Abaqus Analysis Intro-book

(1)

w w w .3d s .c om | © Das s au lt S y s tèm es R

Introduction to Abaqus/Standard

and Abaqus/Explicit

6.12 s .c om | © Das s au lt S y s tèm es

Course objectives

Upon completion of this course you will be able to:

Complete finite element models using Abaqus keywords. Submit and monitor analysis jobs.

View and evaluate simulation results.

Solve structural analysis problems using Abaqus/Standard and Abaqus/Explicit, including the effects of material nonlinearity, large deformation and contact.

Targeted audience

Simulation Analysts

Prerequisites

(2)

w w w .3d s .c om | © Das s au lt S y s tèm es

Day 1

Lesson 1

Defining an Abaqus Model

Workshop 1

Basic Input and Output

Lesson 2

Linear Static Analysis

Workshop 2

Linear Static Analysis of a Cantilever Beam:

Multiple Load Cases

Lesson 3

Nonlinear Analysis in Abaqus/Standard

Workshop 3

Nonlinear Statics

Day 2

Lesson 4

Multistep Analysis in Abaqus

Workshop 4

Unloading Analysis

Lesson 5

Constraints and Contact

Workshop 5

Seal Contact

Lesson 6

Introduction to Dynamics

(3)

Day 3

Lesson 7

Using Abaqus/Explicit

Workshop 7

Contact with Abaqus/Explicit

Lesson 8

Quasi-Static Analysis in Abaqus/Explicit

Workshop 8

Quasi-Static Analysis (Optional)

Lesson 9

Combining Abaqus/Standard and Abaqus/Explicit

Workshop 9

Import Analysis (Optional)

s .c om | © Das s au lt S y s tèm es

Additional Material

Appendix 1 Element Selection Criteria

Appendix 2 Contact Issues Specific to Abaqus/Standard

Appendix 3 Contact Issues Specific to Abaqus/Explicit

(4)

Legal Notices

The Abaqus Software described in this documentation is available only under license from Dassault

Systèmes and its subsidiary and may be used or reproduced only in accordance with the terms of such

license.

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

prior notice.

Dassault Systèmes and its subsidiaries shall not be responsible for the consequences of any errors or

omissions that may appear in this documentation.

No part of this documentation may be reproduced or distributed in any form without prior written

permission of Dassault Systèmes or its subsidiary.

© Dassault Systèmes, 2012.

Printed in the United States of America

Abaqus, the 3DS logo, SIMULIA and CATIA are trademarks or registered trademarks of Dassault

Systèmes or its subsidiaries in the US and/or other countries.

Other company, product, and service names may be trademarks or service marks of their respective

owners. For additional information concerning trademarks, copyrights, and licenses, see the Legal

Notices in the Abaqus 6.12 Release Notes and the notices at:

http://www.3ds.com/products/simulia/portfolio/product-os-commercial-programs.

Revision Status

Lecture 1 5/12 Updated for 6.12 Lecture 2 5/12 Updated for 6.12 Lecture 3 5/12 Updated for 6.12 Lecture 4 5/12 Updated for 6.12 Lecture 5 5/12 Updated for 6.12 Lecture 6 5/12 Updated for 6.12 Lecture 7 5/12 Updated for 6.12 Lecture 8 6/12 Minor edits Lecture 9 5/12 Updated for 6.12 Appendix 1 5/12 Updated for 6.12 Appendix 2 5/12 Updated for 6.12 Appendix 3 5/12 Updated for 6.12

Workshop 1 5/12 Updated for 6.12 Workshop 2 5/12 Updated for 6.12 Workshop 3 5/12 Updated for 6.12 Workshop 4 5/12 Updated for 6.12 Workshop 5 5/12 Updated for 6.12 Workshop 6 5/12 Updated for 6.12 Workshop 7 5/12 Updated for 6.12 Workshop 8 5/12 Updated for 6.12 Workshop 9 5/12 Updated for 6.12

(5)

(6)

(7)

L1.1 w w w .3d s .c om | © Das s au lt S y s tèm es

Lesson content:

Introduction

Documentation

Components of an Abaqus Model

Details of an Abaqus Input File

Abaqus Input Conventions

Abaqus Output

Example: Cantilever Beam Model

Parts and Assemblies (optional)

Workshop Preliminaries

Workshop 1: Basic Input and Output (IA)

Workshop 1: Basic Input and Output (KW)

Lesson 1: Defining an Abaqus Model

2 hours

Both interactive (IA) and keywords (KW) versions of the workshop are provided. Complete only one.

L1.2 s .c om | © Das s au lt S y s tèm es

Introduction (1/14)

SIMULIA is the Dassault Systèmes brand that delivers a scalable portfolio of Realistic Simulation solutions including

The Abaqus product suite for Unified FEA

Multiphysics solutions for insight into challenging engineering problems

Lifecycle management solutions for managing simulation data, processes, and intellectual property Headquartered in Providence, RI, USA

(8)

Introduction (2/14)

Course preliminaries

This course introduces Abaqus/Standard and Abaqus/Explicit; basic knowledge of finite element analysis is assumed.

This course introduces concepts in a manner that gives users a working knowledge of Abaqus as quickly as possible—the lecture notes do not attempt to cover all the details of Abaqus completely. There are several sources for additional information on the topics presented in this course:

SIMULIA Home Page (available via the Internet at

http://www.3ds.com/products/simulia/overview).

Abaqus documentation—all usage details are covered in the user’s manuals.

Extensive library of courses developed by SIMULIA on particular topics (course descriptions available at http://www.3ds.com/products/simulia/overview). L1.4 w w w .3d s .c om | © Das s au lt S y s tèm es

Introduction (3/14)

(9)

Introduction (4/14)

Abaqus/CAE

Complete Abaqus Environment

for modeling, managing, and monitoring Abaqus analyses, as well as visualizing results.

Intuitive and consistent user interface throughout the system.

Based on the concepts of parts

and assemblies of part instances, which are common to many CAD systems.

Parts can be created within Abaqus/CAE or imported from other systems as geometry (to be meshed in Abaqus/CAE) or as meshes.

Built-in feature-based parametric modeling

system for creating parts. Abaqus/CAE main user interface

Introduction (5/14)

Analysis modules

Abaqus/Standard and Abaqus/Explicit provide the user with two complementary analysis tools.* Abaqus/Standard’s capabilities: General analyses Static stress/displacement analysis: I. Rate-independent response II. Rate-dependent (viscoelastic/creep/viscoplastic) response

(10)

Introduction (6/14)

Multiphysics: Thermal-mechanical analysis Structural-acoustic analysis Linear piezoelectric analysis Thermal-electrical (Joule heating) analysis

Thermal-electrical-structural analysis Fully or partially saturated

pore fluid flow-deformation Fluid-structure interaction

Thermal stresses in an exhaust manifold

Introduction (7/14)

Linear perturbation analyses

Static stress/displacement analysis: I. Linear static

stress/displacement analysis II. Eigenvalue buckling

load prediction

Dynamic stress/displacement analysis:

I. Determination of natural modes and frequencies II. Transient response via modal superposition

III. Steady-state response resulting from harmonic loading

» Includes alternative ―subspace projection‖ method for efficient analysis of large models with frequency-dependent properties (like damping)

Harmonic excitation of a tire

(11)

Introduction (8/14)

Abaqus/Explicit’s capabilities: High-speed dynamics Quasi-static analysis

Coupled Eulerian-Lagrangian (CEL) Adaptive meshing using ALE Multiphysics

Thermal-mechanical analysis

I. Fully coupled: Explicit algorithms for both the mechanical and thermal responses

II. Can include adiabatic heating effects

Structural-acoustic analysis Fluid-structure interaction

Drop test of a cell phone

Introduction (9/14)

Comparing Abaqus/Standard and Abaqus/Explicit Abaqus/Standard

A general-purpose finite element program.

I. Nonlinear problems require iterations.

Can solve for true static equilibrium in structural simulations.

Provides a large number of capabilities

Abaqus/Explicit

A general-purpose finite element program for explicit dynamics.

I. Solution procedure does not require iteration.

Solves highly discontinuous high-speed dynamic problems efficiently.

(12)

Introduction (10/14)

Interactive postprocessing

Abaqus/Viewer is the postprocessing module of Abaqus/CAE.

Available with Abaqus/CAE or as a stand-alone product

Can be used to visualize Abaqus results whether or not the model was created in Abaqus/CAE

Provides efficient visualization of large models

Contour plot of an aluminum wheel hitting a curb in

Abaqus/Viewer L1.12 w w w .3d s .c om | © Das s au lt S y s tèm es

Introduction (11/14)

What is covered in this course

Introduction to the analysis modules and interactive postprocessing

Details of using Abaqus to solve a variety of structural analysis problems:

Linear Static Analysis

Workshop 1: Basic Input and Output— analysis of forces on a connecting lug

Workshop 2: Linear Static Analysis of a Cantilever Beam—multiple load cases

(13)

Introduction (12/14)

Nonlinear Finite Element Analysis Workshop 3: Nonlinear Statics—large

deformation analysis of a skew plate

Simulations with Several Analysis Steps Workshop 4:Unloading analysis—unloading of a skew plate

Contact among Multiple Bodies

Workshop 5: Seal Contact—compression analysis of a rubber seal.

Introduction (13/14)

Linear and Nonlinear Dynamic Analysis Workshop 6: Dynamics—frequency analysis and implicit and explicit free

vibration analysis of a cantilever beam

High-Speed Dynamics in Abaqus/Explicit Workshop 7: Contact with Abaqus/Explicit— pipe whip problem

(14)

Introduction (14/14)

Quasi-Static Combined Analysis in Abaqus/Standard and Abaqus/Explicit Workshop 8 (Optional): Quasi-Static Analysis—deep drawing of a can bottom

Workshop 9 (Optional): Import Analysis— springback analysis of formed can bottom Nonstructural applications—such as heat transfer, soils consolidation, and acoustics— are not discussed.

All Abaqus analysis techniques use the same framework.

The knowledge gained in this course will help in learning to use Abaqus for other applications. L1.16 w w w .3d s .c om | © Das s au lt S y s tèm es

Documentation (1/7)

Primary reference materials

Abaqus Analysis User’s Manual Abaqus/CAE User’s Manual Abaqus Example Problems Manual Abaqus Benchmarks Manual Abaqus Verification Manual

Abaqus Keywords Reference Manual Abaqus User Subroutines Reference Manual Abaqus Theory Manual

All documentation is available in HTML and PDF format

(15)

Documentation (2/7)

Additional reference materials

Abaqus Installation and Licensing Guide (print version available)

Installation instructions

Abaqus Release Notes

Explains changes since previous release

Advanced lecture notes on various topics (print only) Tutorials

Getting Started with Abaqus: Interactive Edition Getting Started with Abaqus: Keywords Edition

Programming

Scripting and GUI Toolkit manuals

SIMULIA home page

http://www.3ds.com/products/simulia/overview/ L1.18 s .c om | © Das s au lt S y s tèm es

Documentation (3/7)

HTML documentation

The documentation for Abaqus is organized into a collection, with manuals grouped by function. Viewed through a web browser.

(16)

Documentation (4/7)

Searching the documentation

Enter one or more search terms in the search field

The table of contents entry is highlighted

The text frame displays the corresponding section Terms in the search field:

Appear in any order May or may not be adjacent Appear within the proximity criterion

(default is a single section)

Documentation (5/7)

Searching the documentation (cont’d) Use quotes to search for exact strings

(17)

Documentation (6/7)

Advanced search

Advanced search allows you to control the proximity criterion

Documentation (7/7)

(18)

Components of an Abaqus Model (1/6)

The Abaqus analysis modules run as batch programs.

The primary input to the analysis modules is an input file, which contains options from element, material, procedure, and loading libraries.

These options can be combined in any reasonable way, allowing a tremendous variety of problems to be modeled.

The input file is divided into two parts: model data and history data.

Model data Geometric options—nodes, elements Material options

Other model options History data Procedure options

Loading options Output options L1.24 w w w .3d s .c om | © Das s au lt S y s tèm es

Model data—define the physical model

Discretized model geometry— nodes,elements

Material properties

(19)

L1.25 w w w .3d s .c om | © Das s au lt S y s tèm es Model data v₀ Fixed constraints Initial conditions

Components of an Abaqus Model (3/6)

pin dof 2 fixed ENCASTRE L1.26 s .c om | © Das s au lt S y s tèm es

Components of an Abaqus Model (4/6)

History data—specify what happens to the model

Types of analysis procedures—static, dynamic, soil, heat transfer, etc. Loadings

Prescribed constraints

(20)

Components of an Abaqus Model (5/6)

History subdivided into analysis steps

Steps are convenient subdivisions in an analysis history.

Different steps can contain different analysis procedures—for example, static followed by dynamic. Distinction between general and linear perturbation steps:

General steps define a sequence of events that follow one another.

I. The state of the model at the end of the previous general step provides the initial conditions for the start of the next general step.

II. This is needed for any history-dependent analysis.

Linear perturbation steps provide the linear response about the base state, which is the state at the end of the most recent general step.

Components of an Abaqus Model (6/6)

Example: Bow and arrow simulation

Step 1: String the bow

Step 2: Pull back on the bow string

Step 3: Linear perturbation step to extract the natural frequencies of the system— Step 1 = pretension Step 2 = pull back _{Step 4 = dynamic release}

Step 3 = natural frequency extraction

(21)

Details of an Abaqus Input File (1/9)

Option blocks

All data are defined in ―option blocks‖ that describe specific aspects of the problem definition, such as an element definition, etc. Together the option blocks build the model.

Node option block Property reference option block Material option block Element option block Boundary conditions option block Contact option block Initial conditions option block Analysis procedure

option block Loading option block

Output request option block Model data History data L1.30 s .c om | © Das s au lt S y s tèm es

Details of an Abaqus Input File (2/9)

Each option block begins with a keyword line (first character is *).

Data lines, if needed, follow the keyword line.

Comment lines, starting with **, can be included anywhere.

All input lines have a limit of 256 characters (including blanks).

Names can be up to 80 characters long and must begin with a letter. For example, the following would be a permissible name:

nodes_at_the_top_of_the_block_next_to_the_gasket

(22)

Details of an Abaqus Input File (3/9)

Keyword lines

Begin with a single * followed directly by the name of the option.

May include a combination of required and optional parameters, along with their values, separated by commas.

Example: A material option block defines a set of material properties.

keyword

*MATERIAL, NAME=

material name

parameter parameter value

The first line in a material option block

Details of an Abaqus Input File (4/9)

Data lines

Define the bulk data for a given option; for example, element definitions. A keyword line may have many data lines associated with it.

Example: An element option block defines elements by specifying the element type, the element numbers, and the nodal connectivity.

*ELEMENT, TYPE=B21 560, 101, 102 564, 102, 103 572, 103, 104 : : keyword line data lines

node numbers (as required for beam B21 elements)

(23)

Details of an Abaqus Input File (5/9)

Example: The elastic material option block defines the type of elasticity model as well as the elastic material properties. *ELASTIC, TYPE=ISOTROPIC 200.0E4, 0.30, 20.0 150.0E3, 0.35, 400.0 · · keyword line data lines temperature Poisson’s ratio modulus of elasticity L1.34 s .c om | © Das s au lt S y s tèm es

Details of an Abaqus Input File (6/9)

Ordering of option blocks

Each option block belongs in either the model data or the history data—one or the other—as specified in the user’s manual.

The ordering within the model data or history data is arbitrary, except for a few cases. Examples:

*HEADING must be the first option in the input file.

*ELASTIC, *DENSITY, and *PLASTIC are suboptions of *MATERIAL. As such, they must follow *MATERIAL directly. Suboptions have no name references of their own.

(24)

Details of an Abaqus Input File (7/9)

Node sets and element sets

Used for efficient cross-referencing.

Allow you to refer to a set all at once instead of each node or element individually.

Node set

TOPNODES contains

nodes 101,102, ...

Boundary condition applied to all nodes in node set TOPNODES

Example: Node sets

*NODE, NSET=TOPNODES 101, 0.345, 0.679, 0.223 102, 0.331, 0.699, 0.234 . . *BOUNDARY, TYPE=DISPLACEMENT TOPNODES, YSYMM L1.36 w w w .3d s .c om | © Das s au lt S y s tèm es

Details of an Abaqus Input File (8/9)

Example: Element sets

*ELEMENT, TYPE=B21, ELSET=SEATPOST 560, 101, 102,

564, 102, 103 .

.

*BEAM SECTION, SECTION=PIPE, MATERIAL=STEEL, ELSET=SEATPOST

0.12, 0.004

pipe radius wall thickness

These beam cross-section properties apply to all elements in element set

SEATPOST

Element setSEATPOST

contains elements 560, 564, ...

(25)

Details of an Abaqus Input File (9/9)

Including data from other files

Abaqus reads data from an include file as if the data were directly in the Abaqus input file.

An include file can include any portion of an input file and can contain references to other include files. Data must be in the same format as required for input file data—all rules that apply to input file syntax apply to data from included files.

Example: Input file referencing an include file

*HEADING

*INCLUDE, INPUT=node_and_element_numbers.txt .

.

Contents of include file node_and_element_numbers.txt: *NODE, NSET=TOPNODES

101, 0.345, 0.679, 0.223 102, 0.331, 0.699, 0.234

*ELEMENT, TYPE=B21, ELSET=SEATPOST 560, 101, 102, 564, 102, 103 L1.38 s .c om | © Das s au lt S y s tèm es

Abaqus Input Conventions (1/8)

Units

Abaqus uses no inherent set of units.

It is the user’s responsibility to use consistent units. Example:

I. N, kg, m, s or

II. N, 103_{kg, mm, s}

(26)

Abaqus Input Conventions (2/8)

Example: Properties of mild steel at room temperature

Quantity U.S. units SI units

Conductivity 28.9 Btu/ft hr ºF 50 W/m ºC

2.4 Btu/in hr ºF

Density 15.13 slug/ft3_{(lbf s}2_/ft4₎ _{7800 kg/m}3

0.730 × 10−3_{lbf s}2_/in4

0.282 lbm/in3

Elastic modulus 30 × 106_psi _{207 × 10}9_Pa

Specific heat 0.11 Btu/lbm ºF 460 J/kg ºC Yield stress 30 × 103_psi _{207 × 10}6_Pa

Abaqus Input Conventions (3/8)

Time measures

Abaqus keeps track of both total time in an analysis and step time for each analysis step. Time is physically meaningful for some analysis procedures, such as transient dynamics.

Time is not physically meaningful for some procedures. In rate-independent, static procedures ―time‖ is just a convenient, monotonically increasing measure for incrementing loads.

(27)

Abaqus Input Conventions (4/8)

Coordinate systems

For input of initial nodal coordinates:

The default is a rectangular Cartesian system.

Specify an alternative system using *SYSTEM or *NODE, SYSTEM=[RECTANGULAR | CYLINDRICAL | SPHERICAL].

Do not affect loading or output because automatically converted internally to the global rectangular Cartesian system.

Abaqus Input Conventions (5/8)

For nodal loads, boundary conditions, initial conditions: The default is a rectangular Cartesian system.

Specify an alternative system using the *TRANSFORM option.

These directions do not rotate with the material in large-displacement analyses. Example: Boundary conditions on a skew edge.

Use *TRANSFORM on these nodes with YSYMM

(28)

Abaqus Input Conventions (6/8)

For material point directions (directions associated with each element’s material or integration points):

Affect input: Anisotropic material directions.

Affect output: Stress/strain output directions.

The default depends on the element type.

I. Solid elements use a global rectangular Cartesian system. II. Shell and membrane elements

use a projection of the global Cartesian system onto the surface.

Default material directions for shell and membrane elements Default material directions for solid elements

Abaqus Input Conventions (7/8)

Alternative local material coordinate systems can be specified using the *ORIENTATION option. These directions rotate with the material in large-displacement analyses.

2 1

(29)

Abaqus Input Conventions (8/8)

Degrees of freedom

Primary solution variables at the nodes.

Available nodal degrees of freedom depend on the element type.

Each degree of freedom is labeled with a number: 1=x-displacement, 2=y-displacement, 11=temperature, etc. L1.46 s .c om | © Das s au lt S y s tèm es

Abaqus Output (1/8)

Output

Four types of output are available:

Neutral binary output can be written to the output database (.odb) file using the *OUTPUT option and related suboptions.

Printed output can be written to the data (.dat) file.

I. This is available only for Abaqus/Standard.

Restart output can be written to the restart (.res) file using the *RESTART option for the purpose of conducting restart analyses (discussed in Lecture 4).

(30)

Abaqus Output (2/8)

Output to the output database file The output database file is used by Abaqus/Viewer.

An interface (API) is available in Python and C++ to use for external postprocessing (e.g.,

to add data to display in Abaqus/Viewer).

Two types of output data: field and history data.

Field data is used for model (deformed, contour, etc.) and

X–Y plots:

*OUTPUT, FIELD

History data is used for X–Y plots:

*OUTPUT, HISTORY L1.48 w w w .3d s .c om | © Das s au lt S y s tèm es

Abaqus Output (3/8)

Frequency of output for either type can be controlled Field output can be requested according to

Number of increments (Abaqus/Standard only) *OUTPUT, FIELD, FREQUENCY=n

Number of intervals

*OUTPUT, FIELD, NUMBER INTERVAL=n

Time intervals

*OUTPUT, FIELD, TIME INTERVAL=x

Time points

*OUTPUT, FIELD, TIME POINTS=t_out *TIME POINTS, name = t_out

Every

n

increments

At

n

evenly spaced time intervals

At user-specified time points

(31)

Abaqus Output (4/8)

History output can be requested according to: Number of increments

*OUTPUT, HISTORY, FREQUENCY=n

Number of intervals (Abaqus/Standard only) *OUTPUT, HISTORY, NUMBER INTERVAL=n

Time intervals

*OUTPUT, HISTORY, TIME INTERVAL=x

Time points (Abaqus/Standard only)

*OUTPUT, HISTORY, TIME POINTS=t_out *TIME POINTS, name=t_out

Abaqus Output (5/8)

Requesting output to the output database file

If you have no output requests in your model, behavior depends on environment file (abaqus_v6.env)

settings:

odb_output_by_default=ON: pre-selected output is written to the ODB

I. This is the default setting; output depends on the procedure type

odb_output_by_default=OFF: no ODB will be generated for your analysis

(32)

Abaqus Output (6/8)

Pre-selected ODB output

Pre-selected output depends on the procedure type. For example, for a general static procedure:

The default field output requests are for: Stresses – S

Total Strains – E (or logarithmic strain LE if NLGEOM is active) Plastic Strains – PE, PEEQ, and PEMAG

Displacements and Rotations – U Reaction Forces and Moments– RF

Concentrated (applied) Forces and Moments – CF Contact Stresses – CSTRESS

Contact Displacements – CDISP

The default history output request includes all model energies For other procedures, see the Abaqus Analysis User’s Manual

Abaqus Output (7/8)

Output to the printed output file

These options allow tabular data to be written to an ASCII file that can be read with a text editor. These options are available only for Abaqus/Standard.

Syntax:

*NODE PRINT *EL PRINT *ENERGY PRINT

(33)

Abaqus Output (8/8)

Output to the restart file

If a simulation stops prematurely, the restart data can be used to start the simulation from some intermediate point without repeating any calculations.

*RESTART, WRITE

This option is discussed further in Lecture 4. Output to the results file

The results file can be used by third-party postprocessors.

*FILE OUTPUT (This option required for Abaqus/Explicit only) *NODE FILE

*EL FILE *ENERGY FILE

Select specific output variables

Example: Cantilever Beam Model (1/11)

(34)

Example: Cantilever Beam Model (2/11)

Abaqus input file with some annotations Model data

*HEADING

CANTILEVER BEAM EXAMPLE UNITS IN MM, N, MPa *NODE 1, 0.0, 0.0 : 11, 200.0, 0.0 *NSET, NSET=END 11,

*ELEMENT, TYPE=B21, ELSET=BEAMS 1, 1, 3

:

5, 9, 11

*BEAM SECTION, SECTION=RECT, ELSET=BEAMS, MATERIAL=MAT1 50.0, 5.0

** Material from XXX testing lab *MATERIAL, NAME=MAT1 *ELASTIC 2.0E5, 0.3 *BOUNDARY 1, ENCASTRE comment line property reference option block

heading option block

node option block

node set definition

element option block

material option block fixed boundary condition

option block

This line will appear on each page of output.

elastic option block

Example: Cantilever Beam Model (3/11)

History data

*STEP

APPLY POINT LOAD *STATIC

*CLOAD

11, 2, -1200.0

*OUTPUT, FIELD, VARIABLE=PRESELECT, FREQUENCY=10 *OUTPUT, HISTORY, FREQUENCY=1

*NODE OUTPUT, NSET=END U,

*EL PRINT, FREQUENCY=10 S, E

*NODE FILE, FREQUENCY=5 U,

*END STEP

The history data begin with the first *STEP option.

The history data end with the last *END STEP option.

(35)

Example: Cantilever Beam Model (4/11)

Property references using set names

*ELEMENT, TYPE=B21, ELSET=BEAMS 1, 1, 3

*BEAM SECTION, SECTION=RECT, ELSET=BEAMS, MATERIAL=MAT1 50.0, 5.0

*MATERIAL, NAME=MAT1 *ELASTIC

2.0E5, 0.3

The property reference *BEAM SECTION associates the element set BEAMS with the material definition MAT1.

The option can also provide geometric information. In this case the

cross-section type is rectangular (RECT); the width is 50.0, and the height is 5.0.

All elements in a model must have an appropriate property reference. Solid elements reference *SOLID SECTION, shell elements reference *SHELL SECTION, etc.

Example: Cantilever Beam Model (5/11)

Material data

2.0E5, 0.3

Definition for an isotropic linear elastic material

Abaqus interprets the options following a *MATERIAL option as part of the same material option block until the next *MATERIAL option or the next nonmaterial property option, such as the *NODE option, is encountered.

Poisson’s ratio

elastic modulus

(36)

Example: Cantilever Beam Model (6/11)

Fixed boundary conditions

*BOUNDARY 1, 1, 6

Fixed boundary condition constraints are applied to active DOFs.

Prescribed nonzero boundary conditions can be included only in the history data.

Abaqus activates only the necessary degrees of freedom at a node. Thus, for this two-dimensional example with only degrees of freedom 1, 2, and 6 active, the following are equivalent input data:

1, 1, 2 1, 6, 6 or 1, 1, 6 or 1, ENCASTRE

The input file processor will issue a warning about inactive degrees of freedom.

node or node set

range of degrees of freedom or type of BC (pinned, encastre, symmetry, antisymmetry)

Example: Cantilever Beam Model (7/11)

History definition

*STEP

APPLY POINT LOAD *STATIC

The *STEP option block can include a title of any length. The procedure definition must be the first option after *STEP.

Begins the history data

This line appears on every page of results Specifies a static analysis procedure

(37)

Example: Cantilever Beam Model (8/11)

Loading

Definition of a concentrated load in the global negative 2-direction:

*CLOAD

11, 2, -1200.0

Many distributed loadings are also available, including surface pressure, body forces, centrifugal and Coriolis loads, etc.

node or node set degree of freedom magnitude L1.62 s .c om | © Das s au lt S y s tèm es

Example: Cantilever Beam Model (9/11)

Output requests

*OUTPUT, FIELD, VARIABLE=PRESELECT, FREQUENCY=10 *OUTPUT, HISTORY, FREQUENCY=1

*NODE OUTPUT, NSET=END U,

In this case we have requested field output of a preselected set of the most commonly used output variables.

We have also requested history output of displacements for the previously defined node set END.

Since history output is usually requested at relatively high frequencies, the sets should be as output to the output database file

(38)

Example: Cantilever Beam Model (10/11)

*EL PRINT, FREQUENCY=10

S, E

*NODE FILE, FREQUENCY=5 U,

Tabular output is printed to the data (.dat) file for visual inspection using the *EL PRINT option.

In this case we have requested output of the stress (S) and strain (E) components.

Binary output is written to the legacy Abaqus results (.fil) file using the *NODE FILE option; output is used for postprocessing in other postprocessors.

In this case we have requested output of the displacement (U) components.

Printed output to the data file Output to the results file

Example: Cantilever Beam Model (11/11)

End of step

*END STEP

Each analysis step ends with the *END STEP option.

The final option in the input file is the *END STEP option for the final analysis step.

ends the analysis step

(39)

Parts and Assemblies (1/4)

The input file can be defined in terms of parts, part instances, and an assembly. The same concept is employed when building a model in Abaqus/CAE.

Provides an inherent means of referring to distinct regions of the model. The user need not define separate sets for this purpose.

Allows reuse of part definitions, which is valuable for creating large, complex models.

Labels—node and element numbers, set names—need be unique only within the level in which they are defined. L1.66 s .c om | © Das s au lt S y s tèm es

Parts and Assemblies (2/4)

Defining parts

A part is defined by using the *PART and *END PART options, which must appear outside of the assembly definition. Each part must have a unique name.

Defining part instances

A part instance is defined by using the *INSTANCE and *END INSTANCE options within the assembly definition. Each part instance must have a unique name.

Defining an assembly

The assembly is defined by using the *ASSEMBLY and *END ASSEMBLY options. Only one assembly can be defined in a model.

(40)

Parts and Assemblies (3/4)

Example assembly input file

*HEADING ...

*PART, NAME=Tire

Node, element, section, set, and surface definitions

*END PART

*PART, NAME=Rim

Node, element, section, set, and surface definitions

*END PART

...

*ASSEMBLY, NAME=Tire_and_rim *INSTANCE, NAME=I_Tire, PART=Tire

<positioning data>

set and surface definitions (optional)

*END INSTANCE

*INSTANCE, NAME=I_Rim, PART=Rim

<positioning data>

set and surface definitions (optional)

*END INSTANCE

Additional set and surface definitions

*NSET, NSET=Output

I_Tire.514, I_Tire.520 I_Rim.101, I_Rim.102 *END ASSEMBLY ... *MATERIAL, NAME=Rubber *AMPLITUDE *INITIAL CONDITIONS *PHYSICAL CONSTANTS ... *STEP *STATIC *BOUNDARY I_Rim.101, 1, 3, 0.0 *CLOAD I_Tire.514, 2, 1000.0

*OUTPUT, HISTORY, FREQUENCY=10 *NODE OUTPUT, NSET=Output

RF, CF *END STEP L1.68 w w w .3d s .c om | © Das s au lt S y s tèm es

Parts and Assemblies (4/4)

Node labels for parts and the assembly

node label: 101

Part: Rim

node label:

514 I_Tire.514

(41)

L1.69 w w w .3d s .c om | © Das s au lt S y s tèm es 1. Objectives

a. When you complete this exercise you will be able to extract all the files necessary to complete the demonstrations and workshops associated with this course

2. Workshop file setup (option 1: installation via plug-in) a. From the main menu bar, select

Plug-ins→Tools →Install Courses.

b. In the Install Courses dialog box:

i. Specify the directory to which the files will be written. ii. Chooses the course(s) for which the files will be

extracted. iii. Click OK.

Workshop Preliminaries (1/2)

5 minutes L1.70 s .c om | © Das s au lt S y s tèm es

3. Workshop file setup (option 2: manual installation)

a. Find out where the Abaqus release is installed by typing

abqxxx whereami

where abqxxx is the name of the Abaqus execution procedure on your system. It can be defined to

have a different name. For example, the command for the 6.12–1 release might be aliased to abq6121. This command will give the full path to the directory where Abaqus is installed, referred to here as

abaqus_dir.

b. Extract all the workshop files from the course tar file by typing

UNIX: abqxxx perl abaqus_dir/samples/course_setup.pl

Windows NT: abqxxx perl abaqus_dir\samples\course_setup.pl

(42)

L1.71 w w w .3d s .c om | © Das s au lt S y s tèm es 1. Workshop tasks

1. Use some of the Abaqus utility programs.

2. Open the online documentation, and search for useful information. 3. Use the online documentation to determine the syntax for various options. 4. Complete the model of a connecting lug.

5. Submit analyses a few different ways (datacheck only, complete analysis, interactive, and batch submission).

6. View the results using Abaqus/Viewer.

7. Become familiar with the contents of the printed output files. 8. Modify the model, and understand the changes to the results.

Workshop 1: Basic Input and Output (IA)

1 hour

Interactive version. Choose either the interactive or keywords version of this workshop.

L1.72 w w w .3d s .c om | © Das s au lt S y s tèm es 1. Workshop tasks

1. Use some of the Abaqus utility programs.

2. Open the online documentation, and search for useful information. 3. Use the online documentation to determine the syntax for various options.

4. Add some details to an existing input file to complete the model of a connecting lug.

5. Submit analyses a few different ways (datacheck only, complete analysis, interactive, and batch submission).

6. View the results using Abaqus/Viewer.

7. Become familiar with the contents of the printed output files. 8. Modify the model, and understand the changes to the results.

Workshop 1: Basic Input and Output (KW)

Keywords version. Choose either the interactive or keywords version of this workshop.

(43)

(44)

(45)

Lesson content:

Linear and Nonlinear Procedures

Linear Static Analysis and Multiple Load Cases

Multiple Load Case Usage

Examples

Workshop 2: Linear Static Analysis of a Cantilever Beam (IA)

Workshop 2: Linear Static Analysis of a Cantilever Beam (KW)

Lesson 2: Linear Static Analysis

2 hours

Linear and Nonlinear Procedures (1/6)

A fundamental concept in Abaqus is the division of the problem history into steps.

A step is any convenient phase of the history—a thermal transient, a creep hold, a dynamic transient, etc.

In its simplest form a step can be just a static analysis of a load change from one magnitude to another.

For each step the user chooses an analysis procedure.

This choice defines the type of analysis to be performed during the step: static stress analysis, dynamic stress analysis, eigenvalue buckling, transient heat transfer analysis, etc.

(46)

Linear and Nonlinear Procedures (2/6)

For example, consider the bow and arrow in the figure. The analysis consists of four steps:

Step 1: Pretension the bowstring (static response). Step 2: Pull back the string (static response). Step 3: Investigate the natural frequencies of the loaded system.

Step 4: Release the bowstring (dynamic response).

Step 3 = Natural frequency extraction L2.4 w w w .3d s .c om | © Das s au lt S y s tèm es

Linear and Nonlinear Procedures (3/6)

Abaqus distinguishes between two kinds of analysis procedures: General analysis procedures*

Response can be linear or nonlinear.

Steps that use general procedures are known as general steps.

The starting point for each general step is the state of the model at the end of the last general step.

Linear perturbation procedures Response can only be linear.

The linear perturbation is about a base state, which can be either the initial or the current configuration of the model.

(47)

Linear and Nonlinear Procedures (4/6)

General procedures Static Direct cyclic Dynamic (transient) Implicit Explicit Heat transfer Mass diffusion Coupled-field analysis Thermal-mechanical Thermal-electrical Thermal-electrical-structural Pore fluid diffusion/stress

Linear procedures

Static

Eigenvalue buckling Linear dynamics

Natural frequency extraction Transient modal dynamics Steady-state dynamics Response spectrum analysis Random response analysis

Linear and Nonlinear Procedures (5/6)

Default amplitude references

Different defaults for different analysis procedures

AMPLITUDE=RAMP for procedures without natural time scales:

*STATIC

*HEAT TRANSFER, STEADY STATE

*COUPLED TEMPERATURE-DISPLACEMENT, STEADY STATE *SOILS, STEADY STATE

*COUPLED THERMAL-ELECTRICAL, STEADY STATE *STEADY STATE TRANSPORT

(48)

Linear and Nonlinear Procedures (6/6)

AMPLITUDE=STEP for procedures with natural time scales: *DYNAMIC

*VISCO

*HEAT TRANSFER (transient)

*COUPLED TEMPERATURE-DISPLACEMENT (transient) *DYNAMIC TEMPERATURE-DISPLACEMENT, EXPLICIT *COUPLED THERMAL-ELECTRICAL (transient) *SOILS, CONSOLIDATION

*STEADY STATE DYNAMICS *RANDOM RESPONSE *MODAL DYNAMIC

A nonzero displacement boundary condition prescribed in an explicit dynamic procedure (*DYNAMIC, EXPLICIT) must refer to an amplitude option.

Note: Frequency domain proceduresamplitude references define load versus frequency.

Linear Static Analysis and Multiple Load Cases (1/5)

Static analysis is the only procedure that can be performed as either a general or perturbation step: General step: response can be linear or nonlinear

*STEP *STATIC

Perturbation step: linear response

*STEP, PERTURBATION

*STATIC

One advantage of static linear perturbation steps is that they can consider multiple load cases. A load case defines a set of loads and boundary conditions and may contain the following:

Concentrated and distributed loads

Boundary conditions (may change from load case to load case) Inertia relief

In addition to the static linear perturbation procedure, multiple load cases can also be used for steady-state dynamic (SSD) analysis (either direct or SIM-based modal analysis).

For SIM-based SSD analysis, base motion may also be defined as part of a load case.

(49)

Linear Static Analysis and Multiple Load Cases (2/5)

Multiple load cases are advantageous when analyzing components that are subjected to many different types of loads.

Common in many industries.

For example, an aircraft experiences different loads during take-off, climb, cruise, descent, landing, and taxiing.

Each load case is applied independently.

If the stiffness of the structure is assumed constant over all phases of the loading history (linear assumption), a multiple load case analysis is an attractive option to determine the loading envelope.

When investigating the linear static response of a structure subjected to distinct sets of loads and boundary conditions, it is convenient (and generally more efficient) to use multiple load cases in a single linear perturbation step rather than using multiple general or linear perturbation steps.

Linear Static Analysis and Multiple Load Cases (3/5)

Element loop (stiffness/ multiple RHS) Primary factorization (w/ possibly multiple small factorizations) Element loop (stiffness/ single RHS) Factorization (or read factorized matrix from .fct file)

(50)

Linear Static Analysis and Multiple Load Cases (4/5)

Example: An agricultural implement

This is an agricultural implement attached to and towed behind a tractor through a 3-point hitch. The purpose of the hitch is to transfer towing loads to the implement, but otherwise to allow the implement to float and move more or less independently of the tractor.

Linear Static Analysis and Multiple Load Cases (5/5)

Three load cases

The connection is very flexible and the loads on the implement are not well defined, but are a combination of many different types of loads.

Vertical Loads

Lateral Loads

(51)

Multiple Load Case Usage (1/7)

*Step, perturbation *Static

*Load Case, name="Bending A"

*Boundary right, 1, 6 *Cload left, 3, 1.

*End Load Case

*Load Case, name="Bending B"

*Boundary left, 1, 6 *Cload

right, 3, 1.

*End Load Case

*End Step

Node set left

Node set right

Bending A

Bending B

Example: Bending of a plate

Multiple Load Case Usage (2/7)

Basic rules

• Load case names (Load Case, name=...) must be unique.

• Load options specified outside of load cases apply to all load cases. • Base state boundary conditions propagate to all load cases. • Rules for using OP=NEW:

• If used anywhere in a load case step, must be used everywhere in that step.

• If used on any BOUNDARY in a load case step, propagated boundary conditions will be removed in all load cases.

(52)

Multiple Load Case Usage (3/7)

Changing boundary conditions from load case to load case

No performance penalty when boundary conditions change only in magnitude. Limit number of boundary conditions that change location from load case to load case.

Depending on number and distribution of boundary conditions that change location, multiple load case analysis may be significantly slower than equivalent multiple step analysis (very problem dependent).

If in doubt, run datacheck analyses (multiple step versus multiple load case) and compare solver information in data (.dat) file (e.g., memory requirements, number of floating point operations,

Multiple Load Case Usage (4/7)

Problem size

Combination of number of degrees of freedom and number of load cases determines “problem size.” Multiple load case analyses may require more:

Memory than equivalent multiple step analyses (e.g., all right-hand sides must be kept in core during backsubstitution).

Disk space (element and nodal databases).

If necessary, “spread” load cases over several steps to reduce memory/disk usage per step. Worst case: Resort to multiple perturbation steps (again, compare solver information in data (.dat) file).

(53)

Multiple Load Case Usage (5/7)

Output

Output requested per step (not per load case) Available for the output database (.odb) and

data (.dat) files

For the output database file:

All output variables for a load case are mapped to a frame.

I. Similar to the way increments are mapped to frames.

Frame contains load case name. Field output only (no history output).

Multiple Load Case Usage (6/7)

Postprocessing with Abaqus/Viewer

Operations on entire frames supported For selected frames, can create:

Linear combinations (e.g., linear combination of load cases) Min/Max envelope (e.g., find max stresses over all load cases)

(54)

Multiple Load Case Usage (7/7)

Mises stress: Bending A Mises stress: Bending B

Examples (1/5)

Square plate benchmark

Number of load cases: 8 and 16

*Static, perturbation

Changing boundary condition locations at corners Default output

Changing BCs

Model # nodes/edge # variables (# dof)

1 101 61206

2 201 242406

3 501 1506006

(55)

Examples (2/5)

Performance results: Total CPU time

0.E+00 1.E+04 2.E+04 3.E+04 4.E+04

0.E+00 1.E+06 2.E+06 3.E+06 4.E+06

C P U t im e ( s e c ) Number of variables

8 Steps

8 Load Cases

16 Steps

16 Load Cases

Examples (3/5)

Performance: Details for 751  751 model

Relative CPU time—3.4 M variable case

8 steps/8 load Cases

16 steps/16 load cases

Solver

7.52

14.3

(56)

Examples (4/5)

Modify 501  501 model 8 load cases

Boundary conditions on opposite edges changing per load case

Relative total CPU time: ~0.153 (multiple load case ~6.6 slower!) Watch number and location of changing boundary conditions! Changing BCs L2.24 w w w .3d s .c om | © Das s au lt S y s tèm es

Examples (5/5)

A steady-state dynamics example : Chassis-bracket mobility analysis

Number of variables: 534,000 Number of equations: 483,000 Number of load cases: 60

*Steady-state dynamics, direct

(10 frequency points) Output: U (output database)

CPU time (sec)

60 steps (projected

based on 1 step)

60 load cases

Solver

1290



60 = 77,400

1990

(39



faster)

(57)

a. When you complete this workshop you will be able to

i. Run a linear static analysis using a perturbation procedure with linear load cases ii. Combine load case results and create envelope plots

Workshop 2: Linear Static Analysis of a Cantilever Beam (IA)

1 hour

Force-X Force-Y Force-Z

Moment-X Moment-Y Moment-Z

Interactive version. Choose either the interactive or keywords version of this workshop.

a. When you complete this workshop you will be able to

i. Run a linear static analysis using a perturbation procedure with linear load cases ii. Combine load case results and create envelope plots

Workshop 2: Linear Static Analysis of a Cantilever Beam (KW)

Force-X Force-Y Force-Z

Keywords version. Choose either the interactive or keywords version of this workshop.

(58)

(59)

(60)

(61)

Lesson content:

Nonlinearity in Structural Mechanics

Equations of Motion

Nonlinear Analysis Using Implicit Methods

Nonlinear Analysis Using Explicit Methods

Input File for Nonlinear Analysis

Status File

Message File

Output from Nonlinear Cantilever Beam Analysis

Workshop 3: Nonlinear Statics (IA)

Workshop 3: Nonlinear Statics (KW)

Lesson 3: Nonlinear Analysis in Abaqus

2 hours

Nonlinearity in Structural Mechanics (1/4)

Sources of nonlinearity Material nonlinearities: Nonlinear elasticity Plasticity Material damage Failure mechanisms Etc.

(62)

An example of self-contact: Example Problem 1.1.17, Compression of a jounce bumper

Nonlinearity in Structural Mechanics (2/4)

Boundary nonlinearities:

Contact problems

I. Boundary conditions change during the analysis.

Nonlinearity in Structural Mechanics (3/4)

Geometric nonlinearities:

Large deflections and deformations Large rotations

Structural instabilities (buckling) Preloading effects

(63)

Nonlinearity in Structural Mechanics (4/4)

Typical nonlinear problems have all three forms of nonlinearity. Must include the nonlinear terms in the equations.

Generally, the nonlinear equations for each degree of freedom are coupled.

Equations of Motion (1/3)

Static equilibrium

The basic statement of static equilibrium is that the internal forces exerted on the nodes

I

(resulting from the element stresses) and external forces

P

acting at every node must balance:

Dynamic equilibrium

The major difference between a static and a dynamic analysis is the inclusion of the inertial forces :

where

M

is the mass and is the acceleration of the structure. This equation is simply Newton’s second law of motion.

.  0 P I ,

 

P

I

Mu

u Mu

(64)

Equations of Motion (2/3)

Equations of Motion (3/3)

Incremental solution schemes

Nonlinear problems are generally solved in an incremental fashion.

For a static problem a fraction of the total load is applied to the structure and the equilibrium solution corresponding to the current load level is obtained.

I. The load level is then increased (i.e., incremented) and the process is repeated until the full load level is applied.

For a dynamic problem, the equations of motion are numerically integrated in time using discrete time increments.

There are two techniques available to solve the nonlinear equations: Implicit method

Can solve for both static and dynamic equilibrium.

Requires direct solution of a set of matrix equations to obtain the state at the end of the increment.

I. Iteration required.

This method is used by Abaqus/Standard and is the focus of this lecture. Explicit method

Can only solve the dynamic equilibrium equations. I. Can perform quasi-static simulations, however.

(65)

Nonlinear Analysis Using Implicit Methods (1/4)

Steps, increments, and iterations Analysis steps

The load history for a simulation consists of one or more steps. Increments

An increment is part of a step.

I. In static problems the total load applied in a step is broken into smaller increments so that the nonlinear solution path may be followed.

II. In dynamic problems the total time period is broken into smaller increments to integrate the equations of motion.

Iterations

An iteration is an attempt at finding the equilibrium solution in an increment. Newton-Raphson method

Abaqus/Standard uses an incremental-iterative solution technique based on the Newton-Raphson method.

The method is unconditionally stable (any size increments can be used). Accuracy in dynamic analysis is affected by the increment size.

Each increment usually requires several iterations to achieve convergence, and each step is usually made up of several increments.

Nonlinear Analysis Using Implicit Methods (2/4)

Residual

Additional iterations

not shown Two convergence criteria:

Small residuals

Small corrections 1

2 1

(66)

Nonlinear Analysis Using Implicit Methods (3/4)

Equilibrium in a mesh: summary

1. Apply an increment of load or time.

2. Iterate until the sum of all forces acting on each node is small (statics) or is equal to the inertia force (dynamics).

3. Update the state once equilibrium has been satisfied. 4. Go back to Step 1, and apply the next increment.

Nonlinear Analysis Using Implicit Methods (4/4)

Automatic time incrementation

Abaqus automatically adjusts the size of the increments so that nonlinear problems are solved easily and efficiently.

Heuristic algorithm (based on many years of experience).

In static problems it is based on number of iterations required to converge. Convergence is easily achieved:

I. increase increment size

Convergence difficult or divergence occurs: I. cut back increment size

Otherwise:

I. maintain same increment size

Tip: For highly nonlinear problems, it is recommended that the initial time increment be chosen as a small fraction (e.g., 10%) of the total step time.

In implicit dynamic problems, automatic time incrementation is based on the convergence behavior of the Newton iterations and the accuracy of the time integration.

Details of the time increment control algorithm depend on the type of dynamic application. Discussed further later.

(67)

Nonlinear Analysis Using Explicit Methods

Abaqus/Explicit solves for dynamic equilibrium using an explicit solution scheme:

Velocity and displacements at time

t

+ D

t

updated explicitly. Solution is trivial:

Diagonal mass matrix. No iteration is required! Conditionally stable.

The size of the time increment must be controlled.

Explicit methods generally require many, many more time increments than implicit methods for the same problem.

Discontinuous forms of nonlinearity (e.g., contact) are handled more easily by explicit methods. Explicit dynamics will be discussed further later.

1 ( )t

(

)

( )t 







u

M

P

I

Input File for Nonlinear Analysis (1/4)

*HEADING

CANTILEVER BEAM EXAMPLE--LARGE DISPLACEMENT *NODE 1, 0., 0. 11, 200., 0. *NGEN 1, 11, 1 *ELEMENT, TYPE=B21 1, 1, 3 *ELGEN, ELSET=BEAMS 1, 5, 2, 1

*BEAM SECTION, SECTION=RECT, ELSET=BEAMS, MATERIAL=MAT1 50., 5.

(68)

Input File for Nonlinear Analysis (2/4)

*STEP, NLGEOM=YES, INC=25

APPLY POINT LOAD *STATIC 0.1, 1.0, 0.001, 1.0 *CLOAD, AMPLITUDE=RAMP 11, 2, -1200. *END STEP major differences from linear input

minimum time increment maximum time increment time period of the step suggested initial time increment previously defined

amplitude function for load application

major differences from linear input

Input File for Nonlinear Analysis (3/4)

Step and procedure input

*STEP, NLGEOM=YES, INC=25

NLGEOM=YES: include all nonlinear geometric effects due to: Large deflections, rotations, deformation.

Preloading (initial stresses). Load stiffness.

If the above effects are not significant, the predicted response of the model will be the same as with NLGEOM=NO (default), but the analysis will be more expensive.

INC=25: maximum of 25 increments allowed in this example:

Abaqus will stop if the maximum number of increments is reached before the total load is applied. Keeps the analysis from running too long—you can always restart.