abaqus 6 8 user manual

7/22/2019 Abaqus 6 8 User Manual

1/1086

Abaqus Analysis Users Manual


2/1086


3/1086

Abaqus Analysis

Users Manual

Volume IV

Version 6.8


4/1086

Legal Notices

CAUTION: This documentation is intended for qualified users who will exercise sound engineering judgment and expertise in the use of the AbaqusSoftware. The Abaqus Software is inherently complex, and the examples and procedures in this documentation are not intended to be exhaustive or to applyto any particular situation. Users are cautioned to satisfy themselves as to the accuracy and results of their analyses.

Dassault Systmes and its subsidiaries, including Dassault Systmes Simulia Corp., shall not be responsible for the accuracy or usefulness of any analysisperformed using the Abaqus Software or the procedures, examples, or explanations in this documentation. Dassault Systmes and its subsidiaries shall notbe responsible for the consequences of any errors or omissions that may appear in this documentation.

DASSAULT SYSTMES AND ITS SUBSIDIARIES DISCLAIM ALL EXPRESS OR IMPLIED REPRESENTATIONS AND WARRANTIES,INCLUDING ANY IMPLIED WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE OF THE CONTENTS OFTHIS DOCUMENTATION.

IN NO EVENT SHALL DASSAULT SYSTMES, ITS SUBSIDIARIES, OR THEIR THIRD-PARTY PROVIDERS BE LIABLE FOR ANY INDIRECT,

INCIDENTAL, PUNITIVE, SPECIAL, OR CONSEQUENTIAL DAMAGES (INCLUDING, WITHOUT LIMITATION, DAMAGES FOR LOSSOF BUSINESS PROFITS, BUSINESS INTERRUPTION, OR LOSS OF BUSINESS INFORMATION) EVEN IF DASSAULT SYSTMES OR ITSSUBSIDIARY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.

The Abaqus Software is available only under license from Dassault Systmes or its subsidiary and may be used or reproduced only in accordance with theterms of such license.

This documentation and the software described in this documentation are subject to change without prior notice.

No part of this documentation may be reproduced or distributed in any form without prior written permission of Dassault Systmes or its subsidiary.

Export and re-export of theAbaqusSoftware and this documentation is subjectto United Statesand other export control regulations. Eachuser is responsiblefor compliance with applicable export regulations.

The Abaqus Software is a product of Dassault Systmes Simulia Corp., Providence, RI, USA.

Dassault Systmes, 2008

Printed in the United States of America.

U.S. GOVERNMENT USERS: The Abaqus Software and its documentation are commercial items, specifically commercial computer software andcommercial computer software documentation and, consistent with FAR 12.212 and DFARS 227.7202, as applicable, are provided with restricted rightsin accordance with license terms.

Abaqus, the 3DS logo, SIMULIA, and CATIA are trademarks or registered trademarks of Dassault Systmes or its subsidiaries in the United States and/orother countries.

Other company, product, and service names may be trademarks or service marks of their respective owners. For additional informationconcerning trademarks, copyrights, and licenses, see the Legal Notices in the Abaqus Version 6.8 Release Notes and the notices at:http://www.simulia.com/products/products_legal.html.


5/1086

Offices and Representatives

SIMULIA Worldwide Headquarters Rising Sun Mills, 166 Valley Street, Providence, RI 029092499, Tel: +1 401 276 4400,Fax: +1 401 276 4408, [email protected], http://www.simulia.com

SIMULIA European Headquarters Gaetano Martinolaan 95, P. O. Box 1637, 6201 BP Maastricht, The Netherlands, Tel: +31 43 356 6906,Fax: +31 43 356 6908, [email protected]

Sales, Support, and Services

North America Central, West Lafayette, IN, Tel: +1 765 497 1373, [email protected], Cincinnati, West Chester, OH, Tel: +1 513 275 1430, [email protected], Minneapolis/St. Paul, Woodbury, MN, Tel: +1 612 424 9044, [email protected]

East, Warwick, RI, Tel: +1 401 739 3637, [email protected], Beachwood, OH, Tel: +1 216 378 1070, [email protected] Lakes, Northville, MI, Tel: +1 248 349 4669, [email protected], Lewisville, TX, Tel: +1 972 221 6500, [email protected], Fremont, CA, Tel: +1 510 794 5891, [email protected]

Argentina Dassault Systmes Latin America, Buenos Aires, Tel: +54 11 4345 2360, [email protected] Dassault Systmes Australia Pty. Ltd., Richmond VIC, Tel: +61 3 9421 2900, [email protected] Vienna, Tel: +43 1 929 16 25-0, [email protected] Huizen, The Netherlands, Tel: +31 35 52 58 424, [email protected] SMARTtech Mecnica, So Paulo SP, Tel: +55 11 3168 3388, [email protected]

SMARTtech Mecnica, Rio de Janeiro RJ, Tel: + 55 21 3852 2360, [email protected]

Czech Republic Synerma s. r. o., Psry, Tel: +420 603 145 769, [email protected] Versailles, Tel: +33 1 39 24 15 40, [email protected] Germany Aachen, Tel: +49 241 474010, [email protected]

Mnchen, Tel: +49 89 5434 8770, [email protected] Teynampet, Chennai, Tel: +91 44 65651590, [email protected] ADCOM, Givataim, Tel: +972 54 6830290, [email protected] Italy, Milano, Tel: +39 02 39211211, [email protected] Tokyo, Tel: +81 3 5474 5817, [email protected]

Osaka, Tel: +81 6 4803 5020, [email protected] Mapo-Gu, Seoul, Tel: +82 2 785 6707, [email protected]

Malaysia WorleyParsonsAdvancedAnalysis, KualaLumpur,Tel: +603 21612266,[email protected] Zealand Matrix Applied Computing Ltd., Auckland, Tel: +64 9 623 1223, [email protected] BudSoft Sp. z o.o., Sw. Marcin, Tel: +48 61 8508 466, [email protected], Belarus & Ukraine TESIS Ltd., Moscow, Russia, Tel: +7 495 612 4422, [email protected] Vsters, Sweden, Tel : +46 21 150870, [email protected] WorleyParsons Advanced Analysis, Singapore, Tel: +65 6735 8444, [email protected] Africa Finite Element Analysis Services (Pty) Ltd., Mowbray, Tel: +27 21 448 7608, [email protected] Principia Ingenieros Consultores, S.A., Madrid, Tel: +34 91 209 1482, [email protected] APIC, Taipei, Tel: +886 02 25083066, [email protected] WorleyParsons Advanced Analysis Group, Bangkok, Tel: +66 2 689 3000, [email protected]

Turkey A-Ztech Ltd., Istanbul, Tel: +90 216 361 8850, [email protected] United Kingdom Sevenoaks, Kent, Tel: +44 1 925 830900, [email protected], Tel: +44 1 925 830900, [email protected]


6/1086

Sales Only

North America Great Lakes Canada, Toronto, ON, Canada, Tel: +1 416 402 2219, [email protected], Mid-Atlantic, Forest Hill, MD, Tel: +1 410 420 8587, [email protected], Southeast, Acworth, GA, Tel: +1 770 795 0960, [email protected], Southern CA and AZ, Tustin, CA, Tel: +1 714 731 5895, [email protected], Rocky Mountains, Boulder, CO, Tel: +1 303 664 5444, [email protected]

Finland Vantaa, Tel: +358 9 2517 8157, [email protected] New Delhi, Tel: +91 11 55171877, [email protected]

Pune, Tel: +91 20 32913739, [email protected]

China Representative Offices

China Chaoyang District, Beijing, P. R. China, Tel: +86 10 65362345, [email protected] District, Shanghai, P. R. China, Tel: +86 21 5888 0101, [email protected]

Complete contact information is available at http://www.simulia.com/about/locations.html.


7/1086

Preface

This section lists various resources that are available for help with using Abaqus.

Support

Both technical engineering support (for problems with creating a model or performing an analysis) andsystems support (for installation, licensing, and hardware-related problems) for Abaqus are offered througha network of local support offices. Contact information is listed in the front of each Abaqus manual.

SIMULIA Online Support System

The SIMULIA Online Support System (SOSS) has a knowledge database of SIMULIA Answers. TheSIMULIA Answers are solutions to questions that we have had to answer or guidelines on how to useAbaqus. You can also submit new requests for support in the SOSS. All support incidents are tracked in theSOSS. If you are contacting us by means outside the SOSS to discuss an existing support problem and youknow the incident number, please mention it so that we can consult the database to see what the latest actionhas been.

To use the SOSS, you need to register with the system. Visit theMy Supportpage at www.simulia.comfor instructions on how to register.

Many questions about Abaqus can also be answered by visiting theProductspage and theSupportpage at www.simulia.com.

Anonymous ftp site

Useful documents are maintained on an anonymous ftp account on the computer ftp.simulia.com. Login as

user anonymous, and type your e-mail address as your password.

Training

All offices offer regularly scheduled public training classes. We also provide training seminars at customersites. All training classes and seminars include workshops to provide as much practical experience withAbaqus as possible. For a schedule and descriptions of available classes, see www.simulia.com or call yourlocal representative.

Feedback

We welcome any suggestions for improvements to Abaqus software, the support program, or documentation.We will ensure that any enhancement requests you make are considered for future releases. If you wish tomake a suggestion about the service or products, refer to www.simulia.com. Complaints should be addressedby contacting your local office or through www.simulia.com.


8/1086

CONTENTS

Contents

Volume I

PART I INTRODUCTION, SPATIAL MODELING, AND EXECUTION

1. Introduction

Introduction

Introduction: general 1.1.1

Abaqus syntax and conventions

Input syntax rules 1.2.1

Conventions 1.2.2

Defining an Abaqus model

Defining a model in Abaqus 1.3.1

Parametric modeling

Parametric input 1.4.1

2. Spatial Modeling

Defining nodes

Node definition 2.1.1

Parametric shape variation 2.1.2

Nodal thicknesses 2.1.3

Normal definitions at nodes 2.1.4

Transformed coordinate systems 2.1.5

Defining elements

Element definition 2.2.1

Element foundations 2.2.2

Defining reinforcement 2.2.3Defining rebar as an element property 2.2.4

Orientations 2.2.5

Defining surfaces

Surfaces: overview 2.3.1

Defining element-based surfaces 2.3.2

Defining node-based surfaces 2.3.3

Defining analytical rigid surfaces 2.3.4

vii


9/1086

CONTENTS

Defining Eulerian surfaces 2.3.5

Operating on surfaces 2.3.6

Defining rigid bodies

Rigid body definition 2.4.1

Defining integrated output sections

Integrated output section definition 2.5.1

Defining nonstructural mass

Nonstructural mass definition 2.6.1

Defining distributions

Distribution definition 2.7.1

Defining display bodies

Display body definition 2.8.1

Defining an assembly

Defining an assembly 2.9.1

Defining matrices

Defining matrices 2.10.1

3. Execution Procedures

Execution procedures: overview

Execution procedure for Abaqus: overview 3.1.1

Execution procedures

Execution procedure for obtaining information 3.2.1

Execution procedure for Abaqus/Standard and Abaqus/Explicit 3.2.2

Execution procedure for Abaqus/CAE 3.2.3

Execution procedure for Abaqus/Viewer 3.2.4

Execution procedure for Python 3.2.5

Execution procedure for parametric studies 3.2.6

Execution procedure for Abaqus HTML documentation 3.2.7Execution procedure for licensing utilities 3.2.8

Execution procedure for ASCII translation of results (.fil) files 3.2.9

Execution procedure for joining results (.fil) files 3.2.10

Execution procedure for querying the keyword/problem database 3.2.11

Execution procedure for fetching sample input files 3.2.12

Execution procedure for making user-defined executables and subroutines 3.2.13

Execution procedure for input file and output database upgrade utility 3.2.14

Execution procedure for generating output database reports 3.2.15

viii


10/1086

CONTENTS

Execution procedure for joining output database (.odb) files from restarted analyses 3.2.16

Execution procedure for combining output from substructures 3.2.17

Execution procedure for network output database file connector 3.2.18Execution procedure for fixed format conversion utility 3.2.19

Execution procedure for translating NASTRAN bulk data files to Abaqus input files 3.2.20

Execution procedure for translating Abaqus input files to NASTRAN bulk data files 3.2.21

Execution procedure for translating PAM-CRASH input files to partial Abaqus input

files 3.2.22

Execution procedure for translating RADIOSS input files to partial Abaqus input files 3.2.23

Execution procedure for translating Abaqus output database files to NASTRAN

Output2 results files 3.2.24Execution procedure for exchanging Abaqus data with ZAERO 3.2.25

Execution procedure for encrypting and decrypting Abaqus input data 3.2.26

Execution procedures for job execution control 3.2.27

Environment file settings

Using the Abaqus environment settings 3.3.1

Managing memory and disk resources

Managing memory and disk use in Abaqus 3.4.1

File extension definitions

File extensions used by Abaqus 3.5.1

FORTRAN unit numbers

FORTRAN unit numbers used by Abaqus 3.6.1

PART II OUTPUT

4. Output

Output

Output 4.1.1

Output to the data and results files 4.1.2Output to the output database 4.1.3

Output variables

Abaqus/Standard output variable identifiers 4.2.1

Abaqus/Explicit output variable identifiers 4.2.2

The postprocessing calculator

The postprocessing calculator 4.3.1

ix


11/1086

CONTENTS

5. File Output Format

Accessing the results file

Accessing the results file: overview 5.1.1

Results file output format 5.1.2

Accessing the results file information 5.1.3

Utility routines for accessing the results file 5.1.4

OI.1 Abaqus/Standard Output Variable Index

OI.2 Abaqus/Explicit Output Variable Index

x


12/1086

CONTENTS

Volume II

PART III ANALYSIS PROCEDURES, SOLUTION, AND CONTROL

6. Analysis Procedures

Introduction

Procedures: overview 6.1.1

General and linear perturbation procedures 6.1.2

Multiple load case analysis 6.1.3Direct linear equation solver 6.1.4

Iterative linear equation solver 6.1.5

Static stress/displacement analysis

Static stress analysis procedures: overview 6.2.1

Static stress analysis 6.2.2

Eigenvalue buckling prediction 6.2.3

Unstable collapse and postbuckling analysis 6.2.4Quasi-static analysis 6.2.5

Direct cyclic analysis 6.2.6

Low-cycle fatigue analysis using the direct cyclic approach 6.2.7

Dynamic stress/displacement analysis

Dynamic analysis procedures: overview 6.3.1

Implicit dynamic analysis using direct integration 6.3.2

Explicit dynamic analysis 6.3.3

Direct-solution steady-state dynamic analysis 6.3.4

Natural frequency extraction 6.3.5

Complex eigenvalue extraction 6.3.6

Transient modal dynamic analysis 6.3.7

Mode-based steady-state dynamic analysis 6.3.8

Subspace-based steady-state dynamic analysis 6.3.9

Response spectrum analysis 6.3.10

Random response analysis 6.3.11

Steady-state transport analysis

Steady-state transport analysis 6.4.1

Heat transfer and thermal-stress analysis

Heat transfer analysis procedures: overview 6.5.1

Uncoupled heat transfer analysis 6.5.2

Sequentially coupled thermal-stress analysis 6.5.3

xi


13/1086

CONTENTS

Fully coupled thermal-stress analysis 6.5.4

Adiabatic analysis 6.5.5

Electrical analysis

Electrical analysis procedures: overview 6.6.1

Coupled thermal-electrical analysis 6.6.2

Piezoelectric analysis 6.6.3

Coupled pore fluid flow and stress analysis

Coupled pore fluid diffusion and stress analysis 6.7.1

Geostatic stress state 6.7.2Mass diffusion analysis

Mass diffusion analysis 6.8.1

Acoustic and shock analysis

Acoustic, shock, and coupled acoustic-structural analysis 6.9.1

Abaqus/Aqua analysis

Abaqus/Aqua analysis 6.10.1

Annealing

Annealing procedure 6.11.1

7. Analysis Solution and Control

Solving nonlinear problems

Solving nonlinear problems 7.1.1

Contact iterations 7.1.2

Analysis convergence controls

Convergence and time integration criteria: overview 7.2.1

Commonly used control parameters 7.2.2

Convergence criteria for nonlinear problems 7.2.3

Time integration accuracy in transient problems 7.2.4

PART IV ANALYSIS TECHNIQUES

8. Analysis Techniques: Introduction

Analysis techniques: overview 8.1.1

xii


14/1086

CONTENTS

9. Analysis Continuation Techniques

Restarting an analysis

Restarting an analysis 9.1.1

Importing and transferring results

Transferring results between Abaqus analyses: overview 9.2.1

Transferring results between Abaqus/Explicit and Abaqus/Standard 9.2.2

Transferring results from one Abaqus/Standard analysis to another 9.2.3

Transferring results from one Abaqus/Explicit analysis to another 9.2.4

10. Modeling Abstractions

Substructuring

Using substructures 10.1.1

Defining substructures 10.1.2

Submodeling

Submodeling: overview 10.2.1Node-based submodeling 10.2.2

Surface-based submodeling 10.2.3

Generating global matrices

Generating global matrices 10.3.1

Symmetric model generation, results transfer, and analysis of cyclic symmetry models

Symmetric model generation 10.4.1

Transferring results from a symmetric mesh or a partial three-dimensional mesh to

a full three-dimensional mesh 10.4.2

Analysis of models that exhibit cyclic symmetry 10.4.3

Meshed beam cross-sections

Meshed beam cross-sections 10.5.1

11. Special-Purpose Techniques

Inertia relief

Inertia relief 11.1.1

Mesh modification or replacement

Element and contact pair removal and reactivation 11.2.1

Geometric imperfections

Introducing a geometric imperfection into a model 11.3.1

xiii


15/1086

CONTENTS

Fracture mechanics

Fracture mechanics: overview 11.4.1

Contour integral evaluation 11.4.2

Crack propagation analysis 11.4.3

Hydrostatic fluid modeling

Modeling fluid-filled cavities 11.5.1

Surface-based fluid modeling

Surface-based fluid cavities: overview 11.6.1

Defining fluid cavities 11.6.2Defining fluid exchange 11.6.3

Defining inflators 11.6.4

Mass scaling

Mass scaling 11.7.1

Steady-state detection

Steady-state detection 11.8.1

Parallel execution

Parallel execution in Abaqus 11.9.1

Parallel execution in Abaqus/Standard 11.9.2

Parallel execution in Abaqus/Explicit 11.9.3

12. Adaptivity Techniques

Adaptivity techniques: overview

Adaptivity techniques 12.1.1

ALE adaptive meshing

ALE adaptive meshing: overview 12.2.1

Defining ALE adaptive mesh domains in Abaqus/Explicit 12.2.2

ALE adaptive meshing and remapping in Abaqus/Explicit 12.2.3

Modeling techniques for Eulerian adaptive mesh domains in Abaqus/Explicit 12.2.4Output and diagnostics for ALE adaptive meshing in Abaqus/Explicit 12.2.5

Defining ALE adaptive mesh domains in Abaqus/Standard 12.2.6

ALE adaptive meshing and remapping in Abaqus/Standard 12.2.7

Adaptive remeshing

Adaptive remeshing: overview 12.3.1

Error indicators 12.3.2

Solution-based mesh sizing 12.3.3

xiv


16/1086

CONTENTS

Analysis continuation after mesh replacement

Mesh-to-mesh solution mapping 12.4.1

13. Eulerian Analysis

Eulerian analysis 13.1.1

14. Extending Abaqus Analysis Functionality

Co-simulation

Co-simulation: overview 14.1.1Preparing an Abaqus analysis for co-simulation 14.1.2

User subroutines and utilities

User subroutines: overview 14.2.1

Available user subroutines 14.2.2

Available utility routines 14.2.3

15. Design Sensitivity AnalysisDesign sensitivity analysis 15.1.1

16. Parametric Studies

Scripting parametric studies

Scripting parametric studies 16.1.1

Parametric studies: commandsaStudy.combine(): Combine parameter samples for parametric studies 16.2.1

aStudy.constrain(): Constrain parameter value combinations in parametric studies 16.2.2

aStudy.define(): Define parameters for parametric studies 16.2.3

aStudy.execute(): Execute the analysis of parametric study designs 16.2.4

aStudy.gather(): Gather the results of a parametric study 16.2.5

aStudy.generate(): Generate the analysis job data for a parametric study 16.2.6

aStudy.output(): Specify the source of parametric study results 16.2.7

aStudy=ParStudy(): Create a parametric study 16.2.8aStudy.report(): Report parametric study results 16.2.9

aStudy.sample(): Sample parameters for parametric studies 16.2.10

xv


17/1086

CONTENTS

Volume III

PART V MATERIALS

17. Materials: Introduction

Introduction

Material library: overview 17.1.1

Material data definition 17.1.2

Combining material behaviors 17.1.3

General properties

Density 17.2.1

18. Elastic Mechanical Properties

Overview

Elastic behavior: overview 18.1.1

Linear elasticity

Linear elastic behavior 18.2.1

No compression or no tension 18.2.2

Plane stress orthotropic failure measures 18.2.3

Porous elasticity

Elastic behavior of porous materials 18.3.1

Hypoelasticity

Hypoelastic behavior 18.4.1

Hyperelasticity

Hyperelastic behavior of rubberlike materials 18.5.1

Hyperelastic behavior in elastomeric foams 18.5.2

Anisotropic hyperelastic behavior 18.5.3

Stress softening in elastomers

Mullins effect in rubberlike materials 18.6.1

Energy dissipation in elastomeric foams 18.6.2

Viscoelasticity

Time domain viscoelasticity 18.7.1

Frequency domain viscoelasticity 18.7.2

xvi


18/1086

CONTENTS

Hysteresis

Hysteresis in elastomers 18.8.1

Equations of state

Equation of state 18.9.1

19. Inelastic Mechanical Properties

Overview

Inelastic behavior 19.1.1

Metal plasticity

Classical metal plasticity 19.2.1

Models for metals subjected to cyclic loading 19.2.2

Rate-dependent yield 19.2.3

Rate-dependent plasticity: creep and swelling 19.2.4

Annealing or melting 19.2.5

Anisotropic yield/creep 19.2.6

Johnson-Cook plasticity 19.2.7Dynamic failure models 19.2.8

Porous metal plasticity 19.2.9

Cast iron plasticity 19.2.10

Two-layer viscoplasticity 19.2.11

ORNL Oak Ridge National Laboratory constitutive model 19.2.12

Deformation plasticity 19.2.13

Other plasticity modelsExtended Drucker-Prager models 19.3.1

Modified Drucker-Prager/Cap model 19.3.2

Mohr-Coulomb plasticity 19.3.3

Critical state (clay) plasticity model 19.3.4

Crushable foam plasticity models 19.3.5

Fabric materials

Fabric material behavior 19.4.1

Jointed materials

Jointed material model 19.5.1

Concrete

Concrete smeared cracking 19.6.1

Cracking model for concrete 19.6.2

Concrete damaged plasticity 19.6.3

xvii

CONTENTS


19/1086

CONTENTS

Permanent set in rubberlike materials

Permanent set in rubberlike materials 19.7.1

20. Progressive Damage and Failure

Progressive damage and failure: overview

Progressive damage and failure 20.1.1

Damage and failure for ductile metals

Damage and failure for ductile metals: overview 20.2.1

Damage initiation for ductile metals 20.2.2Damage evolution and element removal for ductile metals 20.2.3

Damage and failure for fiber-reinforced composites

Damage and failure for fiber-reinforced composites: overview 20.3.1

Damage initiation for fiber-reinforced composites 20.3.2

Damage evolution and element removal for fiber-reinforced composites 20.3.3

Damage and failure for ductile materials in low-cycle fatigue analysis

Damage and failure for ductile materials in low-cycle fatigue analysis: overview 20.4.1

Damage initiation for ductile materials in low-cycle fatigue 20.4.2

Damage evolution for ductile materials in low-cycle fatigue 20.4.3

21. Other Material Properties

Mechanical properties

Material damping 21.1.1

Thermal expansion 21.1.2

Heat transfer properties

Thermal properties: overview 21.2.1

Conductivity 21.2.2

Specific heat 21.2.3

Latent heat 21.2.4

Acoustic propertiesAcoustic medium 21.3.1

Hydrostatic fluid properties

Hydrostatic fluid models 21.4.1

Mass diffusion properties

Diffusivity 21.5.1

Solubility 21.5.2

xviii

CONTENTS


20/1086

CONTENTS

Electrical properties

Electrical conductivity 21.6.1

Piezoelectric behavior 21.6.2

Pore fluid flow properties

Pore fluid flow properties 21.7.1

Permeability 21.7.2

Porous bulk moduli 21.7.3

Sorption 21.7.4

Swelling gel 21.7.5

Moisture swelling 21.7.6

User materials

User-defined mechanical material behavior 21.8.1

User-defined thermal material behavior 21.8.2

xix

CONTENTS


21/1086

CONTENTS

Volume IV

PART VI ELEMENTS

22. Elements: Introduction

Element library: overview 22.1.1

Choosing the elements dimensionality 22.1.2

Choosing the appropriate element for an analysis type 22.1.3

Section controls 22.1.4

23. Continuum Elements

General-purpose continuum elements

Solid (continuum) elements 23.1.1

One-dimensional solid (link) element library 23.1.2

Two-dimensional solid element library 23.1.3

Three-dimensional solid element library 23.1.4

Cylindrical solid element library 23.1.5Axisymmetric solid element library 23.1.6

Axisymmetric solid elements with nonlinear, asymmetric deformation 23.1.7

Infinite elements

Infinite elements 23.2.1

Infinite element library 23.2.2

Warping elements

Warping elements 23.3.1

Warping element library 23.3.2

24. Structural Elements

Membrane elements

Membrane elements 24.1.1

General membrane element library 24.1.2

Cylindrical membrane element library 24.1.3

Axisymmetric membrane element library 24.1.4

Truss elements

Truss elements 24.2.1

Truss element library 24.2.2

Beam elements

Beam modeling: overview 24.3.1

xx

CONTENTS


22/1086

CONTENTS

Choosing a beam cross-section 24.3.2

Choosing a beam element 24.3.3

Beam element cross-section orientation 24.3.4

Beam section behavior 24.3.5

Using a beam section integrated during the analysis to define the section behavior 24.3.6

Using a general beam section to define the section behavior 24.3.7

Beam element library 24.3.8

Beam cross-section library 24.3.9

Frame elements

Frame elements 24.4.1

Frame section behavior 24.4.2

Frame element library 24.4.3

Elbow elements

Pipes and pipebends with deforming cross-sections: elbow elements 24.5.1

Elbow element library 24.5.2

Shell elements

Shell elements: overview 24.6.1

Choosing a shell element 24.6.2

Defining the initial geometry of conventional shell elements 24.6.3

Shell section behavior 24.6.4

Using a shell section integrated during the analysis to define the section behavior 24.6.5

Using a general shell section to define the section behavior 24.6.6

Three-dimensional conventional shell element library 24.6.7

Continuum shell element library 24.6.8

Axisymmetric shell element library 24.6.9

Axisymmetric shell elements with nonlinear, asymmetric deformation 24.6.10

25. Inertial, Rigid, and Capacitance Elements

Point mass elements

Point masses 25.1.1

Mass element library 25.1.2

Rotary inertia elements

Rotary inertia 25.2.1

Rotary inertia element library 25.2.2

Rigid elements

Rigid elements 25.3.1

Rigid element library 25.3.2

xxi

CONTENTS


23/1086

Capacitance elements

Point capacitance 25.4.1

Capacitance element library 25.4.2

26. Connector Elements

Connector elements

Connectors: overview 26.1.1

Connector elements 26.1.2

Connector actuation 26.1.3

Connector element library 26.1.4

Connection-type library 26.1.5

Connector element behavior

Connector behavior 26.2.1

Connector elastic behavior 26.2.2

Connector damping behavior 26.2.3

Connector functions for coupled behavior 26.2.4

Connector friction behavior 26.2.5

Connector plastic behavior 26.2.6

Connector damage behavior 26.2.7

Connector stops and locks 26.2.8

Connector failure behavior 26.2.9

Connector uniaxial behavior 26.2.10

27. Special-Purpose Elements

Spring elements

Springs 27.1.1

Spring element library 27.1.2

Dashpot elements

Dashpots 27.2.1

Dashpot element library 27.2.2

Flexible joint elements

Flexible joint element 27.3.1

Flexible joint element library 27.3.2

Distributing coupling elements

Distributing coupling elements 27.4.1

Distributing coupling element library 27.4.2

xxii

CONTENTS


24/1086

Cohesive elements

Cohesive elements: overview 27.5.1

Choosing a cohesive element 27.5.2Modeling with cohesive elements 27.5.3

Defining the cohesive elements initial geometry 27.5.4

Defining the constitutive response of cohesive elements using a continuum approach 27.5.5

Defining the constitutive response of cohesive elements using a traction-separation

description 27.5.6

Defining the constitutive response of fluid within the cohesive element gap 27.5.7

Two-dimensional cohesive element library 27.5.8

Three-dimensional cohesive element library 27.5.9Axisymmetric cohesive element library 27.5.10

Gasket elements

Gasket elements: overview 27.6.1

Choosing a gasket element 27.6.2

Including gasket elements in a model 27.6.3

Defining the gasket elements initial geometry 27.6.4

Defining the gasket behavior using a material model 27.6.5Defining the gasket behavior directly using a gasket behavior model 27.6.6

Two-dimensional gasket element library 27.6.7

Three-dimensional gasket element library 27.6.8

Axisymmetric gasket element library 27.6.9

Surface elements

Surface elements 27.7.1

General surface element library 27.7.2Cylindrical surface element library 27.7.3

Axisymmetric surface element library 27.7.4

Hydrostatic fluid elements

Hydrostatic fluid elements 27.8.1

Hydrostatic fluid element library 27.8.2

Fluid link elements 27.8.3

Hydrostatic fluid link library 27.8.4

Tube support elements

Tube support elements 27.9.1

Tube support element library 27.9.2

Line spring elements

Line spring elements for modeling part-through cracks in shells 27.10.1

Line spring element library 27.10.2

xxiii

CONTENTS


25/1086

Elastic-plastic joints

Elastic-plastic joints 27.11.1

Elastic-plastic joint element library 27.11.2

Drag chain elements

Drag chains 27.12.1

Drag chain element library 27.12.2

Pipe-soil elements

Pipe-soil interaction elements 27.13.1

Pipe-soil interaction element library 27.13.2

Acoustic interface elements

Acoustic interface elements 27.14.1

Acoustic interface element library 27.14.2

Eulerian elements

Eulerian elements 27.15.1

Eulerian element library 27.15.2

User-defined elements

User-defined elements 27.16.1

User-defined element library 27.16.2

EI.1 Abaqus/Standard Element Index

EI.2 Abaqus/Explicit Element Index

xxiv

CONTENTS


26/1086

Volume V

PART VII PRESCRIBED CONDITIONS

28. Prescribed Conditions

Overview

Prescribed conditions: overview 28.1.1

Amplitude curves 28.1.2

Initial conditions

Initial conditions 28.2.1

Boundary conditions

Boundary conditions 28.3.1

Loads

Applying loads: overview 28.4.1

Concentrated loads 28.4.2Distributed loads 28.4.3

Thermal loads 28.4.4

Acoustic and shock loads 28.4.5

Pore fluid flow 28.4.6

Prescribed assembly loads

Prescribed assembly loads 28.5.1

Predefined fields

Predefined fields 28.6.1

PART VIII CONSTRAINTS

29. Constraints

Overview

Kinematic constraints: overview 29.1.1

Multi-point constraints

Linear constraint equations 29.2.1

General multi-point constraints 29.2.2

Kinematic coupling constraints 29.2.3

xxv

CONTENTS


27/1086

Surface-based constraints

Mesh tie constraints 29.3.1

Coupling constraints 29.3.2Shell-to-solid coupling 29.3.3

Mesh-independent fasteners 29.3.4

Embedded elements

Embedded elements 29.4.1

Element end release

Element end release 29.5.1

Overconstraint checks

Overconstraint checks 29.6.1

PART IX INTERACTIONS

30. Defining Contact Interactions

Overview

Contact interaction analysis: overview 30.1.1

Defining contact pairs in Abaqus/Standard

Defining contact pairs in Abaqus/Standard 30.2.1

Contact formulations in Abaqus/Standard 30.2.2

Contact constraint enforcement methods in Abaqus/Standard 30.2.3Modeling contact interference fits in Abaqus/Standard 30.2.4

Adjusting initial surface positions and specifying initial clearances in Abaqus/Standard

contact pairs 30.2.5

Smoothing contact surfaces in Abaqus/Standard 30.2.6

Removing/reactivating Abaqus/Standard contact pairs 30.2.7

Defining tied contact in Abaqus/Standard 30.2.8

Extending master surfaces and slide lines 30.2.9

Contact modeling if substructures are present 30.2.10Contact modeling if asymmetric-axisymmetric elements are present 30.2.11

Contact diagnostics in an Abaqus/Standard analysis 30.2.12

Common difficulties associated with contact modeling in Abaqus/Standard 30.2.13

Adjusting contact controls in Abaqus/Standard 30.2.14

Defining general contact in Abaqus/Explicit

Defining general contact interactions in Abaqus/Explicit 30.3.1

Assigning surface properties for general contact in Abaqus/Explicit 30.3.2

xxvi

CONTENTS


28/1086

Assigning contact properties for general contact in Abaqus/Explicit 30.3.3

Contact formulation for general contact in Abaqus/Explicit 30.3.4

Resolving initial overclosures and specifying initial clearances for general contact in

Abaqus/Explicit 30.3.5

Contact controls for general contact in Abaqus/Explicit 30.3.6

Defining contact pairs in Abaqus/Explicit

Defining contact pairs in Abaqus/Explicit 30.4.1

Assigning surface properties for contact pairs in Abaqus/Explicit 30.4.2

Assigning contact properties for contact pairs in Abaqus/Explicit 30.4.3

Contact formulations for contact pairs in Abaqus/Explicit 30.4.4

Adjusting initial surface positions and specifying initial clearances for contact pairs

in Abaqus/Explicit 30.4.5

Common difficulties associated with contact modeling using contact pairs in

Abaqus/Explicit 30.4.6

31. Contact Property Models

Mechanical contact properties

Mechanical contact properties: overview 31.1.1

Contact pressure-overclosure relationships 31.1.2

Contact damping 31.1.3

Contact blockage 31.1.4

Frictional behavior 31.1.5

User-defined interfacial constitutive behavior 31.1.6

Pressure penetration loading 31.1.7

Interaction of debonded surfaces 31.1.8Breakable bonds 31.1.9

Surface-based cohesive behavior 31.1.10

Thermal contact properties

Thermal contact properties 31.2.1

Electrical contact properties

Electrical contact properties 31.3.1

Pore fluid contact properties

Pore fluid contact properties 31.4.1

32. Contact Elements in Abaqus/Standard

Contact modeling with elements

Contact modeling with elements 32.1.1

xxvii

CONTENTS


29/1086

Gap contact elements

Gap contact elements 32.2.1

Gap element library 32.2.2

Tube-to-tube contact elements

Tube-to-tube contact elements 32.3.1

Tube-to-tube contact element library 32.3.2

Slide line contact elements

Slide line contact elements 32.4.1

Axisymmetric slide line element library 32.4.2

Rigid surface contact elements

Rigid surface contact elements 32.5.1

Axisymmetric rigid surface contact element library 32.5.2

33. Defining Cavity Radiation in Abaqus/Standard

Cavity radiation 33.1.1

xxviii


30/1086


31/1086

Part VI: Elements Chapter 22, Elements: Introduction Chapter 23, Continuum Elements Chapter 24, Structural Elements Chapter 25, Inertial, Rigid, and Capacitance Elements

Chapter 26, Connector Elements Chapter 27, Special-Purpose Elements


32/1086

ELEMENTS: INTRODUCTION


33/1086

22. Elements: Introduction

Introduction 22.1


34/1086

INTRODUCTION


35/1086

22.1 Introduction

Element library: overview, Section 22.1.1 Choosing the elements dimensionality, Section 22.1.2 Choosing the appropriate element for an analysis type, Section 22.1.3 Section controls, Section 22.1.4

22.11


36/1086

ELEMENT LIBRARY


37/1086

22.1.1 ELEMENT LIBRARY: OVERVIEW

Abaqus has an extensive element library to provide a powerful setof tools for solving many different problems.

Characterizing elements

Five aspects of an element characterize its behavior:

Family Degrees of freedom (directly related to the element family)

Number of nodes Formulation Integration

Each element in Abaqus has a unique name, such as T2D2, S4R, C3D8I, or C3D8R. The elementname identifies each of the five aspects of an element. For details on defining elements, see Elementdefinition, Section 2.2.1.

Family

Figure 22.1.11shows the element families that are used most commonly in a stress analysis. One ofthe major distinctions between different element families is the geometry type that each family assumes.

Continuum

(solid) elementsShell

elementsBeam

elements

Rigid

elements

Membraneelements Infiniteelements Connector elementssuch as springs

and dashpots

Trusselements

Figure 22.1.11 Commonly used element families.

The first letter or letters of an elements name indicate to which family the element belongs. Forexample, S4R is a shell element, CINPE4 is an infinite element, and C3D8I is a continuum element.

22.1.11

ELEMENT LIBRARY
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


38/1086

Degrees of freedom

The degrees of freedom are the fundamental variables calculated during the analysis. For a

stress/displacement simulation the degrees of freedom are the translations and, for shell and beamelements, the rotations at each node. For a heat transfer simulation the degrees of freedom are thetemperatures at each node; for a coupled thermal-stress analysis temperature degrees of freedom existin addition to displacement degrees of freedom at each node. Heat transfer analyses and coupledthermal-stress analyses therefore require the use of different elements than does a stress analysis sincethe degrees of freedom are not the same. See Conventions, Section 1.2.2, for a summary of thedegrees of freedom available in Abaqus for various element and analysis types.

Number of nodes and order of interpolation

Displacements or other degrees of freedom are calculated at the nodes of the element. At any other pointin the element, the displacements are obtained by interpolating from the nodal displacements. Usuallythe interpolation order is determined by the number of nodes used in the element.

Elements that have nodes only at their corners, such as the 8-node brick shown in Figure 22.1.12(a),use linear interpolation in each direction and are often called linear elements orfirst-order elements.

In Abaqus/Standard elements with midside nodes, such as the 20-node brick shown inFigure 22.1.12(b), use quadratic interpolation and are often called quadratic elements orsecond-order elements.

Modified triangular or tetrahedral elements with midside nodes, such as the 10-node tetrahedronshown in Figure 22.1.12(c), use a modified second-order interpolation and are often calledmodified or modified second-order elements.

(a) Linear element(8-node brick, C3D8)

(b) Quadratic element(20-node brick, C3D20)

(c) Modified second-order element(10-node tetrahedron, C3D10M)

Figure 22.1.12 Linear brick, quadratic brick, and modified tetrahedral elements.

Typically, the number of nodes in an element is clearly identified in its name. The 8-node brickelement is called C3D8, and the 4-node shell element is called S4R.

The beam element family uses a slightly different convention: the order of interpolation is identifiedin the name. Thus, a first-order, three-dimensional beam element is called B31, whereas a second-order,three-dimensional beam element is called B32. A similar convention is used for axisymmetric shell andmembrane elements.

22.1.12

ELEMENT LIBRARY
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


39/1086

Formulation

An elements formulation refers to the mathematical theory used to define the elements behavior. In theLagrangian, or material, description of behavior the element deforms with the material. In the alternativeEulerian, or spatial, description elements are fixed in space as the material flows through them. Eulerianmethods are used commonly in fluid mechanics simulations. Abaqus/Standard uses Eulerian elementsto model convective heat transfer. Abaqus/Explicit also offers multimaterial Eulerian elements for usein stress/displacement analyses. Adaptive meshing in Abaqus/Explicit combines the features of pureLagrangian and Eulerian analyses and allows the motion of the element to be independent of the material(see ALE adaptive meshing: overview, Section 12.2.1). All other stress/displacement elements in

Abaqus are based on the Lagrangian formulation. In Abaqus/Explicit the Eulerian elements can interactwith Lagrangian elements through general contact (see Eulerian analysis, Section 13.1.1).

To accommodate different types of behavior, some element families in Abaqus include elementswith several different formulations. For example, the conventional shell element family has threeclasses: one suitable for general-purpose shell analysis, another for thin shells, and yet another for thickshells. In addition, Abaqus also offers continuum shell elements, which have nodal connectivities likecontinuum elements but are formulated to model shell behavior with as few as one element through theshell thickness.

Some Abaqus/Standard element families have a standard formulation as well as some alternativeformulations. Elements with alternative formulations are identified by an additional character at the endof the element name. For example, the continuum, beam, and truss element families include memberswith a hybrid formulation (to deal with incompressible or inextensible behavior); these elements areidentified by the letter H at the end of the name (C3D8H or B31H).

Abaqus/Standard uses the lumped mass formulation for low-order elements; Abaqus/Explicit usesthe lumped mass formulation for all elements. As a consequence, the second mass moments of inertia

can deviate from the theoretical values, especially for coarse meshes.

Integration

Abaqus uses numerical techniques to integrate various quantities over the volume of each element,thus allowing complete generality in material behavior. Using Gaussian quadrature for most elements,Abaqus evaluates the material response at each integration point in each element. Some continuumelements in Abaqus can use full or reduced integration, a choice that can have a significant effect on the

accuracy of the element for a given problem.Abaqus uses the letter R at the end of the element name to label reduced-integration elements. For

example, CAX4R is the 4-node, reduced-integration, axisymmetric, solid element.

Shell and beam element properties can be defined as general section behaviors; or each cross-section of the element can be integrated numerically, so that nonlinear response associated with nonlinearmaterial behavior can be tracked accurately when needed. In addition, a composite layered section canbe specified for shells and, in Abaqus/Standard, three-dimensional bricks, with different materials foreach layer through the section.

22.1.13

ELEMENT LIBRARY


40/1086

Combining elements

The element library is intended to provide a complete modeling capability for all geometries. Thus, anycombination of elements can be used to make up the model; multi-point constraints (General multi-pointconstraints, Section 29.2.2) are sometimes helpful in applying the necessary kinematic relations to formthe model (for example, to model part of a shell surface with solid elements and part with shell elementsor to use a beam element as a shell stiffener).

Heat transfer and thermal-stress analysis

In cases where heat transfer analysis is to be followed by thermal-stress analysis, corresponding heattransfer and stress elements are provided in Abaqus/Standard. See Sequentially coupled thermal-stressanalysis, Section 6.5.3, for additional details.

Information available for element libraries

The complete element library in Abaqus is subdivided into a number of smaller libraries. Each libraryis presented as a separate section in this manual. In each of these sections, information regarding thefollowing topics is provided where applicable:

conventions; element types; degrees of freedom; nodal coordinates required; element property definition; element faces;

element output; loading (general loading, distributed loads, foundations, distributed heat fluxes, film conditions,radiation types, distributed flows, distributed impedances, electrical fluxes, distributed electriccurrent densities, and distributed concentration fluxes);

nodes associated with the element; node ordering and face ordering on elements; and numbering of integration points for output.

For element libraries that are available in both Abaqus/Standard and Abaqus/Explicit, individualelement or load types that are available only in Abaqus/Standard are designated with an (S) ; similarly,individual element or load types that are available only in Abaqus/Explicit are designated with an (E) .Element or load types that are available in Abaqus/Aqua are designated with an (A) .

Most of the element output variables available for an element are discussed. Additional variablesmay be available depending on the material model or the analysis procedure that is used. Some elementshave solution variables that do not pertain to other elements of the same type; these variables are specifiedexplicitly.

22.1.14

ELEMENT DIMENSIONALITY


41/1086

22.1.2 CHOOSING THE ELEMENTS DIMENSIONALITY

Products:Abaqus/Standard Abaqus/Explicit Abaqus/CAE

Reference

Element library: overview, Section 22.1.1 Part modeling space, Section 11.4.1 of the Abaqus/CAE Users Manual Assigning Abaqus element types, Section 17.5 of the Abaqus/CAE Users Manual

Overview

The Abaqus element library contains the following for modeling a wide range of spatial dimensionality:

one-dimensional elements; two-dimensional elements; three-dimensional elements;

cylindrical elements; axisymmetric elements; and axisymmetric elements with nonlinear, asymmetric deformation.

One-dimensional (link) elements

One-dimensional heat transfer, coupled thermal/electrical, and acoustic elements are available only inAbaqus/Standard. In addition, structural link (truss) elements are available in both Abaqus/Standard and

Abaqus/Explicit. These elements can be used in two- or three-dimensional space to transmit loads orfluxes along the length of the element.

Two-dimensional elements

Abaqus provides several different types of two-dimensional elements. For structural applications theseinclude plane stress elements and plane strain elements. Abaqus/Standard also provides generalizedplane strain elements for structural applications.

Plane stress elements

Plane stress elements can be used when the thickness of a body or domain is small relative to its lateral(in-plane) dimensions. The stresses are functions of planar coordinates alone, and the out-of-planenormal and shear stresses are equal to zero.

Plane stress elements must be defined in theXY plane, and all loading and deformation are alsorestricted to this plane. This modeling method generally applies to thin, flat bodies. For anisotropicmaterials theZ-axis must be a principal material direction.

22.1.21



42/1086

Plane strain elements

Plane strain elements can be used when it can be assumed that the strains in a loaded body or domain arefunctions of planar coordinates alone and the out-of-plane normal and shear strains are equal to zero.

Plane strain elements must be defined in theXY plane, and all loading and deformation are alsorestricted to this plane. This modeling method is generally used for bodies that are very thick relative totheir lateral dimensions, such as shafts, concrete dams, or walls. Plane strain theory might also apply toa typical slice of an underground tunnel that lies along theZ-axis. For anisotropic materials theZ-axismust be a principal material direction.

Since plane strain theory assumes zero strain in the thickness direction, isotropic thermal expansion

may cause large stresses in the thickness direction.

Generalized plane strain elements

Generalized plane strain elements provide for the modeling of cases in Abaqus/Standard where thestructure has constant curvature (and, hence, no gradients of solution variables) with respect to onematerial directionthe axial direction of the model. The formulation, thus, involves a model thatlies between two planes that can move with respect to each other and, hence, cause strain in the axialdirection of the model that varies linearly with respect to position in the planes, the variation being due tothe change in curvature. In the initial configuration the bounding planes can be parallel or at an angle toeach other, the latter case allowing the modeling of initial curvature of the model in the axial direction.The concept is illustrated inFigure 22.1.21. Generalized plane strain elements are typically used tomodel a section of a long structure that is free to expand axially or is subjected to axial loading.

Each generalized plane strain element has three, four, six, or eight conventional nodes, at eachof whichx- andy-coordinates, displacements, etc. are stored. These nodes determine the position andmotion of the element in the two bounding planes. Each element also has a reference node, which is

usually the same node for all of the generalized plane strain elements in the model. The reference node ofa generalized plane strain element should not be used as a conventional node in any element in the model.The reference node has three degrees of freedom 3, 4, and 5: ( , , and ). Thefirst degreeof freedom ( ) is the change in length of the axial material fiber connecting this node and its imagein the other bounding plane. This displacement is positive as the planes move apart; therefore, there is atensile strain in the axial fiber. The second and third degrees of freedom ( , ) are the componentsof the relative rotation of one bounding plane with respect to the other. The values stored are the twocomponents of rotation about the X-and Y-axes in the bounding planes (that is, in the cross-section of themodel). Positive rotation about theX-axis causes increasing axial strain with respect to they-coordinatein the cross-section; positive rotation about theY-axis causes decreasing axial strain with respect tothex-coordinate in the cross-section. Thex- andy-coordinates of a generalized plane strain elementreference node ( and discussed below) remainfixed throughout all steps of an analysis. From thedegrees of freedom of the reference node, the length of the axial material fiber passing through the pointwith current coordinates (x,y) in a bounding plane is defined as

22.1.22


Bounding planes


43/1086

y

x

(x,y)

Conventional element nodeReference node

Length of line through the thickness at (x,y) is

t0+ uz+ x(y - Y0) - y(x - X0)

where quantities are defined in the text.

Bounding planes

(X ,Y )0 0

Figure 22.1.21 Generalized plane strain model.

where

t is the current length of the fiber,is the initial length of the fiber passing through the reference node (given as partof the element section definition),

is the displacement at the reference node (stored as degree of freedom 3 at thereference node),

and are the total values of the components of the angle between the boundingplanes (the original values of , are given as part of the elementsection definitionsee Defining the elements section properties in Solid(continuum) elements, Section 23.1.1: the changes in these values are thedegrees of freedom 4 and 5 of the reference node), and

and are the coordinates of the reference node in a bounding plane.

22.1.23


The strain in the axial direction is defined immediately from this axial fiber length The strain


44/1086

The strain in the axial direction is defined immediately from this axial fiber length. The straincomponents in the cross-section of the model are computed from the displacements of the regular nodesof the elements in the usual way. Since the solution is assumed to be independent of the axial position,

there are no transverse shear strains.

Three-dimensional elements

Three-dimensional elements are defined in the globalX,Y,Z space. These elements are used whenthe geometry and/or the applied loading are too complex for any other element type with fewer spatialdimensions.

Cylindrical elements

Cylindrical elements are three-dimensional elements defined in the global X, Y, Z space. These elementsare used to model bodies with circular or axisymmetric geometry subjected to general, nonaxisymmetricloading. Cylindrical elements are available only in Abaqus/Standard.

Axisymmetric elements

Axisymmetric elements provide for the modeling of bodies of revolution under axially symmetric loadingconditions. A body of revolution is generated by revolving a plane cross-section about an axis (thesymmetry axis) and is readily described in cylindrical polar coordinatesr,z, and . Figure 22.1.22shows a typical reference cross-section at . The radial and axial coordinates of a point on thiscross-section are denoted byr andz, respectively. At , the radial and axial coordinates coincidewith the global CartesianX- andY-coordinates.

Abaqus does not apply boundary conditions automatically to nodes that are located on the symmetryaxis in axisymmetric models. If required, you should apply them directly. Radial boundary conditions at

nodes located on thez-axis are appropriate for most problems because without them nodes may displaceacross the symmetry axis, violating the principle of compatibility. However, there are some analyses,such as penetration calculations, where nodes along the symmetry axis should be free to move; boundaryconditions should be omitted in these cases.

If the loading and material properties are independent of , the solution in any rzplane completelydefines the solution in the body. Consequently, axisymmetric elements can be used to analyze theproblem by discretizing the reference cross-section at . Figure 22.1.22shows an element of anaxisymmetric body. The nodes i,j,k, andl are actually nodal circles, and the volume of materialassociated with the element is that of a body of revolution, as shown in the

fi

gure. The value of aprescribed nodal load or reaction force is the total value on the ring; that is, the value integrated aroundthe circumference.

Regular axisymmetric elements

Regular axisymmetric elements for structural applications allow for only radial and axial loadingand have isotropic or orthotropic material properties, with being a principal direction. Any radialdisplacement in such an element will induce a strain in the circumferential direction (hoop strain);

22.1.24


z (Y)
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


45/1086

z (Y)

r (X)

cross-section

at = 0

i j

l

k

Figure 22.1.22 Reference cross-section and element in an axisymmetric solid.

and since the displacement must also be purely axisymmetric, there are only four possible nonzerocomponents of strain ( , , , and ).

Generalized axisymmetric stress/displacement elements with twist

Axisymmetric solid elements with twist are available only in Abaqus/Standard for the analysis ofstructures that are axially symmetric but can twist about their symmetry axis. This element family issimilar to the axisymmetric elements discussed above, except that it allows for a circumferential loading

component (which is independent of ) and for general material anisotropy. Under these conditions,there may be displacements in the -direction that vary withr and zbut not with . The problem remainsaxisymmetric because the solution does not vary as a function of so that the deformation of anyrzplane characterizes the deformation in the entire body. Initially the elements define an axisymmetricreference geometry with respect to therz plane at , where ther-direction corresponds to theglobalX-direction and thez-direction corresponds to the globalY-direction.Figure 22.1.23shows anaxisymmetric model consisting of two elements. The figure also shows the local cylindrical coordinatesystem at node 100.

22.1.25



46/1086

Y (z at = 0)

e z

e

e r

100

X (r at = 0)

Y

ez

e r100

X

e

100

(b)(a)

Figure 22.1.23 Reference and deformed cross-section

in an axisymmetric solid with twist.

The motion at a node of an axisymmetric element with twist is described by the radial displacement, the axial displacement , and the twist (in radians) about thez-axis, each of which is constant in

the circumferential direction, so that the deformed geometry remains axisymmetric. Figure 22.1.23(b)shows the deformed geometry of the reference model shown in Figure 22.1.23(a) and the localcylindrical coordinate system at the displaced location of node 100, for a twist .

The formulation of these elements is discussed in Axisymmetric elements, Section 3.2.8 of the

Abaqus Theory Manual.Generalized axisymmetric elements with twist cannot be used in contour integral calculations and

in dynamic analysis. Elastic foundations are applied only to degrees of freedom and .These elements should not be mixed with three-dimensional elements.Axisymmetric elements with twist and the nodes of these elements should be used with caution

within rigid bodies. If the rigid body undergoes large rotations, incorrect results may be obtained. Itis recommended that rigid constraints on axisymmetric elements with twist be modeled with kinematiccoupling (see Kinematic coupling constraints, Section 29.2.3).

Stabilization should not be used with these elements if the deformation is dominated by twist, sincestabilization is applied only to the in-plane deformation.

Axisymmetric elements with nonlinear, asymmetric deformation

These elements are intended for the linear or nonlinear analysis of structures that are initiallyaxisymmetric but undergo nonlinear, nonaxisymmetric deformation. They are available only inAbaqus/Standard.

22.1.26


The elements use standard isoparametric interpolation in therz plane, combined with Fourier
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


47/1086

p p p ,interpolation with respect to . The deformation is assumed to be symmetric with respect to therzplane at .

Up to four Fourier modes are allowed. For more general cases, full three-dimensional modeling orcylindrical element modeling is probably more economical because of the complete coupling betweenall deformation modes.

These elements use a set of nodes in each of severalrzplanes: the number of such planes dependson the orderN of Fourier interpolation used with respect to , as follows:

Number of

Fourier modesNNumber

of nodal

planes

Nodal plane locations

with respect to

1 2

2 3

3 4

4 5

Each element type is defined by a name such as CAXA8RN(continuum elements) or SAXA1N(shell elements). The numberNshould be given as the number of Fourier modes to be used with theelement (N=1, 2, 3, or 4). For example, element type CAXA8R2 is a quadrilateral in therzplane withbiquadratic interpolation in this plane and two Fourier modes for interpolation with respect to . Thenodal planes associated with various Fourier modes are illustrated inFigure 22.1.24.

22.1.27



48/1086

Y (z at = 0)

e z

e

e r

X (r at = 0)

yy

yy

(a)

(c)

(b)

(d)

x

xx

0 0

00

3

4

2

2

3 4

2

3

Figure 22.1.24 Nodal planes of a second-order axisymmetric element with nonlinear,asymmetric deformation and (a) 1, (b) 2, (c) 3, or (d) 4 Fourier modes.

22.1.28

ANALYSIS TYPE

22.1.3 CHOOSING THE APPROPRIATE ELEMENT FOR AN ANALYSIS TYPE


49/1086


Reference

Element library: overview, Section 22.1.1 Element type assignment, Section 17.5.3 of the Abaqus/CAE Users Manual

Overview

The Abaqus element library contains the following:

stress/displacement elements, including contact elements, connector elements such as springs, andspecial-purpose elements such as Eulerian elements and surface elements;

pore pressure elements; coupled temperature-displacement elements; heat transfer or mass diffusion elements;

forced convection heat transfer elements; coupled thermal-electrical elements; piezoelectric elements; acoustic elements; hydrostatic fluid elements; and user-defined elements.

Each of these element types is described below.Within Abaqus/Standard or Abaqus/Explicit, a model can contain elements that are not appropriatefor the particular analysis type chosen; such elements will be ignored. However, an Abaqus/Standardmodel cannot contain elements that are not available in Abaqus/Standard; likewise, an Abaqus/Explicitmodel cannot contain elements that are not available in Abaqus/Explicit.

Stress/displacement elements

Stress/displacement elements are used in the modeling of linear or complex nonlinear mechanicalanalyses that possibly involve contact, plasticity, and/or large deformations. Stress/displacementelements can also be used for thermal-stress analysis, where the temperature history can be obtainedfrom a heat transfer analysis carried out with diffusive elements.

Analysis types

Stress/displacement elements can be used in the following analysis types:

static and quasi-static analysis (Static stress analysis procedures: overview, Section 6.2.1);

22.1.31

ANALYSIS TYPE

implicit transient dynamic, explicit transient dynamic, modal dynamic, and steady-state dynamicl i (D i l i d i S i 6 3 1)


50/1086

analysis (Dynamic analysis procedures: overview, Section 6.3.1);

Acoustic, shock, and coupled acoustic-structural analysis, Section 6.9.1; and

Fracture mechanics: overview, Section 11.4.1.

Active degrees of freedom

Stress/displacement elements have only displacement degrees of freedom. See Conventions,Section 1.2.2, for a discussion of the degrees of freedom in Abaqus.

Choosing a stress/displacement element

Stress/displacement elements are available in several different element families.

Continuum elements

Solid (continuum) elements, Section 23.1.1; and Infinite elements, Section 23.2.1.

Structural elements

Membrane elements, Section 24.1.1; Truss elements, Section 24.2.1; Beam modeling: overview, Section 24.3.1; Frame elements, Section 24.4.1; Pipes and pipebends with deforming cross-sections: elbow elements, Section 24.5.1; and Shell elements: overview, Section 24.6.1.

Rigid elements

Point masses, Section 25.1.1; Rotary inertia, Section 25.2.1; and Rigid elements, Section 25.3.1.

Connector elements

Connector elements, Section 26.1.2; Springs, Section 27.1.1;

Dashpots, Section 27.2.1; Flexible joint element, Section 27.3.1; Tube support elements, Section 27.9.1; and Drag chains, Section 27.12.1.

Special-purpose elements

Cohesive elements: overview, Section 27.5.1;

22.1.32

ANALYSIS TYPE

Gasket elements: overview, Section 27.6.1;S f l S i 27 7 1


51/1086

Surface elements, Section 27.7.1; Hydrostatic fluid elements, Section 27.8.1; Line spring elements for modeling part-through cracks in shells, Section 27.10.1; Elastic-plastic joints, Section 27.11.1; and Eulerian elements, Section 27.15.1.

Contact elements

Gap contact elements, Section 32.2.1; Tube-to-tube contact elements, Section 32.3.1; Slide line contact elements, Section 32.4.1; and Rigid surface contact elements, Section 32.5.1.

Pore pressure elements

Pore pressure elements are provided in Abaqus/Standard for modeling fully or partially saturated fluidflow through a deforming porous medium. The names of all pore pressure elements include the letter P(pore pressure). These elements cannot be used with hydrostatic fluid elements.

Analysis types

Pore pressure elements can be used in the following analysis types:

soils analysis (Coupled pore fluid diffusion and stress analysis, Section 6.7.1); and geostatic analysis (Geostatic stress state, Section 6.7.2).


Pore pressure elements have both displacement and pore pressure degrees of freedom. In second-orderelements the pore pressure degrees of freedom are active only at the corner nodes. See Conventions,Section 1.2.2, for a discussion of the degrees of freedom in Abaqus.

Interpolation

These elements use either linear- or second-order (quadratic) interpolation for the geometry anddisplacements in two or three directions. The pore pressure is interpolated linearly from the cornernodes. Curved element edges should be avoided; exact linear spatial pore pressure variations cannot beobtained with curved edges.

For output purposes the pore pressure at the midside nodes of second-order elements is determinedby linear interpolation from the corner nodes.

Choosing a pore pressure element

Pore pressure elements are available only in the following element family:

Solid (continuum) elements, Section 23.1.1.

22.1.33

ANALYSIS TYPE

Coupled temperature-displacement elements


52/1086

Coupled temperature displacement elements

Coupled temperature-displacement elements are used in problems for which the stress analysis dependson the temperature solution and the thermal analysis depends on the displacement solution. An exampleis the heating of a deforming body whose properties are temperature dependent by plastic dissipation orfriction. The names of all coupled temperature-displacement elements include the letter T.

Analysis types

Coupled temperature-displacement elements are for use in fully coupled temperature-displacementanalysis (Fully coupled thermal-stress analysis, Section 6.5.4).


Coupled temperature-displacement elements have both displacement and temperature degrees offreedom. In second-order elements the temperature degrees of freedom are active at the corner nodes.In modified triangle and tetrahedron elements the temperature degrees of freedom are active at everynode. See Conventions, Section 1.2.2, for a discussion of the degrees of freedom in Abaqus.

InterpolationCoupled temperature-displacement elements use either linear or parabolic interpolation for the geometryand displacements. The temperature is always interpolated linearly. In second-order elements curvededges should be avoided; exact linear spatial temperature variations for these elements cannot be obtainedwith curved edges.

For output purposes the temperature at the midside nodes of second-order elements is determinedby linear interpolation from the corner nodes.

Choosing a coupled temperature-displacement element

Coupled temperature-displacement elements are available in the following element families:

Solid (continuum) elements, Section 23.1.1; Truss elements, Section 24.2.1; Shell elements: overview, Section 24.6.1; Gap contact elements, Section 32.2.1; and

Slide line contact elements, Section 32.4.1.

Diffusive (heat transfer) elements

Diffusive elements are provided in Abaqus/Standard for use in heat transfer analysis (Uncoupled heattransfer analysis, Section 6.5.2), where they allow for heat storage (specific heat and latent heat effects)and heat conduction. They provide temperature output that can be used directly as input to the equivalentstress elements. The names of all diffusive heat transfer elements begin with the letter D.

22.1.34

ANALYSIS TYPE

Analysis types


53/1086

y yp

The diffusive elements can be used in mass diffusion analysis (Mass diffusion analysis, Section 6.8.1)

as well as in heat transfer analysis.


When used for heat transfer analysis, the diffusive elements have only temperature degrees of freedom.When they are used in a mass diffusion analysis, they have normalized concentration, instead oftemperature, degrees of freedom. See Conventions, Section 1.2.2, for a discussion of the degrees offreedom in Abaqus.

Interpolation

The diffusive elements use either first-order (linear) interpolation or second-order (quadratic)interpolation in one, two, or three dimensions.

Choosing a diffusive element

Diffusive elements are available in the following element families:

Solid (continuum) elements, Section 23.1.1; Shell elements: overview, Section 24.6.1 (these elements cannot be used in a mass diffusion

analysis); and

Gap contact elements, Section 32.2.1.

Forced convection heat transfer elements

Forced convection heat transfer elements are provided in Abaqus/Standard to allow for heat storage(specific heat) and heat conduction, as well as the convection of heat by a fluid flowing through the mesh(forced convection). All forced convection heat transfer elements provide temperature output, whichcan be used directly as input to the equivalent stress elements. The names of all forced convection heattransfer elements begin with the letters DCC.

Analysis types

The forced convection heat transfer elements can be used in heat transfer analyses (Uncoupled heattransfer analysis, Section 6.5.2), including fully implicit or approximate cavity radiation modeling(Cavity radiation, Section 33.1.1). The forced convection heat transfer elements can be used togetherwith the diffusive elements.


The forced convection heat transfer elements have temperature degrees of freedom. See Conventions,Section 1.2.2, for a discussion of the degrees of freedom in Abaqus.

22.1.35

ANALYSIS TYPE

Interpolation


54/1086

The forced convection heat transfer elements use only first-order (linear) interpolation in one, two, or

three dimensions.

Choosing a forced convection heat transfer element

Forced convection heat transfer elements are available only in the following element family:


Coupled thermal-electrical elements

Coupled thermal-electrical elements are provided in Abaqus/Standard for use in modeling heating thatarises when an electrical current flows through a conductor (Joule heating).

Analysis types

The Joule heating effect requires full coupling of the thermal and electrical problems (seeCoupled thermal-electrical analysis, Section 6.6.2). The coupling arises from two sources:temperature-dependent electrical conductivity and the heat generated in the thermal problem by electric

conduction.These elements can also be used to perform uncoupled electric conduction analysis in all or part of

the model. In such analysis only the electric potential degree of freedom is activated, and all heat transfereffects are ignored. This capability is available by omitting the thermal conductivity from the materialdefinition.

The coupled thermal-electrical elements can also be used in heat transfer analysis (Uncoupled heattransfer analysis, Section 6.5.2), in which case all electric conduction effects are ignored. This feature isquite useful if a coupled thermal-electrical analysis is followed by a pure heat conduction analysis (such

as a welding simulation followed by cool down).The elements cannot be used in any of the stress/displacement analysis procedures.


Coupled thermal-electrical elements have both temperature and electrical potential degrees of freedom.See Conventions, Section 1.2.2, for a discussion of the degrees of freedom in Abaqus.

InterpolationCoupled thermal-electrical elements are provided with first- or second-order interpolation of thetemperature and electrical potential.

Choosing a coupled thermal-electrical element

Coupled thermal-electrical elements are available only in the following element family:


22.1.36

ANALYSIS TYPE

Piezoelectric elements


55/1086

Piezoelectric elements are provided in Abaqus/Standard for problems in which a coupling between the

stress and electrical potential (the piezoelectric effect) must be modeled.

Analysis types

Piezoelectric elements are for use in piezoelectric analysis (Piezoelectric analysis, Section 6.6.3).


The piezoelectric elements have both displacement and electric potential degrees of freedom. See

Conventions, Section 1.2.2, for a discussion of the degrees of freedom in Abaqus. The piezoelectriceffect is discussed further in Piezoelectric analysis, Section 6.6.3.

Interpolation

Piezoelectric elements are available with first- or second-order interpolation of displacement andelectrical potential.

Choosing a piezoelectric element

Piezoelectric elements are available in the following element families:

Solid (continuum) elements, Section 23.1.1; and Truss elements, Section 24.2.1.

Acoustic elements

Acoustic elements are used for modeling an acoustic medium undergoing small pressure changes. The

solution in the acoustic medium is defined by a single pressure variable. Impedance boundary conditionsrepresenting absorbing surfaces or radiation to an infinite exterior are available on the surfaces of theseacoustic elements.

Acoustic infinite elements, which improve the accuracy of analyses involving exterior domains, andacoustic-structural interface elements, which couple an acoustic medium to a structural model, are alsoprovided.

Analysis types

Acoustic elements are for use in acoustic and coupled acoustic-structural analysis (Acoustic, shock, andcoupled acoustic-structural analysis, Section 6.9.1).


Acoustic elements have acoustic pressure as a degree of freedom. Coupled acoustic-structural elementsalso have displacement degrees of freedom. See Conventions, Section 1.2.2, for a discussion of thedegrees of freedom in Abaqus.

22.1.37

ANALYSIS TYPE

Choosing an acoustic element


56/1086

Acoustic elements are available in the following element families:

Solid (continuum) elements, Section 23.1.1; Infinite elements, Section 23.2.1; and Acoustic interface elements, Section 27.14.1.

The acoustic elements can be used alone but are often used with a structural model in a coupledanalysis. Acoustic interface elements, Section 27.14.1, describes interface elements that allow thisacoustic pressure field to be coupled to the displacements of the surface of the structure. Acousticelements can also interact with solid elements through the use of surface-based tie constraints; seeAcoustic, shock, and coupled acoustic-structural analysis, Section 6.9.1.

Using the same mesh with different analysis or element types

You may want to use the same mesh with different analysis or element types. This may occur, forexample, if both stress and heat transfer analyses are intended for a particular geometry or if the effectof using either reduced- or full-integration elements is being investigated. Care should be taken whendoing this since unexpected error messages may result for one of the two element types if the mesh is

distorted. For example, a stress analysis with C3D10 elements may run successfully, but a heat transferanalysis using the same mesh with DC3D10 elements may terminate during the datacheckportion ofthe analysis with an error message stating that the elements are excessively distorted or have negativevolumes. This apparent inconsistency is caused by the different integration locations for the differentelement types. Such problems can be avoided by ensuring that the mesh is not distorted excessively.

22.1.38

SECTION CONTROLS

22.1.4 SECTION CONTROLS


57/1086


References

*SECTION CONTROLS *HOURGLASS STIFFNESS Element type assignment, Section 17.5.3 of the Abaqus/CAE Users Manual

Overview

Section controls in Abaqus/Standard:

choose the hourglass control formulation for mostfirst-order elements with reduced integration; select the hourglass control scale factors for all elements with reduced integration; and select the choice of element deletion and the value of maximum degradation for cohesive elements,

connector elements, elements with plane stress formulations (plane stress, shell, continuum shell,

and membrane elements) with constitutive behavior that includes damage evolution, and anyelement that can be used with the damage evolution law in a low-cycle fatigue analysis.

Section controls in Abaqus/Explicit:

choose the hourglass control formulation or scale factors for all elements with reduced integration; define the distortion control for solid elements; deactivate the drill stiffness for small-strain shell elements S3RS and S4RS; select an amplitude for ramping of any initial stresses in membrane elements;

select the kinematic formulation for hexahedron solid elements; select the accuracy order of the formulation for solid and shell elements; select the scale factors for linear and quadratic bulk viscosity parameters; and select the choice of element deletion and the value of maximum degradation for elements with

constitutive behavior that includes damage evolution.

In Abaqus/CAE section controls are specified when you assign an element type to particular mesh regionsand are referred to as element controls.

Using section controls

In Abaqus/Standard section controls are used to select the enhanced hourglass control formulation forsolid, shell, and membrane elements. This formulation provides improved coarse mesh accuracy withslightly higher computational cost and performs better for nonlinear material response at high strainlevels when compared with the default total stiffness formulation. Section controls can also be used toselect some element formulations that may be relevant for a subsequent Abaqus/Explicit analysis.

22.1.41

SECTION CONTROLS

In Abaqus/Explicit the default formulations for solid, shell, and membrane elements have beenchosen to perform satisfactorily on a wide class of quasi-static and explicit dynamic simulations.H t i f l ti i i t t d ff b t d f


58/1086

However, certain formulations give rise to some trade-off between accuracy and performance.

Abaqus/Explicit provides section controls to modify these element formulations so that you canoptimize these objectives for a specific application. Section controls can also be used in Abaqus/Explicitto specify scale factors for linear and quadratic bulk viscosity parameters. You can also control theinitial stresses in membrane elements for applications such as airbags in crash simulations and introducethe initial stresses gradually based on an amplitude definition.

In addition, section controls are used to specify the maximum stiffness degradation and to choosethe behavior upon complete failure of an element, once the material stiffness is fully degraded,including the removal of failed elements from the mesh. This functionality applies only to elements

with a material definition that includes progressive damage (see Progressive damage and failure,Section 20.1.1; Connector damage behavior, Section 26.2.7; and Defining the constitutive responseof cohesive elements using a traction-separation description, Section 27.5.6). In Abaqus/Standard thisfunctionality is limited to

cohesive elements with a traction-separation constitutive response that includes damage evolution, any element that can be used with the damage evolution law in a low-cycle fatigue analysis, and connector elements with a constitutive response that includes damage evolution.

Input File Usage: Use the following option to specify a section controls definition:*SECTION CONTROLS, NAME=name

This option is used in conjunction with one or more of the following options toassociate the section control definition with an element section definition:

*COHESIVE SECTION, CONTROLS=name*CONNECTOR SECTION, CONTROLS=name*EULERIAN SECTION, CONTROLS=name

abaqus 6 8 user manual

Documents