
7 rue Jean Mermoz Theaterstraße 30-32
78000 Versailles D-52062 Aachen
Tel: +33 01 39 24 15 40 Tel: +49 241 474010
Fax: +33 01 39 24 15 45 Fax: +49 241 4090963
E-mail: [email protected] E-mail: [email protected]
INDIA (Chennai) ITALY
ABAQUS Engineering Analysis Solutions (Pvt.) Ltd. ABAQUS Italia s. r. l.
3M, Prince Arcade Via Domodossola, 17
22-A Cathedral Road 20145 Milano (MI)
Chennai, 600 086 Tel: +39 02 39211211
Tel: +91 44 28114624 Fax: +39 02 39211210
Fax: +91 44 28115087 E-mail: [email protected]
JAPAN (Tokyo) JAPAN (Osaka)
ABAQUS, Inc. ABAQUS, Inc.
3rd Floor, Akasaka Nihon Building 9th Floor, Higobashi Watanabe Building
5-24, Akasaka 9-chome, Minato-ku 6-10, Edobori 1-chome, Nishi-ku
Tokyo, 107-0052 Osaka, 550-0002
Tel: +81 3 5474 5817 Tel: +81 6 4803 5020
Fax: +81 3 5474 5818 Fax: +81 6 4803 5021
E-mail: [email protected] E-mail: [email protected]
KOREA MALAYSIA
ABAQUS Korea, Inc. Worley Advanced Analysis
Suite 306, Sambo Building 13th Floor, Empire Tower
13-2 Yoido-Dong, Youngdeungpo-ku City Square Centre
Seoul, 150-010 182 Jalan Tun Razak
Tel: +82 2 785 6707 50400 Kuala Lumpur
Fax: +82 2 785 6709 Tel: +60 3 2163 4275
E-mail: [email protected] Fax: +60 3 2163 0524
E-mail: [email protected]
NEW ZEALAND POLAND
Matrix Applied Computing Ltd. BudSoft Sp. z o.o.
P. O. Box 56-316, Auckland 61-807 Poznan´
Courier: Unit 2-5, 72 Dominion Road, Mt Eden, Sw. Marcin 58/64
Auckland Tel: +48 61 8508 466
Tel: +64 9 623 1223 Fax: +48 61 8508 467
Fax: +64 9 623 1134 E-mail: [email protected]
E-mail: [email protected]
RUSSIA, BELARUS & UKRAINE SINGAPORE
TESIS Ltd. Worley Advanced Analysis
Office 701-703, 491B River Valley Road
18, Unnatov Str. #09-01 Valley Point
127083 Moscow, Russia Singapore, 248373
Tel: +7 095 212-44-22 Tel: +65 6735 8444
Fax: +7 095 212-42-62 Fax: +65 6735 7444
SOUTH AFRICA SPAIN
Finite Element Analysis Services (Pty) Ltd. Principia Ingenieros Consultores, S.A.
Unit 4, The Waverley Velázquez, 94
Wyecroft Road E-28006 Madrid
Mowbray 7700 Tel: +34 91 209 1482
Tel: +27 21 448 7608 Fax: +34 91 575 1026
Fax: +27 21 448 7679 E-mail: [email protected]
E-mail: [email protected]
SWEDEN TAIWAN
ABAQUS Scandinavia AB APIC
Pilgatan 8c 7F-2, No. 131 SungChiang Road
SE-721 30 Västerås Taipei, 10428
Tel: +46 21 12 64 10 Tel: +886 02 25083066
Fax: +46 21 18 12 44 Fax: +886 02 25077185
E-mail: [email protected] E-mail: [email protected]
TURKEY UNITED KINGDOM (Cheshire)
A-Ztech Ltd. ABAQUS UK Ltd.
PERDEMSAC Business Center, The Genesis Centre
Technology House Science Park South, Birchwood
17 Gulbahar Str., Bayar Road Warrington, Cheshire WA3 7BH
Kozyatagi Tel: +44 1 925 810166
34742 Istanbul Fax: +44 1 925 810178
Tel: +90 216 361 8850 E-mail: [email protected]
Fax: +90 216 361 8851
Sales Only UNITED STATES
ABAQUS East, LLC, Mid-Atlantic Office ABAQUS South, Inc., Southeast Office
114 Zachary Court 484 Broadstone Way
Forest Hill, MD 21050 Acworth, GA 30101
Tel: +1 410 420 8587 Tel: +1 770 795 0960
Fax: +1 410 420 8908 Fax: +1 770 795 7614
E-mail: [email protected] E-mail: [email protected]
ABAQUS West, Inc., Southern CA and AZ Office ABAQUS West, Inc., Rocky Mountains Office
1100 Irvine Boulevard #248 2894 Hughs Drive
Tustin, CA 92780 Erie, CO 80516
Tel: +1 714 731 5895 Tel: +1 303 664 5444
Fax: +1 714 731 5895 Fax: +1 303 664 5445
E-mail: [email protected] E-mail: [email protected]
FINLAND GERMANY (Munich)
ABAQUS Finland Oy ABAQUS Deutschland GmbH
Tekniikantie 12 Sendlinger-Tor-Platz 8
FIN-02150 Espoo D-80336 München
Tel: +358 9 2517 2973 Tel: +49 89 5999 1768
Fax: +358 9 2517 2200 Fax: +49 89 5999 1767
E-mail: [email protected] E-mail: [email protected]
INDIA (Pune) UNITED KINGDOM (Kent)
ABAQUS Engineering Analysis Solutions (Pvt.) Ltd. ABAQUS UK Ltd.
C-9, 3rd Floor Great Hollanden Business Centre, Unit A
Bramha Estate, Kondwa Road Mill Lane, Underriver
Pune-411040 Nr. Sevenoaks, Kent TN15 OSQ
Tel: +91 20 31037511 Tel: +44 1 732 834930
E-mail: [email protected] Fax: +44 1 732 834720
Preface
This section lists various resources that are available for help with using ABAQUS, including technical engineering and systems support, training seminars, and documentation.
Support
ABAQUS, Inc., offers both technical engineering support and systems support for ABAQUS. Technical engineering and systems support are provided through the nearest local support office. You can contact our offices by telephone, fax, electronic mail, or regular mail. Information on how to contact each office is listed in the front of each ABAQUS manual. Support is also available on the World Wide Web for your convenience. The ABAQUS Online Support System (AOSS) is accessible through the MY ABAQUS section of the ABAQUS Home Page (www.abaqus.com). When contacting your local support office, please specify whether you would like technical engineering support (you have encountered problems performing an ABAQUS analysis or creating a model in ABAQUS) or systems support (ABAQUS will not install correctly, licensing does not work correctly, or other hardware-related issues have arisen).
The ABAQUS Online Support System has a knowledge database of ABAQUS Answers. The ABAQUS Answers are solutions to questions that we have had to answer or guidelines on how to use ABAQUS. We welcome any suggestions for improvements to the support program or documentation. We will ensure that any enhancement requests you make are considered for future releases. If you wish to file a complaint about the service or products provided by ABAQUS, refer to the ABAQUS Home Page.
Technical engineering support
ABAQUS technical support engineers can assist in clarifying ABAQUS features and checking errors by giving both general information on using ABAQUS and information on its application to specific analyses. If you have concerns about an analysis, we suggest that you contact us at an early stage, since it is usually easier to solve problems at the beginning of a project rather than trying to correct an analysis at the end.
Please have the following information ready before calling the technical engineering support hotline, and include it in any written contacts:
• Your site identifier, which can be obtained by typing abaqus whereami at your system prompt (or by
selecting Help!On Version from the main menu bar in ABAQUS/CAE or ABAQUS/Viewer).
• The version of ABAQUS that are you using.
– The version numbers for ABAQUS/Standard and ABAQUS/Explicit are given at the top of the data (.dat) file.
– The version numbers for ABAQUS/CAE and ABAQUS/Viewer can be found by selecting
Help!On Versionfrom the main menu bar.
– The version numbers for the ABAQUS Interface for MOLDFLOW and the ABAQUS Interface for MSC.ADAMS are output to the screen.
• The type of computer on which you are running ABAQUS.
• 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 helpful in answering questions that the support engineer may ask you.
The support engineer will try to diagnose your problem from the model description and a description of the difficulties you are having. Frequently, the support engineer will need model sketches, which can be faxed or sent in the mail. Plots of the final results or the results near the point that the analysis 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 supply the input data. The data can be attached to a support incident in the ABAQUS Online Support System. It may also be sent by means of e-mail, tape, disk, or ftp. Please check the ABAQUS Home Page (http://www.abaqus.com) for the media formats that are currently accepted.
All support incidents are tracked in the ABAQUS Online Support System. This enables you (as well as the support engineer) to monitor the progress of a particular problem and to check that we are resolving support issues efficiently. To use the ABAQUS Online Support System, you need to register with the system. Visit the MY ABAQUS section of the ABAQUS Home Page for instructions on how to register. If you are contacting us by means outside the AOSS to discuss an existing support problem and you know the incident number, please mention it so that we can consult the database to see what the latest action has been and, thus, avoid duplication of effort. In addition, please give the receptionist the support engineer’s name or include it at the top of any e-mail correspondence.
Systems support
ABAQUS systems support engineers can help you resolve issues related to the installation and running of ABAQUS, including licensing difficulties, that are not covered by technical engineering support.
You should install ABAQUS by carefully following the instructions in the ABAQUS Installation and Licensing Guide. If you are able to complete the installation, please make sure that the product verification procedure was run successfully at the end of the installation procedure. Successful verification for licensed products would indicate that you can run these products on your computer; unsuccessful verification for licensed products indicates problems with the installation or licensing (or both). If you encounter problems with the installation, licensing, or verification, first review the instructions in the ABAQUS Installation and Licensing Guide to ensure that they have been followed correctly. If this does not resolve the problems, consult the ABAQUS Answers database in the ABAQUS Online Support System for information about known installation problems. If this does not address your situation, please create an incident in the AOSS and describe your problem, including the output from abaqus info=support. If you call, mail, e-mail, or fax us about a problem (instead of using the AOSS), please provide the output from abaqus info=support. It is important that you provide as much information as possible about your problem: error messages from an aborted analysis, output from the abaqus info=support command, etc.
ABAQUS Web server
For users connected to the Internet, many questions can be answered by visiting the ABAQUS Home Page on the World Wide Web at
http://www.abaqus.com
The information available on the ABAQUS Home Page includes:
• Frequently asked questions
• ABAQUS systems information and computer requirements • ABAQUS performance data
• Error status reports
• ABAQUS documentation price list • Training seminar schedule
• Newsletters Anonymous ftp site
For users connected to the Internet, ABAQUS maintains useful documents on an anonymous ftp account on the computer ftp.abaqus.com. Simply ftp to ftp.abaqus.com. Login as user anonymous, and type your e-mail address as your password. Directions will come up automatically upon login.
Writing to technical support Address of ABAQUS Headquarters:
ABAQUS, Inc. 1080 Main Street
Pawtucket, RI 02860-4847, USA Attention: Technical Support
Addresses for other offices and representatives are listed in the front of each manual. Support for academic institutions
Under the terms of the Academic License Agreement we do not provide support to users at academic institutions. Academic users can purchase technical support on an hourly basis. For more information, please see the ABAQUS Home Page or contact your local ABAQUS support office.
Training
All ABAQUS offices offer regularly scheduled public training classes.
The Introduction to ABAQUS/Standard and ABAQUS/Explicit seminar covers basic usage and nonlinear applications, such as large deformation, plasticity, contact, and dynamics. Workshops provide as much practical experience with ABAQUS as possible.
The Introduction to ABAQUS/CAE seminar discusses modeling, managing simulations, and viewing results with ABAQUS/CAE. “Hands-on” workshops are complemented by lectures.
Advanced seminars cover topics of interest to customers with experience using ABAQUS, such as engine 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 days in duration, depending on customer requirements. The training topics can include a combination of
material from our introductory and advanced seminars. Workshops allow customers to exercise ABAQUS on their own computers.
For a schedule of seminars, see the ABAQUS Home Page or call ABAQUS, Inc., or your local ABAQUS representative.
Documentation
The following documentation and publications are available from ABAQUS, unless otherwise specified, in printed form and through the ABAQUS online documentation. For more information on accessing the online books, refer to the discussion of execution procedures in the ABAQUS Analysis User’s Manual. Modeling and Visualization
• ABAQUS/CAE User’s Manual: This reference document for ABAQUS/CAE includes three comprehensive tutorials as well as detailed descriptions of how to use ABAQUS/CAE for model generation, analysis, and results evaluation and visualization. ABAQUS/Viewer users should refer to the information on the Visualization module in this manual.
Analysis
• ABAQUS Analysis User’s Manual: This volume contains a complete description of the elements, material models, procedures, input specifications, etc. It is the basic reference document for ABAQUS/Standard and ABAQUS/Explicit.
Examples
• ABAQUS Example Problems Manual: This volume contains more than 75 detailed examples designed to illustrate the approaches and decisions needed to perform meaningful linear and nonlinear 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 thin ring; consolidation under a footing; buckling of a composite shell with a hole; and deep drawing of a metal sheet. It is generally useful to look for relevant examples in this manual and to review them when embarking on a new class of problem.
• ABAQUS Benchmarks Manual: This online-only volume contains over 200 benchmark problems and standard analyses used to evaluate the performance of ABAQUS; the tests are multiple element tests of simple geometries or simplified versions of real problems. The NAFEMS benchmark problems are included in this manual.
Training
• Getting Started with ABAQUS: This document is a self-paced tutorial designed to help new users become familiar with using ABAQUS/CAE to create solid, shell, and framework models and ABAQUS/Standard or ABAQUS/Explicit to perform static, quasi-static, and dynamic stress analysis simulations. It contains a number of fully worked examples that provide practical guidelines for performing structural analyses with ABAQUS.
• Getting Started with ABAQUS/Standard: Keywords Version: This online-only document is designed to help new users become familiar with the ABAQUS/Standard input file syntax for static and dynamic stress analysis simulations. The ABAQUS/Standard keyword interface is used to model examples similar to those included in Getting Started with ABAQUS.
• Getting Started with ABAQUS/Explicit: Keywords Version: This online-only document is designed to help new users become familiar with the ABAQUS/Explicit input file syntax for quasi-static and dynamic stress analysis simulations. The ABAQUS/Explicit keyword interface is used to model examples similar to those included in Getting Started with ABAQUS.
• Lecture Notes: These notes are available on many topics to which ABAQUS is applied. They are used in the technical seminars that ABAQUS, Inc., presents to help users improve their understanding and usage 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 they can usually be used in that mode. The list of available lecture notes is included in the Documentation Price List.
Documentation Information
• Using ABAQUS Online Documentation: This online-only manual contains instructions for viewing and searching the ABAQUS online documentation.
Reference
• ABAQUS Keywords Reference Manual: This volume contains a complete description of all the input options that are available in ABAQUS/Standard and ABAQUS/Explicit.
• ABAQUS Theory Manual: This online-only volume contains detailed, precise discussions of all theoretical aspects of ABAQUS. It is written to be understood by users with an engineering background. • ABAQUS Verification Manual: This online-only volume contains more than 5000 basic test cases, 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 these problems when learning to use a new capability. In addition, the supplied input data files provide good starting points to check the behavior of elements, materials, etc.
• Quality Assurance Plan: This document describes the QA procedures followed by ABAQUS. It is a controlled document, provided to customers who subscribe to either the Nuclear QA Program or the Quality Monitoring Service.
Update Information
• ABAQUS Release Notes: This document contains brief descriptions of the new features available in the latest release of the ABAQUS product line.
Programming
• ABAQUS Scripting User’s Manual: This online-only manual provides a description of the ABAQUS Scripting Interface. 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 on using the ABAQUS Scripting Interface or C++ as an application programming interface (API) to the output database.
• ABAQUS Scripting Reference Manual: This online-only manual provides a command reference that lists the syntax of each command in the ABAQUS Scripting Interface.
• ABAQUS GUI Toolkit User’s Manual: This online-only manual provides a description of the ABAQUS GUI Toolkit. The manual describes the components and organization of the ABAQUS GUI. It also describes how you can customize the ABAQUS GUI to build a particular application. • ABAQUS GUI Toolkit Reference Manual: This online-only manual provides a command reference
that lists the syntax of each command in the ABAQUS GUI Toolkit. Interfaces
• ABAQUS Interface for MSC.ADAMS User’s Manual: This document describes how to use the ABAQUS Interface for MSC.ADAMS, which creates ABAQUS models of MSC.ADAMS components and converts the ABAQUS results into an MSC.ADAMS modal neutral file
that can be used by the ADAMS/Flex program. It is the basic reference document for the
ABAQUS Interface for MSC.ADAMS.
• ABAQUS Interface for MOLDFLOW User’s Manual: This document describes how to use the ABAQUS Interface for MOLDFLOW, which creates a partial ABAQUS input file by translating results from a MOLDFLOW polymer processing simulation. It is the basic reference document for the ABAQUS Interface for MOLDFLOW.
Installation and Licensing
• ABAQUS Installation and Licensing Guide: This document describes how to install ABAQUS and how to configure the installation for particular circumstances. Some of this information, of most relevance to users, is also provided in the ABAQUS Analysis User’s Manual.
CONTENTS
CONTENTS
1. Static Stress/Displacement Analyses
Static and quasi-static stress analyses
Axisymmetric analysis of bolted pipe flange connections 1.1.1
Elastic-plastic collapse of a thin-walled elbow under in-plane bending and internal
pressure 1.1.2
Parametric study of a linear elastic pipeline under in-plane bending 1.1.3
Indentation of an elastomeric foam specimen with a hemispherical punch 1.1.4
Collapse of a concrete slab 1.1.5
Jointed rock slope stability 1.1.6
Notched beam under cyclic loading 1.1.7
Hydrostatic fluid elements: modeling an airspring 1.1.8
Shell-to-solid submodeling and shell-to-solid coupling of a pipe joint 1.1.9
Stress-free element reactivation 1.1.10
Transient loading of a viscoelastic bushing 1.1.11
Indentation of a thick plate 1.1.12
Damage and failure of a laminated composite plate 1.1.13
Analysis of an automotive boot seal 1.1.14
Pressure penetration analysis of an air duct kiss seal 1.1.15
Self-contact in rubber/foam components: jounce bumper 1.1.16
Self-contact in rubber/foam components: rubber gasket 1.1.17
Submodeling of a stacked sheet metal assembly 1.1.18
Axisymmetric analysis of a threaded connection 1.1.19
Direct cyclic analysis of a cylinder head under cyclic thermal-mechanical loadings 1.1.20 Buckling and collapse analyses
Snap-through buckling analysis of circular arches 1.2.1
Laminated composite shells: buckling of a cylindrical panel with a circular hole 1.2.2
Buckling of a column with spot welds 1.2.3
Elastic-plastic K-frame structure 1.2.4
Unstable static problem: reinforced plate under compressive loads 1.2.5
Buckling of an imperfection-sensitive cylindrical shell 1.2.6
Forming analyses
Upsetting of a cylindrical billet: quasi-static analysis with mesh-to-mesh solution
mapping (ABAQUS/Standard) and adaptive meshing (ABAQUS/Explicit) 1.3.1
Superplastic forming of a rectangular box 1.3.2
Stretching of a thin sheet with a hemispherical punch 1.3.3
Deep drawing of a cylindrical cup 1.3.4
Extrusion of a cylindrical metal bar with frictional heat generation 1.3.5
Rolling of thick plates 1.3.6
vii
CONTENTS
Axisymmetric forming of a circular cup 1.3.7
Cup/trough forming 1.3.8
Forging with sinusoidal dies 1.3.9
Forging with multiple complex dies 1.3.10
Flat rolling: transient and steady-state 1.3.11
Section rolling 1.3.12
Ring rolling 1.3.13
Axisymmetric extrusion: transient and steady-state 1.3.14
Two-step forming simulation 1.3.15
Upsetting of a cylindrical billet: coupled temperature-displacement and adiabatic
analysis 1.3.16
Unstable static problem: thermal forming of a metal sheet 1.3.17
Fracture mechanics
A plate with a part-through crack: elastic line spring modeling 1.4.1
Conical crack in a half-space with and without submodeling 1.4.2
Elastic-plastic line spring modeling of a finite length cylinder with a part-through
axial flaw 1.4.3
Crack growth in a three-point bend specimen 1.4.4
Import analyses
Springback of two-dimensional draw bending 1.5.1
Deep drawing of a square box 1.5.2
2. Dynamic Stress/Displacement Analyses
Dynamic stress analyses
Nonlinear dynamic analysis of a structure with local inelastic collapse 2.1.1
Detroit Edison pipe whip experiment 2.1.2
Rigid projectile impacting eroding plate 2.1.3
Eroding projectile impacting eroding plate 2.1.4
Tennis racket and ball 2.1.5
Pressurized fuel tank with variable shell thickness 2.1.6
Modeling of an automobile suspension 2.1.7
Explosive pipe closure 2.1.8
Knee bolster impact with general contact 2.1.9
Crimp forming with general contact 2.1.10
Collapse of a stack of blocks with general contact 2.1.11
Cask drop with foam impact limiter 2.1.12
Oblique impact of a copper rod 2.1.13
Water sloshing in a baffled tank 2.1.14
Seismic analysis of a concrete gravity dam 2.1.15
viii
CONTENTS
Mode-based dynamic analyses
Analysis of a rotating fan using substructures and cyclic symmetry 2.2.1
Linear analysis of the Indian Point reactor feedwater line 2.2.2
Response spectra of a three-dimensional frame building 2.2.3
Eigenvalue analysis of a structure using the parallel Lanczos eigensolver 2.2.4
Brake squeal analysis 2.2.5
3. Tire and Vehicle Analyses
Tire analyses
Symmetric results transfer for a static tire analysis 3.1.1
Steady-state rolling analysis of a tire 3.1.2
Subspace-based steady-state dynamic tire analysis 3.1.3
Steady-state dynamic analysis of a tire substructure 3.1.4
Coupled acoustic-structural analysis of a tire filled with air 3.1.5
Import of a steady-state rolling tire 3.1.6
Analysis of a solid disc with Mullins effect 3.1.7
Vehicle analyses
Inertia relief in a pick-up truck 3.2.1
Substructure analysis of a pick-up truck model 3.2.2
4. Mechanism Analyses
Resolving overconstraints in a multi-body mechanism model 4.1.1
Crank mechanism 4.1.2 Snubber-arm mechanism 4.1.3 Flap mechanism 4.1.4 Tail-skid mechanism 4.1.5 Cylinder-cam mechanism 4.1.6 Driveshaft mechanism 4.1.7 Geneva mechanism 4.1.8
Trailing edge flap mechanism 4.1.9
Substructure analysis of a one-piston engine model 4.1.10
5. Heat Transfer and Thermal-Stress Analyses
Thermal-stress analysis of a disc brake 5.1.1
Exhaust manifold assemblage 5.1.2
Coolant manifold cover gasketed joint 5.1.3
Radiation analysis of a plane finned surface 5.1.4
ix
CONTENTS
6. Electrical Analyses
Piezoelectric analyses
Eigenvalue analysis of a piezoelectric transducer 6.1.1
Transient dynamic nonlinear response of a piezoelectric transducer 6.1.2
Joule heating analyses
Thermal-electrical modeling of an automotive fuse 6.2.1
7. Mass Diffusion Analyses
Hydrogen diffusion in a vessel wall section 7.1.1
Diffusion toward an elastic crack tip 7.1.2
8. Acoustic and Shock Analyses
Coupled acoustic-structural analysis of a car 8.1.1
Fully and sequentially coupled acoustic-structural analysis of a muffler 8.1.2
Coupled acoustic-structural analysis of a speaker 8.1.3
Response of a submerged cylinder to an underwater explosion shock wave 8.1.4
Coupled acoustic-structural analysis of a pick-up truck 8.1.5
Long-duration response of a submerged cylinder to an underwater explosion 8.1.6
9. Soils Analyses
Plane strain consolidation 9.1.1
Calculation of phreatic surface in an earth dam 9.1.2
Axisymmetric simulation of an oil well 9.1.3
Analysis of a pipeline buried in soil 9.1.4
10. ABAQUS/Aqua Analyses
Jack-up foundation analyses 10.1.1
Riser dynamics 10.1.2
11. Design Sensitivity Analyses
Overview
Design sensitivity analysis: overview 11.1.1
Examples
Design sensitivity analysis of a composite centrifuge 11.2.1
Design sensitivities for tire inflation, footprint, and natural frequency analysis 11.2.2
Design sensitivity analysis of a windshield wiper 11.2.3
Design sensitivity analysis of a rubber bushing 11.2.4
x
CONTENTS
12. Postprocessing of ABAQUS Results Files
User postprocessing of ABAQUS results files: overview 12.1.1
Joining data from multiple results files and converting file format: FJOIN 12.1.2
Calculation of principal stresses and strains and their directions: FPRIN 12.1.3
Creation of a perturbed mesh from original coordinate data and eigenvectors: FPERT 12.1.4
Output radiation viewfactors and facet areas: FRAD 12.1.5
Creation of a data file to facilitate the postprocessing of elbow element results:
FELBOW 12.1.6
xi
INTRODUCTION
1.0.1 INTRODUCTION
This is the Example Problems Manual for ABAQUS. It contains many solved examples that illustrate the use of the program for common types of problems. Some of the problems are quite difficult and require combinations of the capabilities in the code.
The problems have been chosen to serve two purposes: to verify the capabilities in ABAQUS by exercising the code on nontrivial cases and to provide guidance to users who must work on a class of problems with which they are relatively unfamiliar. In each worked example the discussion in the manual states why the example is included and leads the reader through the standard approach to an analysis: element and mesh selection, material model, and a discussion of the results. Many of these problems are worked with different element types, mesh densities, and other variations.
Input data files for all of the analyses are included with the ABAQUS release in compressed archive files. The ABAQUS/Fetch utility is used to extract these input files for use. For example, to fetch input file boltpipeflange_3d_cyclsym.inp, type
abaqus fetch job=boltpipeflange_3d_cyclsym.inp
Parametric study script (.psf) and user subroutine (.f) files can be fetched in the same manner. All files for a particular problem can be obtained by leaving off the file extension. The ABAQUS/Fetch execution procedure is explained in detail in “Execution procedure for ABAQUS/Fetch,” Section 3.2.12 of the ABAQUS Analysis User’s Manual.
It is sometimes useful to search the input files. The findkeyword utility is used to locate input files that contain user-specified input. This utility is defined in “Execution procedure for querying the keyword/ problem database,” Section 3.2.11 of the ABAQUS Analysis User’s Manual.
To reproduce the graphical representation of the solution reported in some of the examples, the output frequency used in the input files may need to be increased. For example, in “Linear analysis of the Indian Point reactor feedwater line,” Section 2.2.2, the figures that appear in the manual can be obtained only if the solution is written to the results file every increment; that is, if the input files are changed to read
*NODE FILE, ..., FREQUENCY=1 instead of FREQUENCY=100 as appears now.
In addition to the Example Problems Manual, there are two other manuals that contain worked problems. The ABAQUS Benchmarks Manual contains benchmark problems (including the NAFEMS suite of test problems) and standard analyses used to evaluate the performance of ABAQUS. The tests in 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 as elementary verification of the basic modeling capabilities.
The verification of ABAQUS consists of running the problems in the ABAQUS Example Problems Manual, the ABAQUS Benchmarks Manual, and the ABAQUS Verification Manual. Before a version of ABAQUS is released, it must run all verification, benchmark, and example problems correctly.
1.0.1–1
BOLTED PIPE JOINT
1.1.1 AXISYMMETRIC ANALYSIS OF BOLTED PIPE FLANGE CONNECTIONS
Product: ABAQUS/Standard
A bolted pipe flange connection is a common and important part of many piping systems. Such connections are typically composed of hubs of pipes, pipe flanges with bolt holes, sets of bolts and nuts, and a gasket. These components interact with each other in the tightening process and when operation loads such as internal pressure and temperature are applied. Experimental and numerical studies on different types of interaction among these components are frequently reported. The studies include 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 analysis of the entire pipe joint assembly (Sawa et al., 1991). To establish an optimal design, a full stress analysis determines factors such as the contact stresses that govern the sealing performance, the relationship between bolt force and internal pressure, the effective gasket seating width, and the bending moment produced in the bolts. This example shows how to perform such a design analysis by using an economical axisymmetric model and how to assess the accuracy of the axisymmetric solution by comparing the results to those obtained from a simulation using a three-dimensional segment model. In addition, several three-dimensional models that use multiple levels of substructures are analyzed to demonstrate the use of substructures with a large number of retained degrees of freedom.
Geometry and model
The bolted joint assembly being analyzed is depicted in Figure 1.1.1–1. The geometry and dimensions of the various parts are taken from Sawa et al. (1991), modified slightly to simplify the modeling. The inner wall radius of both the hub and the gasket is 25 mm. The outer wall radii of the pipe flange and the gasket are 82.5 mm and 52.5 mm, respectively. The thickness of the gasket is 2.5 mm. The pipe flange has eight bolt holes that are equally spaced in the pitch circle of radius 65 mm. The radius of the bolt hole is modified in this analysis to be the same as that of the bolt: 8 mm. The bolt head (bearing surface) 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 pipe hub/flange. The gasket is modeled with either solid continuum or gasket elements. When continuum elements are used, the gasket’s Young’s modulus,E, equals 68.7 GPa and its Poisson’s ratio, , equals 0.3.
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 shear stiffness, 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 the flange and between the gasket and the hub. Contact between the bolt shank and the bolt hole is ignored.
1.1.1–1
BOLTED PIPE JOINT
The finite element idealizations of the symmetric half of the pipe joint are shown in Figure 1.1.1–2 and Figure 1.1.1–3, corresponding to the axisymmetric and three-dimensional analyses, respectively. The mesh used for the axisymmetric analysis consists of a mesh for the pipe hub/flange and gasket and a separate mesh for the bolts. In Figure 1.1.1–2 the 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 the gasket and the bolt in place.
For the axisymmetric model second-order elements with reduced integration, CAX8R, are used throughout the mesh of the pipe hub/flange. The gasket is modeled with either CAX8R solid continuum elements or GKAX6 gasket elements. Contact between the gasket and the pipe hub/flange is modeled with contact pairs between surfaces defined on the faces of elements in the contact region or between such element-based surfaces and node-based surfaces. In an axisymmetric analysis the bolts and the perforated flange must be modeled properly. The bolts are modeled as plane stress elements since they do not carry hoop stress. Second-order plane stress elements with reduced integration, CPS8R, are employed for this purpose. The contact surface definitions, which are associated with the faces of the elements, account for the plane stress condition automatically. To account for all eight bolts used in the joint, the combined cross-sectional areas of the shank and the head of the bolts must be calculated and redistributed to the bolt mesh appropriately using the area attributes 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 stress element represents a volume that extends out of the x–y plane. For example, element A represents a volume calculated as (HA) 2 (AreaA). Likewise, element B represents a volume calculated as (HB)2 (AreaB). The sectional area in thex–z plane pertaining to a given element can be calculated as Area = 2 Z X2 X1 [(R20 x2)12]dx = [x(R20 x2)12 + R2arcsin ( x jRj)] X2 X1;
whereR is the bolt head radius, Rbolthead, or the shank radius, Rshank (depending on the element location), andX1andX2arex-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 obtain representative element thicknesses. Multiplying each element thickness by eight (the number of bolts in 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 are used 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=A4C; A9=A4F;
A2=A2C; A4= A2D; A6= A2E; A8=A2F;
A3= (AC+ AD)=4; A5= (AD+ AE)=4; A7= (AE+ AF)=4;
whereA1throughA9 are contact areas that are associated with contact nodes 1–9 andActhroughAF are sectional areas that are associated with bolt head elementsC–F . Multiplying the above areas by
1.1.1–2
BOLTED PIPE JOINT
eight (the number of bolts in the model) provides the nodal contact areas found under the *SURFACE INTERACTION options.
A common way of handling the presence of the bolt holes in the pipe flange in axisymmetric analyses is to smear the material properties used in the bolt hole area of the mesh and to use inhomogeneous material properties that correspond to a weaker material in this region. General guidelines for determining the effective material properties for perforated flat plates are found in ASME Section VIII Div 2 Article 4–9. For the type of structure under study, which is not a flat plate, a common approach to 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 this model the annular area of the pitch circle is given by
AA = 6534.51 mm2
, and the total area of the bolt holes is given by AH = 882 = 1608.5 mm2 . Hence, the reduction factor is simply10AH=AA = 0.754. The effective in-plane moduli of elasticity, E10 and E20, are obtained by multiplying the respective 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 such that E0=E30 = 106
. The in-plane shear modulus is then calculated based on the effective elasticity modulus: G120 = E0=2(1 + ): The shear moduli in the hoop direction are also calculated similarly but with set to zero (they are not used
in an axisymmetric model). Hence, we have E10 = E20 = 155292 MPa, E30 = 0.155292 MPa,
G0
12 = 59728 MPa, and G013 = G023 = 0.07765 MPa. These elasticity moduli are specified using
*ELASTIC, TYPE=ENGINEERING CONSTANTS for the bolt hole part of the mesh.
The mesh for the three-dimensional analysis without substructures, shown in Figure 1.1.1–3, represents a 22.5 segment of the pipe joint and employs second-order brick elements with reduced integration, C3D20R, for the pipe hub/flange and bolts. The gasket is modeled with C3D20R elements or GK3D18 elements. The top figure shows the mesh of the pipe hub and flange, and the bottom figure shows both the gasket and bolt (in the lighter color). Contact is modeled by the interaction of contact surfaces defined by grouping specific faces of the elements in the contacting regions. For three-dimensional contact where both the master and slave surfaces are deformable, the SMALL SLIDING parameter must be used on the *CONTACT PAIR option to indicate that small relative sliding occurs between contacting surfaces. No special adjustments need be made for the material properties used in the three-dimensional model because all parts are modeled appropriately.
Four different meshes that use substructures to model the flange are tested. A first-level substructure is created for the entire 22.5 segment of the flange shown in Figure 1.1.1–3, while the gasket and the bolt are meshed as before. The nodes on the flange in contact with the bolt cap form a node-based surface, while the nodes on the flange in contact with the gasket form another node-based surface. These node-based surfaces will form contact pairs with the master surfaces on the bolt cap and on the gasket, which are defined with *SURFACE as before. The retained degrees of freedom on the substructure include all three degrees of freedom for the nodes in these node-based surfaces as well as for the nodes on the 0 and 22.5 faces of the flange. Appropriate boundary conditions are specified at the substructure usage level.
A second-level substructure of 45is created by reflecting the first-level substructure with respect to the 22.5plane. The nodes on the 22.5face belonging to the reflected substructure are constrained in all three degrees of freedom to the corresponding nodes on the 22.5face belonging to the original first-level substructure. The half-bolt and the gasket sector corresponding to the reflected substructure
1.1.1–3
BOLTED PIPE JOINT
are also constructed by reflection. The retained degrees of freedom include all three degrees of freedom of all contact node sets and of the nodes on the 0and 45faces of the flange. MPC-type CYCLSYM is used to impose cyclic symmetric boundary conditions on these two faces.
A third-level substructure of 90is created by reflecting the original 45second-level substructure with respect to the 45plane and by connecting it to the original 45substructure. The remaining part of the gasket and the bolts corresponding to the 45–90sector of the model is created by reflection and appropriate constraints. In this case it is not necessary to retain any degrees of freedom on the 0 and 90faces of the flange because this 90substructure will not be connected to other substructures and appropriate boundary conditions can be specified at the substructure creation level.
The final model is set up by mirroring the 90mesh with respect to the symmetry plane of the gasket perpendicular to they-axis. Thus, an otherwise large analysis ( 750,000 unknowns) when no substructures are used can be solved conveniently ( 80,000 unknowns) by using the third-level substructure twice. The sparse solver is used because it significantly reduces the run time for this model.
Loading and boundary conditions
The only boundary conditions are symmetry boundary conditions. In the axisymmetric modeluz= 0
is applied to the symmetry plane of the gasket and to the bottom of the bolts. In the three-dimensional model 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 boundary conditions are enforced by invoking suitable nodal transformations and applying boundary conditions to 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
are imposed everywhere except for the dependent nodes associated with the C BIQUAD MPC and nodes on 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 constraint associated with the *FRICTION, ROUGH option.
In the models where substructures are used, the boundary conditions are specified depending on what substructure is used. For the first-level 22.5substructure the boundary conditions and constraint equations are the same as for the three-dimensional model shown in Figure 1.1.1–3. For the 45 second-level substructure the symmetry boundary conditions are enforced on the =45 plane with the constraint equationuz+ux= 0. A transform could have been used as well. For the 90third-level substructure the face =90is constrained with the boundary conditionux= 0.
A clamping force of 15 kN is applied to each bolt by using the *PRE-TENSION SECTION option. The pre-tension section is identified by means of the *SURFACE option. The pre-tension is then prescribed by applying a concentrated load to the pre-tension node. In the axisymmetric analysis the actual load applied is 120 kN since there are eight bolts. In the three-dimensional model with no substructures the actual load applied is 7.5 kN since only half of a bolt is modeled. In the models using substructures all half-bolts are loaded with a 7.5 kN force. For all of the models the pre-tension section is specified about half-way down the bolt shank.
Sticking contact conditions are assumed in all surface interactions in all analyses and are simulated with the *FRICTION, ROUGH and *SURFACE BEHAVIOR, NO SEPARATION options.
1.1.1–4
BOLTED PIPE JOINT
Results and discussion
All 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 between the 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 the compressive normal stress is highest at the outer edge of the gasket, decreases radially inward, and changes from compression to tension at a radius of about 35 mm, which is consistent with findings reported by Sawa et al. (1991). The close agreement in the overall solution between axisymmetric and three-dimensional analyses is quite apparent, indicating that, for such problems, axisymmetric analysis offers 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 between the 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 solution between the axisymmetric and three-dimensional analyses is also seen in this case. The gasket starts carrying 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 thickness direction. This solution is physically more realistic since, in most cases, gaskets separate from their neighboring parts when subjected to tensile loading. Removing the *SURFACE BEHAVIOR, NO SEPARATION option from the gasket/flange contact surface definition in the input files that model the gasket 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 the gasket thickness direction).
The models in this example can be modified to study other factors, such as the effective seating width of the gasket or the sealing performance of the gasket under operating loads. The gasket elements offer the 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 including user-defined material models. Figure 1.1.1–7 shows a comparison of the normal stress distributions in the 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 for gasket elements. The results in Figure 1.1.1–7 compare well with the results in Figure 1.1.1–5 from analyses in which solid and axisymmetric elements are used to simulate the gasket.
Figure 1.1.1–8 shows the distribution of the normal stresses in the gasket at the interface in the planez = 0. The results are plotted for the three-dimensional model containing only solid continuum elements and no substructures and for the four models containing the substructures described above.
A C++ program is available to combine model and results data from a series of substructure output databases into a single output database. For more information, see “Combining model and results data from more than one output database into a single output database,” Section 9.14.4 of the ABAQUS Scripting User’s Manual.
1.1.1–5
BOLTED PIPE JOINT
Input files
boltpipeflange_axi_solidgask.inp Axisymmetric analysis containing a gasket modeled with
solid continuum elements.
boltpipeflange_axi_node.inp Node definitions for boltpipeflange_axi_solidgask.inp
and boltpipeflange_axi_gkax6.inp.
boltpipeflange_axi_element.inp Element definitions for
boltpipeflange_axi_solidgask.inp.
boltpipeflange_3d_solidgask.inp Three-dimensional analysis containing a gasket modeled
with solid continuum elements.
boltpipeflange_axi_gkax6.inp Axisymmetric analysis containing a gasket modeled with
gasket elements.
boltpipeflange_3d_gk3d18.inp Three-dimensional analysis containing a gasket modeled
with gasket elements.
boltpipeflange_3d_substr1.inp Three-dimensional analysis using the first-level
substructure (22.5model).
boltpipeflange_3d_substr2.inp Three-dimensional analysis using the second-level
substructure (45model).
boltpipeflange_3d_substr3_1.inp Three-dimensional analysis using the third-level
substructure once (90model).
boltpipeflange_3d_substr3_2.inp Three-dimensional analysis using the third-level
substructure twice (90mirrored model).
boltpipeflange_3d_gen1.inp First-level substructure generation data referenced by
boltpipeflange_3d_substr1.inp and boltpipeflange_3d_gen2.inp.
boltpipeflange_3d_gen2.inp Second-level substructure generation data referenced by
boltpipeflange_3d_substr2.inp and boltpipeflange_3d_gen3.inp.
boltpipeflange_3d_gen3.inp Third-level substructure generation data referenced by
boltpipeflange_3d_substr3_1.inp and boltpipeflange_3d_substr3_2.inp.
boltpipeflange_3d_node.inp Nodal coordinates used in
boltpipeflange_3d_substr1.inp, boltpipeflange_3d_substr2.inp, boltpipeflange_3d_substr3_1.inp, boltpipeflange_3d_substr3_2.inp, boltpipeflange_3d_cyclsym.inp, boltpipeflange_3d_gen1.inp, boltpipeflange_3d_gen2.inp, and boltpipeflange_3d_gen3.inp.
boltpipeflange_3d_cyclsym.inp Same as file boltpipeflange_3d_substr2.inp except that
CYCLSYM type MPCs are used.
1.1.1–6
BOLTED PIPE JOINT
boltpipeflange_3d_missnode.inp Same as file boltpipeflange_3d_gk3d18.inp except that
the option to generate missing nodes is used for gasket elements.
boltpipeflange_3d_isomat.inp Same as file boltpipeflange_3d_gk3d18.inp except that
gasket elements are modeled as isotropic using the *MATERIAL option.
boltpipeflange_3d_ortho.inp Same as file boltpipeflange_3d_gk3d18.inp except that
gasket elements are modeled as orthotropic and the *ORIENTATION option is used.
boltpipeflange_axi_isomat.inp Same as file boltpipeflange_axi_gkax6.inp except that
gasket elements are modeled as isotropic using the *MATERIAL option.
boltpipeflange_3d_usr_umat.inp Same as file boltpipeflange_3d_gk3d18.inp except that
gasket elements are modeled as isotropic with user subroutine UMAT.
boltpipeflange_3d_usr_umat.f User subroutine UMAT used in
boltpipeflange_3d_usr_umat.inp.
boltpipeflange_3d_solidnum.inp Same as file boltpipeflange_3d_gk3d18.inp except that
solid element numbering is used for gasket elements. References
• Bibel, G. D., and R. M. Ezell, “An Improved Flange Bolt-Up Procedure Using Experimentally Determined Elastic Interaction Coefficients,” Journal of Pressure Vessel Technology, vol. 114, pp. 439–443, 1992.
• Chaaban, A., and U. Muzzo, “Finite Element Analysis of Residual Stresses in Threaded End Closures,” Transactions of ASME, vol. 113, pp. 398–401, 1991.
• Fukuoka, T., “Finite Element Simulation of Tightening Process of Bolted Joint with a Tensioner,” Journal of Pressure Vessel Technology, vol. 114, pp. 433–438, 1992.
• Sawa, T., N. Higurashi, and H. Akagawa, “A Stress Analysis of Pipe Flange Connections,” Journal of Pressure Vessel Technology, vol. 113, pp. 497–503, 1991.
1.1.1–7
BOLTED PIPE JOINT 80 θ = π 4 d = 50 d = 105 d = 130 d = 165 r = 8 15 d = 105 d = 50 centerline Top View Side View 2.5 Gasket Bolt 24 16 10 26 47 20
Figure 1.1.1–1 Schematic of the bolted joint. All dimensions in mm.
1.1.1–8
BOLTED PIPE JOINT 1 2 3 1 2 3 1 2 3 1 2 3
Figure 1.1.1–2 Axisymmetric model of the bolted joint.
1.1.1–9
BOLTED PIPE JOINT 1 2 3 1 2 3 1 2 3 1 2 3
Figure 1.1.1–3 22.5segment three-dimensional model of the bolted joint.
1.1.1–10
BOLTED PIPE JOINT y 1 2 3 4 5 6 7 8 9 C D E F z x WB WA HA HB contact nodes area A area B element A element B TOP VIEW FRONT VIEW Rbolthead Rshank
Figure 1.1.1–4 Cross-sectional views of the bolt head and the shank.
1.1.1–11
BOLTED PIPE JOINT 1 2 3 12 1 2 3 11 1 2 3 7 8 9 12 11 10 8 11 9 9 9 11 8 9 9 8 12 8 10 11 7 12 1 2 3 4 5 6 1 2 3 4 5 6 8 7 7 1 2 3 4 5 6 7 12 12 1 2 3 4 5 6 11 10 10 11 10 10 7 12 2 3 4 5 6 2 3 4 5 6 1 2 3 S22 VALUE 1 -1.00E+02 2 -8.90E+01 3 -7.81E+01 4 -6.72E+01 5 -5.63E+01 6 -4.54E+01 7 -3.45E+01 8 -2.36E+01 9 -1.27E+01 10 -1.81E+00 11 +9.09E+00 12 +2.00E+01 1 2 3 12 11 10 10 10 10 10 10 11 10 9 9 9 9 11 9 8 8 8 8 8 11 8 8 8 11 11 11 9 32 4 5 6 12 12 7 7 7 7 2 3 4 5 6 7 7 7 12 2 3 4 5 6 12 2 3 4 5 6 12 9 7 10 12 9 12 11 2 3 4 5 6 2 3 4 5 6 2 3 4 5 6 2 3 4 5 6 1 2 3 S22 VALUE 1 -1.00E+02 2 -8.90E+01 3 -7.81E+01 4 -6.72E+01 5 -5.63E+01 6 -4.54E+01 7 -3.45E+01 8 -2.36E+01 9 -1.27E+01 10 -1.81E+00 11 +9.09E+00 12 +2.00E+01
Figure 1.1.1–5 Normal stress distribution in the gasket contact surface when solid elements are used to
model the gasket: three-dimensional versus axisymmetric results.
1.1.1–12
BOLTED PIPE JOINT 1 2 3 3 7 8 9 1011 5 6 4 4 4 4 4 4 3 7 8 9 1011 7 8 9 1011 7 8 9 1011 5 6 5 6 5 6 4 5 6 3 5 6 5 6 3 3 3 3 3 7 8 9 1011 4 7 8 9 1011 7 8 91011 78 91011 5 6 4 4 4 4 4 4 4 5 6 5 6 5 6 5 6 5 6 5 6 5 6 3 4 5 6 7 8 9 1011 7 8 9 1011 7 8 9 1011 7 8 9 1011 7 8 9 1011 7 8 9 1011 7 8 91011 4 78 91011 3 3 3 3 3 3 3 1 2 3 S11 VALUE 1 -2.00E+01 2 -9.09E+00 3 +1.82E+00 4 +1.27E+01 5 +2.36E+01 6 +3.45E+01 7 +4.55E+01 8 +5.64E+01 9 +6.73E+01 10 +7.82E+01 11 +8.91E+01 12 +1.00E+02 1 2 3 7 8 9 3 7 8910 11 7 89 11 8 91011 4 3 3 3 4 6 5 5 6 6 8 7 8 10 7 8910 7 11 7 8 11 7 8 10 5 6 4 3 5 6 3 3 4 5 6 4 5 6 5 6 5 6 3 78 91011 78 910 78 91011 3 78 910 11 78 910 78 91011 3 4 4 4 1 2 3 S11 VALUE 1 -2.00E+01 2 -9.09E+00 3 +1.82E+00 4 +1.27E+01 5 +2.36E+01 6 +3.45E+01 7 +4.55E+01 8 +5.64E+01 9 +6.73E+01 10 +7.82E+01 11 +8.91E+01 12 +1.00E+02
Figure 1.1.1–6 Normal stress distribution in the gasket contact surface when gasket elements are used
with direct specification of the gasket behavior: three-dimensional versus axisymmetric results.
1.1.1–13
BOLTED PIPE JOINT 1 2 3 2 3 4 5 6 9 9 77 10 10 10 2 3 4 5 6 2 3 4 5 6 8 8 8 2 3 4 5 6 7 2 3 4 5 6 7 7 8 8 5432 6 2 3 4 5 6 9 7 12 7 12 1111 8 2 3 4 5 6 11 65432 8 11 10 10 2 12 12 9 9 8 8 10 10 11 11 77 9 9 10 10 12 12 9 12 9 11 11 12 12 11 12 10 9 7 6 543 11 8 7 7 66 554433 12 12 8 11 10 10 9 11 9 8 2 3 4 5 6 8 9 7 10 32 4 5 6 8 10 9 7 8 32 4 5 6 7 9 10 12 2 3 4 5 6 11 7 11 12 8 9 10 12 2 3 4 5 6 10 7 12 11 11 8 9 11 12 3 4 5 6 7 8 9 10 11 12 1 2 3 S11 VALUE 1 -1.00E+02 2 -8.91E+01 3 -7.82E+01 4 -6.73E+01 5 -5.64E+01 6 -4.55E+01 7 -3.45E+01 8 -2.36E+01 9 -1.27E+01 10 -1.82E+00 11 +9.09E+00 12 +2.00E+01 1 2 3 2 3 4 5 8 9 6 7 10 2 3 4 5 8 10 9 6 7 8 432 5 6 7 2 3 4 5 12 9 11 432 5 10 12 8 6 7 8 11 9 10 12 11 11 6 7 10 8 12 11 9 9 432 5 12 10 6 7 11 11 10 9 8 432 5 6 7 12 11 12 10 9 12 8 6 7 2 3 4 5 2 3 4 5 10 9 8 6 7 11 12 2 3 4 5 12 11 10 9 8 7 6 2 3 4 5 8 6 7 9 10 2 3 4 5 8 10 9 6 7 8 432 5 6 7 2 3 4 5 12 9 11 10 2 3 4 5 12 6 7 8 8 11 9 12 10 11 9 6 7 10 8 12 11 11 9 432 5 12 10 6 7 2 3 4 5 11 10 9 8 6 7 2 3 4 5 12 11 12 10 9 8 12 6 7 11 1 2 3 S11 VALUE 1 -1.00E+02 2 -8.91E+01 3 -7.82E+01 4 -6.73E+01 5 -5.64E+01 6 -4.55E+01 7 -3.45E+01 8 -2.36E+01 9 -1.27E+01 10 -1.82E+00 11 +9.09E+00 12 +2.00E+01
Figure 1.1.1–7 Normal stress distribution in the gasket contact surface when gasket elements are used
with isotropic material properties: three-dimensional versus axisymmetric results.
1.1.1–14
BOLTED PIPE JOINT 28. 32. 36. 40. 44. 48. 52. radial distance −80. −60. −40. −20. 0. 20. STRESS - S22 22.5_no_sup 22.5_sup 45_sup 90_sup 90r_sup
Figure 1.1.1–8 Normal stress distribution in the gasket contact surface along the linez = 0 for the
models with and without substructures.
1.1.1–15
ELASTIC-PLASTIC COLLAPSE
1.1.2 ELASTIC-PLASTIC COLLAPSE OF A THIN-WALLED ELBOW UNDER IN-PLANE
BENDING AND INTERNAL PRESSURE
Product: ABAQUS/Standard
Elbows are used in piping systems because they ovalize more readily than straight pipes and, thus, provide flexibility in response to thermal expansion and other loadings that impose significant displacements on the system. Ovalization is the bending of the pipe wall into an oval—i.e., noncircular—configuration. The elbow is, thus, behaving as a shell rather than as a beam. Straight pipe runs do not ovalize easily, so they behave essentially as beams. Thus, even under pure bending, complex interaction occurs between an elbow and the adjacent straight pipe segments; the elbow causes some ovalization in the straight pipe runs, which in turn tend to stiffen the elbow. This interaction can create significant axial gradients of bending strain in the elbow, especially in cases where the elbow is very flexible. This example provides verification of shell and elbow element modeling of such effects, through an analysis of a test elbow for which experimental results have been reported by Sobel and Newman (1979). An analysis is also included with elements of type ELBOW31B (which includes ovalization but neglects axial gradients of strain) for the elbow itself and beam elements for the straight pipe segments. This provides a comparative solution in which the interaction between the elbow and the adjacent straight pipes is neglected. The analyses predict the response up to quite large rotations across the elbow, so as to investigate possible collapse of the pipe and, particularly, the effect of internal pressure on that collapse.
Geometry and model
The elbow configuration used in the study is shown in Figure 1.1.2–1. It is a thin-walled elbow with elbow factor
= Rt
r2p1 0 2 = 0:167
and radius ratio R=r = 3.07, so the flexibility factor from Dodge and Moore (1972) is 10.3. (The flexibility factor for an elbow is the ratio of the bending flexibility of an elbow segment to that of a straight pipe of the same dimensions, for small displacements and elastic response.) This is an extremely flexible case because the pipe wall is so thin.
To demonstrate convergence of the overall moment-rotation behavior with respect to meshing, the two shell element meshes shown in Figure 1.1.2–2 are analyzed. Since the loading concerns in-plane bending only, it is assumed that the response is symmetric about the midplane of the system so that in the shell element model only one-half of the system need be modeled. Element type S8R5 is used, since tests have shown this to be the most cost-effective shell element in ABAQUS (input files using element types S9R5, STRI65, and S8R for this example are included with the ABAQUS release). The elbow element meshes replace each axial division in the coarser shell element model with one ELBOW32 or two ELBOW31 elements and use 4 or 6 Fourier modes to model the deformation around the pipe. Seven integration points are used through the pipe wall in all the analyses. This is usually adequate to provide accurate modeling of the progress of yielding through the section in such cases as these, where essentially monotonic straining is expected.
1.1.2–1