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Contents:

Textbook:References:

Topic 21A DemonstrativeComputer SessionUsing ADINA-Linear Analysis Use of the computer program ADINA for finite elementanalysis, discussion of data preparation, programsolution, and display of results Capabilities of ADINA Computer laboratory demonstrat ion-Part I Linear analysis of a plate with a hole f or the stressconcentration factor Data input preparat ion and mesh generation Solution of the model Study and evaluation of results using plots of stresses,stress jumps, and pressure bands

AppendixThe use of th e ADINA program is described and sample solutions ar egiven inBathe, K. J. , "Finite Elements in CAD - and ADINA," NuclearEngineering and Design, to appear.ADINA, ADINAT, ADINA-IN, and ADINA-PLOT Users Manuals ,ADINA Verification Manual, and ADINA Theory and Modeling Guide,ADINA Engineering, Inc., Watertown, MA 02172, U.S.A.P r o c e e d i n g ~ of the ADINA Conferences, (Bathe, K. J., ed.)Computers & Structures13, 5-6, 198117, 5-6, 198321, 1-2, 1985

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21-2 Computer Session Using ADINA - Linear Analysis

References: The use of pressure band plots to evaluate meshes is discussed in(continued) Sussman, T., and K. J. Bathe, "Studies of Finite Element Procedures-Stress Band Plots and the Evaluation of Finite Element Meshes," Engi-neering Computations, to appear.

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A FINITE ELEMENTANALYSIS - LINEAR

SOLUTION We have presented a considerableamount of theory and example solution results in the lectures. The objective in the next two lectures is to show how an actual finiteelement analysis is performed on thecomputer.

We cannot discuss in detail all theaspects of the analysis, but shallsummarize and demonstrate on thecomputer the major steps of theanalysis, and concentrate on- possible difficulties- possible pitfalls- general recommendations

Topic Twenty-one 21-3

Transparency21-1

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21-4 Computer SessionUsing ADINA - LinearAnalysis

Transparency21-3 We will use as the example problemthe plate with a hole already considered earlier, and perform linear andnonlinear analyseselastic analysis to obtain thestress concentration factorelasto-plastic analysis to estimatethe limit loadan analysis to investigate the effectof a shaft in the plate hole

Plate with hole: Schematic drawingTransparency21-4 1 E = 207000 MPa

j - - - - - : . - - - + 7 7 7 J j r i m ~ v = 0.3thickness = 0.01 m

plane stressconditions

~ ~ ~ t ' " We consider thisquarter of the- - -+ plate anduse symmetryconditions

0.01m -+-_.J

0.1m

I. 0.1m ,I

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The first step for a finite elementanalysis is to select a computer program. We use the ADINA system.ADINA-IN to prepare, generatethe finite elementdataADINA to solve the finiteelement modelADINA-PLOT to display numeri-

cally or graphicallythe solution results

Schematically:

graphics..>displayterminal

User work-station

Topic 1\venty-one 21-5

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Transparency21-7 I I generatedUser - ADINA-IN - ADINAinput file

User types into terminal ADINA-INcommands interactively or for batchmode processing. User checks inputand generated data on graphicsdisplay terminal.

Transparency21-8

ADINA-IN generates the input datafor ADINA. The input data is checked internally

in ADINA-IN for errors and consistency and is displayed as perrequest by the user.

The degree of freedom numbers aregenerated (for a minimum bandwidth).

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--I ADINA

Topic 1\ventyo()ne 21-7

Transparency21-9

User runs ADINA to calculate theresponse of the finite elementmodel. ADINA writes the model dataand calculated results on an outputfile and stores the model data andcalculated results on the portholefile.

ADINA-PLOT IUser _--;1display outputdata, numericallyor graphically

Transparency21-10

User runs ADINA-PLOT to accessthe output data and display selectedresults; displacements, stresses,mode shapes, maxima, . . .

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A brief overview of ADINA Static and dynamic solutions Linear and nonlinear analysis Small and very large finite elementmodels can be solved.The formulations, finite elements andnumerical procedures used in the pro-gram have largely been discussed inthis course.

DISPLACEMENTASSUMPTIONS

Infinitesimally small displacements Large displacements/large rotationsbut small strains Large deformations/large strains

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Transparency21-15 z

ONE-DIMENSIONALELEMENT

I......-.-! RING ELEMENT

xr-------....v

Truss and Cable Element(2,3, or 4 nodes)

Transparency21-16 z

vTwo-Dimensional Solid Element(variable number of nodes)

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z

x

y

z

)(

Three-Dimensional Solid Element(variable number of nodes I

y

Two-Node Beam Element

Topic 1\ventY'one 21-11

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Transparency21-19

z/

r----Vx

Isoparametric Beam Element(2,3,4 nodes)

Transparency21-20

z

AT EACH NODE 6 BEAMDEGREES OF FREEDOMPLUS OVALIZATION~ - - - - - v DEGREES OF FREEDOMx

Pipe Element with Ovalization

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16 Node Element

}-,x

4 Node ElementELEMENTS ARE USED WITH5 OR 6 DEGREES OFFREEDOM PER NODE


Transparency21-21

Plate and Shell Elements

A SUMMARY OF IMPORTANTOBSERVATIONS

We need to check the finite elementdata input carefullyprior to the actual responsesolution run, andafter the response solution hasbeen obtained by studyingwhether the desired boundaryconditions are satisfied, whetherthe displacement and stresssolution is reasonable (for thedesired analysis).

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We need to carefully evaluate andinterpret the calculated responsestudy in detail the calculated dis-placements and stresses alongcertain lines, study stress jumpsstress averaging, stress smooth-ing should only be done after theabove careful evaluation

Data for Construction of64 Element Mesh:

100 MPa

E = 207,000 MPav = 0.3Plane stressthickness = 0.01 m

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Finite element mesh to be generatedusing ADINA-IN: Mesh contains 64 elements,288 nodes.


Transparency21-25

eight-nodeisoparametricelement

DemonstrationPhotograph21-1Finite Element ResearchGroup Laboratorycomputer configuration

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21-16 Computer SessionUsing ADINA - L inearAna lysi s

ADINADemonstration21-1Input data

Transparency21-26(Repeat 21-25)

QUARTER PLATE WITH HOLE - 64 ELEMENTS2261001110 1 0 1 1 1.0000000C. . . MASTER CONTROL99999 0 0 1 0 0 50 30.C * 3 LOAD CONTROLo 4 0 0 0 0 0 0C*.* 4 MASS AND DAMPING CONTROLo 0 0 0 . 0 .0C * 5 EIGENVALUE SOLUTION CONTROLo 0 0 0 0 0C. . . 6 TIME INTEGRATION METHOD CONTROLo 20.500000000.25000000 0 0C * 7 INCREMENTAL SOLUTION CONTROL1 1 210 15.001000000.010000000.05C.*. 8 PRINT-OUT CONTROL11111 0



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Stress vector output: Example


Transparency21-27

integrationpoint/ maximum principal stress

, /----' (tensile)

minimum principal stress(compressive)

The length of the line is proportionalto the magnitude of the stress.

TIME 1.000 DMAX ,300

ADINADemonstration21-2Deformed meshplot

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s-- stress computed at closestintegration point

Stress point numbers and integrationpoint numbers for element 572 integrationpoint6 3X2X3 1 6 55 X4 X7 x 987 X Xx4P 8stress point

Behavior of stresses near the stressconcentration:

radius(J of s - stress computed at nodal pointhole

length of element


Transparency2130

Transparency21-31

distance z = 0

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21-20 Computer Session UsingADINA - Linear Analysis

Transparency21-32

Maximum principal stress calculation:_ {1yy + {1zz + !({1yy - {1ZZ)2 + 2{11 - 2 -V. 4 {1yz


Stress point numbers and integrationpoint numbers for element 57integrationpoint

26

2X5X8 9X x8

3

4 - - _ ~ t - - - - - - - 1. :5stress POint

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RESULTANT SMAX ARITHMETIC EXPRESSION.


lTVV+TZZI ITWO+SllRT IITVV-TZZ) * lTVV-TZZ) IFDUR+TVZHVZ I

EXTREME ELEMENT RESULTS PER ELEMENT GROUP FOR WHOLE MODEL

TVV VV-STRESSTZZ ZZ-STRESSTVZ VZ-STRESSTWO 2.1Il1l l1 ll00FOUR 4.1Il1ll1ll1ll1ll

INTERVAL TSTART- 1.1Il1ll1ll1ll TEND= 1.0000 SCANNED FOR ABSOLUTE MAXIMUM

ADINADemonstration21-3Close-up ofcalculations

ELEMENT BROUP NO . 1 (2-D SOLID) LISTED RESULTS ARE MEASURED INGLOBAL COORD I NATE SYSTEMRESULTANT SMAX ELEMENT POINT TIME STEPIll. 3 4 ~ I S I E + 1 I l 3 ~ 4 Ill. 1IIlIIlIllIllE+1Il 1




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To be confident that the stressdiscontinuities are small everywhere,we should plot stress jumps along eachline in the mesh. An alternative way of presentingstress discontinuities is by means ofa pressure band plot:

- Plot bands of constant pressurewherepressure = - (Txx + ; yy + Tzz )

Sixty-four element mesh: Pressure bandplot

H 5 MPa 5 MPa

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A SUMMARY OF IMPORTANTOBSERVATIONS

We need to check the finite elementdata input carefullyprior to the actual responsesolution run, andafter the response solution hasbeen obtained by studying

whether the desired boundaryconditions are satisfied, whetherthe displacement and stresssolution is reasonable (for thedesired analysis).


ADINADemonstration21-4Close-up ofpressure bands

. Transparency21-37(Repeat 21-221

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21-24 Computer Session Using ADINA - LinearAnalysis

Transparency2138(Repeat 21-23) We need to carefully evaluate andinterpret the calculated responsestudy in detail the calculated dis-placements and stresses alongcertain lines, study stress jumpsstress averaging, stress smooth-ing should only be done after theabove careful evaluation

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MIT OpenCourseWarehttp://ocw.mit.edu

Resource: Finite Element Procedures for Solids and StructuresKlaus-Jrgen Bathe

The following may not correspond to a particular course on MIT OpenCourseWare, but has beenprovided by the author as an individual learning resource.

For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
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