Answers to Common ABAQUS Questions Fall 1994

ABAQUS / Answers

Beam Elements:Torsion and WarpingThis is a continuation of an article on beam elements whichbegan in the last issue of ABAQUS/Answers. In this issuewe focus on the effect of torsion and warping.

Torsion refers to the twisting of a structural member aboutits longitudinal axis. Structural members are often subjectedto torsional moments. These occur in almost any three-dimensional frame structure. Loads which cause bending inone member may cause twisting in another, as in the figurebelow. Torsion is also produced when a member carries a

shear force that does not actthrough its shear center, theposition in the cross sectionthrough which a load must act toavoid twist. A shear forceproduces a twisting momentequal to the force times itseccentricity with respect to theshear center.

This is important because the centroid and the shear centeroften do not coincide in open, thin-walled beam sections(see below). If the nodes are not at the shear center of thecross section (node location in beam sections is discussedlater), the section may twist under either concentratedforces or distributed loads. The effect of eccentric loadingcan be seen in the deflection of a cantilever I-beam (aboveright). Depending upon the cross section dimensions, thetwisting can be significant.

Torsion induced in aframed structure.

sc

cs

s c

cs

s c

c,s

Approximatelocations of shearcenters, s, andcentroids, c, for anumber of beamcross sections.

The torsional responseof a thin open section isvery different from thatof a solid circular shaft,where all cross sectionsnormal to the beam axisremain plane undertorsional loading. If thecross section is notcircular, plane crosssections do not remain plane under torsion: they warp.Warping introduces longitudinal strains as the sectiontwists and significantly affects the torsional stiffness. In thecase of open, thin-walled beams, the constraint of the axialwarping strains provides the primary source of torsionalstiffness. Otherwise these open sections have very littleresistance to torsional loading. Warping restraint alsointroduces axial stresses which can affect the beam’sresponse to other types of loading. The stresses and strainsin the I-section cantilever shown above vary significantly,depending on whether warping is prevented at the fixedend. Since the cantilever shown above is modeled withshell elements, the boundary conditions at the fixed endautomatically constrain any warping displacement there.With beam elements, warping may or may not berestrained.

While warping constraint significantly affects torsionalstiffness for open thin-walled sections, the torsional stiffnessof other types of sections depends primarily on the material’sshear modulus, G, and a torsion constant, J. The torsionconstant depends upon the shape and the warpingcharacteristics of the beam cross section.

To calculate the correct torsional stiffness, ABAQUSidentifies three different classes of beam cross section: solidsections; closed, thin-walled sections; and open, thin-walledsections. The calculation of the warping behavior assumesthat the warping displacements in the cross section are small.

The non-circular RECT and TRAPEZOID solid crosssections are treated as beams in which warping isunrestrained. This is because warping constraints wouldonly affect the solution in the immediate vicinity of theconstrained end. Beam elements B31, B32, B33, B34, B31H,and B32H may all be used for these cross sections.

These same elements are also appropriate for closed, thin-walled sections (PIPE, BOX, and HEXAGON sectiontypes), since they also assume unrestrained warping. Section

1 2

3

MAG. FACTOR =+5.0E+00 DISPLACED MESH ORIGINAL MESH

1 2

3

100 lb

0 lb

Fixed End

Cantilever I - Beam loaded off axis

ContentsBeam elements: Torsion and warping 1

Animation 2

Postprocessing the ABAQUS results (.fil) file 4

Page 2 ABAQUS/Answers

type ARBITRARY is treated as a closed thin-walled sectionif the coordinates of the first and last points are identical.

Open, thin-walled sections are very flexible in torsionwhen warping is unrestrained. The variation of the warpinginduced axial deformation over the cross section is definedby the section’s warping function. The magnitude of thisfunction is treated as an extra degree of freedom, 7, in aspecial family of elements: B31OS, B32OS, B31OSH, andB32OSH. Constraining this degree of freedom preventswarping. Nonzero values represent the warping amplitude—the scale factor of the axial displacement field in the shapeof the warping function. A value of 1.0 implies a maximumaxial displacement of 1.0 due to warping. Open thin-walledshapes such as a channel (defined as an ARBITRARYsection) or an I-section should usually be modeled as opensection beams. The regular beam elements may be used, butno axial stress due to warping can evolve and the responsewill be very different from the open section elementformulation with warping constraint.

Independent nodes should generally be used in eachbranch at a connection in a frame structure, since theamplitude of warping will usually be quite different in eachbranch. However, if the connection is designed so that itprevents warping in all members that intersect there, onlyone node is needed, with a boundary condition applied todegree of freedom 7.

The regular three-dimensional beam elements use twostress components for constitutive calculations: one directaxial stress (output variable S11) and one shear stress due totorsion (S12). The shear stress acts along the section wall ina thin-walled section, and in the direction defined by the St.Venant warping function (which ABAQUS calculatesautomatically) for a solid section. Open section beams useonly S11, since the torsional shear stresses are negligible inthis case.

The torsional stiffness calculations apply equally to∗ BEAM SECTION or ∗ BEAM GENERAL SECTION. Atthe start of an analysis ABAQUS calculates a beam section’selastic stretching, bending, shear and warping properties.For all three-dimensional beam elements, ABAQUS reportsthe following geometric properties in the model printout inthe.dat file:

Use separate nodes for themembers connected at thislocation. Constrain DOFs 1-6to be equal at the connectionbut keep the warping degree offreedom, 7, independent andconstrain it separately ifnecessary.

• Cross sectional area.• Second moments of inertia about the centroid.• Products of inertia about the centroid.• Polar moment of inertia about the centroid.• Torsion constant.• Centroid coordinates relative to the nodal location in the

cross section.• Shear center coordinates relative to the nodal

coordinates.• For open section beams elements, ABAQUS also reports

warping related properties.

When beams are used as stiffeners with shell elements itis convenient to have the same nodes define both the beamsand the shells. This is possible when providing the sectionproperty data for section types I, TRAPEZOID, andARBITRARY.

Geometric properties for ∗ BEAM GENERAL SECTION,SECTION=GENERAL must be given with respect to thecentroid and shear center, but the ∗ SHEAR CENTER and∗ CENTROID suboptions allow these locations to be offsetfrom the node in the cross section, thus making it easier tomodel stiffeners.

AnimationAnimating results in ABAQUS/Post is a two stage process:

• Create an animation file using the ∗ SET, CAPTURE and∗ SEQUENCE commands.

• Play back the animation using the ∗ ANIMATEcommand.

The ∗ SEQUENCE command allows you to create a seriesof frames, by stepping through the restart file in a prescribedmanner. The ∗ SET, CAPTURE command stores the screenimages in a file in a neutral binary format. The time taken tostore the image and the size of the animation (.flc) file are

shell section

same nodeused for shelland beam

22.0

2.4

0.2

0.2 0.2

3.0

1

Input syntax if the reference axis (nodalposition) of the section to the left is shifted tothe midsurface of a shell, of thickness=0.1,attached to the bottom flange.

*BEAM [GENERAL] SECTION, SECTION=I-0.05, 2.4, 3., 2., .2, .2, .2

The first data item refers to the offset of thebeam node from the bottom of the section inthe direction of the local 2-axis.

ABAQUS/Answers Page 3

independent of the contents of the screen. A color contourplot of a large, three-dimensional model will take the sametime to store as a plot of a 10 element beam model. Thephysical size of the window—the number of pixels—determines how long the frame takes to store and how largethe file will be.The smaller the size of the ABAQUS/Postwindow, the shorter the capture time and the smaller the sizeof the .flc file.

The ∗ ANIMATE command plays back the .flc file.ABAQUS/Post normally loads the entire image file intomemory. This means that the animation is fast and smooth.If there is not enough memory to store all the images, theimage data are read directly from the file on disk. This willproduce a less smooth animation sequence.

A number of other considerations need to be borne in mindin order to create effective animation sequences.

By default, ABAQUS/Post always scales the model to fillthe screen. To ensure that the scale factor is constant duringthe animation, the ∗ SET, RESCALE=OFF command shouldbe used before starting screen capture. The scaling requireddepends on how large the model is and how much it is goingto deform. It is therefore desirable to set it to cope with thelargest possible deformation. You can do this by selectingthe restart state with the largest deformations, creating adeformed plot and then typing ∗ SET, RESCALE=OFF.

In small displacement analysis ABAQUS/Post magnifiesthe deformation so it is clearly visible. To avoid thismagnification varying from increment to increment,constant magnification can be specified using the ∗ SET,DMAG or ∗ SET, CMAG commands before the capture isstarted.

The first thing ABAQUS/Post does after the command∗ SET, CAPTURE has been typed is to store the image thatis currently on the screen. It is therefore important to ensurethat the first image you require in the animation sequence isthe image on the screen when ∗ SET, CAPTURE is typed. Toavoid the first frame appearing in the animation twice, anysubsequent sequence commands should start from thesecond frame in the animation. The BSTEP and BINCparameters on the ∗ SEQUENCE command can be used tostart the sequence at the desired point.

For contour plots it is usually best to maintain one set ofcontour levels for the entire animation sequence using the∗ SET, CMIN and ∗ SET, CMAX commands (by defaultABAQUS/Post will set the contour levels to cover the rangeof data in the current plot).

The smoothness of the animation depends on the numberof frames and the changes occurring in the plot between eachframe. For most animations it is desirable to have around 20frames covering the period of the analysis. You may needmore if the deformations are particularly large. You shouldensure that enough states are stored in the restart file to createa reasonable animation.

The following ABAQUS/Post commands create a simpleanimation file. The analysis used is Example Problem 4.2.14.To extract the input file use the command:

abaqus fetch input=4021401 job=punch

This extracts the input file from the examples directory inyour ABAQUS installation and puts it into the currentworking directory as punch.inp. You should edit this fileto modify the ∗ RESTART, WRITE command so that dataare written every 10 increments, and then run the analysis.

Then use the following commands in ABAQUS/Post tocreate the animation. (The commands may be put togetherand submitted as a journal file.)

∗ restart, file=punch∗∗ SET UP THE VIEW∗ zoom, factor=0.9∗ view, view=(1,1,1), up=(0,1,0)∗ set, axisymmetric angle=180∗ detail, elset=metal∗ set, center=(0,0,-18)∗ set, ctitle=off, dtitle=off∗∗ SCALE THE SCREEN∗ draw, displaced∗ set, rescale=off,∗ set, undeformed=off, dcolor=off∗ set, shade=on, normalsmooth=70∗∗ SET CONSTANT CONTOUR LEVELS∗ set, cmin=0, cmax=0.487∗ set, clegend=(0.1,0.5)

1

2

3 1

2

3

SECTION POINT 1

PEEQ VALUE-INFINITY

+2.22E-16

+4.42E-02

+8.85E-02

+1.32E-01

+1.77E-01

+2.21E-01

+2.65E-01

+3.09E-01

+3.54E-01

+3.98E-01

+4.42E-01

+4.87E-01

+INFINITY

1

2

3 1

2

3

SECTION POINT 1

PEEQ VALUE-INFINITY

+2.22E-16

+4.42E-02

+8.85E-02

+1.32E-01

+1.77E-01

+2.21E-01

+2.65E-01

+3.09E-01

+3.54E-01

+3.98E-01

+4.42E-01

+4.87E-01

+INFINITY

1

2

3 1

2

3

SECTION POINT 1

PEEQ VALUE-INFINITY

+2.22E-16

+4.42E-02

+8.85E-02

+1.32E-01

+1.77E-01

+2.21E-01

+2.65E-01

+3.09E-01

+3.54E-01

+3.98E-01

+4.42E-01

+4.87E-01

+5.23E-01

Page 4 ABAQUS/Answers

ABAQUSHIBBITT, KARLSSON & SORENSEN, INC.1080 Main Street, Pawtucket, RI 02860-4847Tel: 401 727 4200 Fax: 401 727 4208 E-mail: hks@hks.com

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Copyright 1994, Hibbitt, Karlsson & Sorensen, Inc.No part of this document may be reproduced in any form or distributed in any way without prior written agreement with Hibbitt, Karlsson & Sorensen, Inc.

∗∗ SET UP THE FIRST FRAME∗ restart, step=1, inc=1∗ contour, var=peeq∗ set, hide=on, erase=off∗ colorset, elset=metal, color=black∗ draw, displaced∗ set, shade=on, erase=on∗∗ START CAPTURING THE ANIMATION∗ set, capture=punch.flc∗∗ SEQUENCE THROUGH ALL STORED DATA∗ sequence, time, bstep=2&contour, v=peeq&set, hide=on, erase=off&colorset, elset=metal, color=black&draw, displaced&set, shade=on, erase=on&end∗∗ CLOSE THE ANIMATION FILE∗ set, capture=close

To play back the animation use the ABAQUS/Postcommand:

∗ animate,file=punch.flc,direct,filecolors

Postprocessing from theABAQUS Results FileThe results (.fil) file produced by ABAQUS is asequential file, in binary or ASCII format, in which eachrecord contains a set of results data. The format of the file isdescribed in Chapter 6 of the User’s manual.

The.fil file can be used for x–y plots in ABAQUS/Post,to transfer results to external postprocessors, or topostprocess results with your own programs.

FORTRAN interface routines are supplied with theABAQUS installation to allow you to access the .fil fileand extract the contents of any record. These routines mustbe called from within a FORTRAN program which iscompiled and linked with the ABAQUS libraries. This isdone by using the make option. To compile and link aprogram stored in a file prog.f, use the command:

abaqus make job=prog user=prog.f

The routines used to read the .fil file are:

• INITPF, with which you specify the name of the file, theinitial unit number to read from, and whether a new.filfile will be written.

• DBRNU, which specifies the unit number for a particularfile.

• DBFILE, which reads a record from a file.

The file contains a series of records, each with a numberof words. The first word gives the number of words in therecord. The second contains an integer key that identifies therecord type. The remainder of the record contains the datarelevant to that particular record type. Section 6.1.1 of theUser’s manual describes these data for each type of record,explains how to extract the data from each record, andpresents a simple example of a program that reads a resultsfile. Chapter 7 of the ABAQUS/Standard Verificationmanual contains further examples of such programs.

FORTRAN errors are the most common problem withuser-written postprocessing programs. You should ensurethat your code compiles successfully before attempting tolink it with the ABAQUS libraries. Another commonproblem is that the compile and link commands may not beset correctly in the abaqus.env environment file. Consultthe ABAQUS Site Guide to determine the correct commandsfor your computer.

The libraries supplied with the ABAQUS installation arecreated using a particular version of the FORTRAN compilerand operating system. If your machine does not havecompatible FORTRAN and operating system levels yourprogram may not link successfully with the ABAQUSlibraries. The correct system requirements for all machinesare given in the ABAQUS Site Guide.

The ∗ FILE FORMAT option allows the .fil file to bewritten in ASCII format, so that it may be moved betweendissimilar computers. The ascfil command line option alsoallows .fil files to be converted between binary and ASCIIformat . ASCII format files are not in a “readable” form: theymust be accessed through the interface routines describedabove.