I AD-A091 649 ARIZONA UNIV TUCSON INTERACTIVE GRAPHICS ENGINEERING LAB F/S 9/2SURVEY OF PRE- AND POSTPROCESSING STRUCTURAL ANLAYSIS SOFTWARE.(U)AUG 80 H A KAMEL N000147-5-C-0O37

UNCLASSIFIED TR-7 NLll*lllommmmI E'hEEEEEEE

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N00014-75-C-0837

SURVEY OF PRE- AND POSTPROCESSING STRUCTURAL ANALYSIS SOFTWARE

0OH. A. Kamel

University of ArizonaAerospace & Mechanical Engineering DepartmentTucson, Arizona 85721

August 5, 1980

Technical Report No. 7

Approved for public release, distribution unlimited

Department of the NavyOffice of Naval ResearchStructural Mechanics Program (Code 474)Arlington, Virginia 22217

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-URVEY OF PRE- AND POSTPROCESSING Technical, 10/24/79

STRUCTURAL ANALYSIS SOFTWARE 6. PERFORMING ORG. REPORT MUMBER

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A/KamelH.i-v8 1

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASKAREA & WORK UNIT NUMUE RS

University of Arizona

Interactive Graphics Engineering Lab NR 064-531/12-17-75Tucson, Arizona 85721 Nava__ _______ 8_

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Dept. of the Navy, Office of Naval AugStructural Mechanics Program (.code 474) - .1,11...Arlington. Virginia 22217 21

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IS. SUPPLEMENTARY NOTES

Finite Element Anlysis, Pre- & Postprocessors, Software design.

19. KEY WORDS (Continue on reverse aide If necessery and Identify by block number)

Finite Element Analysis, Pre & Postprocessors, Software Design.

20. ABSTRAC.j(Contlnue on reveree olde It neceeery mid Identify by block number)

The subject of pre- and postprocessing of finite elementdata has been gaining importance over the last several years. Itis perhaps accurate to state that research in this area has beenas active as research in the numerical method field. In this con-text one has to distinguish between several functions associatedwith what one may call "auxiliary finite element software". Pre-processors perform such functions as geometry definition, geometr

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- .~IYCL.ASS191C'OMNJF rIS A~GF'Wh*..olEntold)rewb ig as el as od an

discretization (mesh generation), model display and verification,model editing, node and element renumbering as well as load and

boundary condition definition. Operations such as load and massdiscretization are best considered as part of the analysis. Postprocessing may be concerned with result interpretation. Computergraphics and interactive processing play a central role in theactivities. ̂ 7

Many commercial organizations are developing and marketingpackages aimed at finite element manipulation. Some of these aimat enhancing a specific analysis program. Others are aimed at aspecific hardware product, but address popular finite element programs. The third group of programs are both hardware and analysiprogram independent. There are obvious advantages and disadvant-ages to each alternative.

Apart from the development of user-oriented pre- and post-processor software, research efforts have been directed at somefundamental points associated with mesh generation and softwareenigneering. Among the subjects addressed are algorithms forgeometry definition, discretization of irregular shapes, and anew and promising subject, grid optimization. The contributionwill address the subjects of geometry definition, mesh gener-ation algorithms available as part of postprocessing software,postprocessing and digitizing techniques, mesh optimization, andthe design of relevant software. No claim to completeness isbeing made.

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SURVEY OF P.RE- AND POSTPRCCESSZNG STRUCTURAL ANALYSIS SCFTWARE

S.A.Kamel, Professor, Aerospace and Mechanical EngineeringDept., University of Arizona, Tucson.

Presented at the Symposium an Mathematical Modeling inkStructural Engineering at NASA Langley Research Centeron October 24-26, 1979.

INTRODUCTION

The subject of ore- and postprcocessing of finite element data hasbeen gaining importance over the last several years. It is perhapsaccurate to state that research in this area has beea as active asresearch in the numerical method field. Zn this context one has todistinguish between several functions associated with what one maycall "auxiliary finite element software". Pre-processors cerform suchfunctions as geometry definition, geometry discretization (meshgeneration), model display and verification, model editing, node andelement renumbering as well as load and boundary condition definition.Operations such as load and mass discretization are best considered aspart of the analysis. Postproces-sing may be concerned with -resultinterpretation. Computer graphics and interactive processing play acentral role in Ihe-activities.

*' Many commercial organizations are developing and markecing packagesaimed at finite element manipulation. Some of these aim at'enhancing aspecific analysis program. Others are aimed at a specific hardwareproduct, but address popular finite elememt programs. The third group

Bof programs are both hardware and analysis program independent. Thereare obvious advantages and disadvantages to each alternative..

Apart from the development of user-oriented pre- and postprocesso-software, research efforts have been directed at some fundamentalpoints associated with mesh generation and software engineering. Amongthe subjects addressed are algorithms for geometry definition,discretization of irregular shapes, and a new and promising subject,grid optimization. This contribution will address t.e subjects o:

4Ngeometry definition, mesh generation algorithms available as part ofpostprocess ing software, postprocass .ng and digitizing echniques,

i. I

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mesh optimization, and the design of relevant software. No claim tocompleteness is being made.

In going beyond analysis to the associated automatic modelgeneration and result presentation, the process changes from that of"computer analysis" to "computer-aided analysis". An increase in thecomputer costs over what is necessary for the analysis itself is to beexpected, but the resulting savings in labor, and the faster response,usually more than compensate for tne additional expense.

The process of model generation is by no means divorced from thatof computer aided design and computer aided manufacturing. It has longbeen recognized that an integration of design and analysis functionswould represent an ideal workLig environment. Although this isindisputable in principle, its practical implementation is notstraightforward by any means, and attempts to construct a formal linkbetween a design data base and analysis programs for complex objectshave been typically costly and laborious. It is in the nature orcomplex systems that an increase in size brings with it a decrease inreliability and flexibility. We may still see some success in suchintegration attempts, but an acceptable solution will only be possibleafter significant advances are made in computer software designtechnology, and more effective use is made of current hardware.

Geometry definition

The process of model definition, in preparation for a finiteelement analysis, comprises several distinct stag-es. First amathematical definition of the geometry is accomplished, and then thediscretization process may be carried out. In creating the geometricalmodel, mathematical methods for the representation of curves andsurfaces in three dimensions, typical of those employed in computeraided design may be employed. Some of the me thods used in thedescription of surfaces for analysis purposes are based on mathematicsused in finite element computations. A typical example is to be foundin isoparamet.ic element formulation. Such methods are usually not assophisticated as those used in surface design, producingdiscontinuities in slopes and curvatures at patch boundaries. They arenontheless popular due to the familiarity of the analysts with theirformulation, the associated ease of implementation, as well as theirability to describe discontinuous geometry. Although these methods aregenerally adequate, it has been found in certain applications, such asthe analysis of arbitrary shells, that the results may be extremelysensitive to curvatures, thus encouraging the use of the moresophisticated formulations for these purposes.

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Curves in three dimensional s=ace may be defined in paramet:ricform(!]. For curves of greater complexiltv, a oiece-WiSe continuousparametric representation is necessary. Of the many possibilities forparamet:ic representation, the Bezier[2] curves may be mentioned. TheBezier method of surface representation, originally developed for theFrench automobile industry, derives the parametric shape of aparticular curve from a so-called control polygon, connecting n+lvertices. The resulting parametric curve of order n passes through thetwo end points, and is tangential to the polygon's first and lastsides. The shape of the control polygon influences :he shame of thecurve. The control exerted by the polygon is global in the sense thata change of the position of one of the points will produce a change ofthe shape of the curve overall. :A relatively few points are used inthe polygon, the control of the shape of the curve is good. A Beziercurve is a surface obtained by forming the product of two Beziercurves.

The use of Bezier method presents some problems in the control ofthe shape of the curves and surfaces, in addition to probl.ms ofgeometric continuity. Another a.proach which avoids these shortcomingsis that based on spline functions. Such functions involve the fittingof a oiacewisa continuous curve through a number of points, andprovides for continuity of geometric deriatives at segment boLdaei.- sthrough constcairit zonditions. it has local control, so that theeffect of :novIng a point on the shape of _he curve apol Las only to t h.imediate neigh.bourhood of the point. is possible co form closed oropen curves, as in the case of the Bezier method, as well as introducecorners. Cubic snlines are tha ones most oftan used.

There exists a number of -ocks which addrzss tlle question of curveand surface description, and ref.(1I could be consulted for additionalder-ail. For example, Rawat[3], describes the use of biariate Solin.sin the .Iiniin If e JnCLll t.,:,ne::v. heilheimer and Mckee[4]survey tie use of saline functions in =he description of ship hullsurfaces. Among the topics covered are the construction of complexcurves from control polygons, the computation of surface intersectionsand the solution of the hidden line problem associated with suchsur faces.

Gordon[5i develops a blended spline apcroach to define complexsurfaces using parametric boundary curves. An examp la of the use ocubic splints as a oasis for a ma.ethema:ical surf3ce definition,followed oy a finite element analysis, is given by Liu[6]. Hedescribes an approach by which the smoothness of the surface generatedfor arbitrary curved shell analysis may bc optimized ising th .;nknowntwist veactors a: the oatzh corners as controling =armi.tars.

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:ash generation la.ocithns.

many papacs ex¢ist, wh.:h eal with mesn generation algoC thm, 2u

for exar.pla (7,8,9,131. an early survey of mesh generation algorithmsis found in £31]. In this section we deal orimarily with methods forthe automatic subdivision of comp lax geometrical configurations, andthe associated computation of the position of intermediate gridpoints. The simolest and most widely solved problem is th a two

dimensional one, in which a complex sha-e, or an interconnected set ofarbitrary shapes, is subdivided into tr angular or quadrilateralsubdomains. Next in degree of difficulty is the problem of IE . a initionand discretization of th c-ae d imens ional Sur f.c-5s, ih Ich nay bo .

interconnected. The additional oroblems arise from the need todetermine a method for the definition of the location * of the surfacein soace, as well as the fact that several surfaces may intersectalong the same curve. At such intersections surface parametercontinuity may be required, although not necessarily. Finally we havethe case of three dimensional solid continua, hece a volume, bound b Vsuch surfas,-..- nay oe sub-Jivi.Jd into i numnbe o :a oro ic k- t.. e y_ .. : a

6. hias 6sen :nent,'ind 13 e6- tIia t mo ad al c r -i-L inZls bo titaat.hamat ical defini tion in continuous 'form, and subsequentdiscr izatioa into finite elem.n t s (subspaces). The .roedure bywhich this may be iccomnolished is not unique, and mAv take several6orms, as is evident from. figureil!. :I is rpossi.le, for exam.ole oc ener continuous forms for bot curves and surfaces, and then

-discretize both independently. Since the curves form the surfaceboundaries, *:at. must be ta.<n 1'aat t" " 6 et za tion iS comotibL.

Alternately, one may proceed from a :ontinuous cv lirectly to .adiscrete cur-ia format, and use this information to form the 1iscesucface 3o .n di t hou t necessarilv proviiing a continuous SuCc::

f1. i tion. tL a ao ossible to define zurves in dicceta f.il.!J i,.= 1, 1.) y goss. ~ in te ,. ti, say by i L i i L. o t by ioint, Ra.nd he1 iococeed to

g eneca sc r 1eta focns for both sucfac-is ans olids.

Another a95nro'ach evolves from -discegar-iing ht n.aturil geonetrical "1i L a ca-chy, and pc tding c c I -o h d-f, anition of -. su6Su-cu sin continuous Corm. Once :ne surfac- s .av3 b-en 1- CLn.:, h. .iaI in-tars.ion i : oinouced, thus defining tneir boundary curves, as 4.._as the form of tne solids bounded by tham. k!l the abova 'praheshave "ieir advantages and disadvantaq.s. A tr-u.ly ;nec-r ouro)senodel ;enecation program shouid allow all possible paths, so tha- theuser may choose whichever ap roach may best suit his particularprobIem.

LI-

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OIRECr OIRECT 31RECTOENIT13.a1 0E1U1TIO. WEIMITIOM

PlNT URVES 3URFACES

OlGITIZEIFO

M ITHEM IT1 C AL ~ ATEMATICAL iNOOEFIMITlONIEF1IIT1

0 13 C.1E 0 1 sCR ET E, 0ISCRETLl T0

F'igure 1.Psi~.aisL. Model. Geeration

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Turning to mesi :3enaratiori lgorithms, a method for subdividing atwo dimensional area, bcund by an arbi:rary polygon, in to triangularfinite elements is given by 3ykat(l!]. The method subdivides the areafirst into a number of convex subregions. This is followed by anautomatic "ore-conditioning" of the boundaries, by introducingadditional boundary points to eleminate sudden changes in gridspacing. Automatic boundary refinement is a.plied at re-entrantcorners. Finally all convex regions are triangulated, producing wellshaped elements. A two dimensional mesh generator wiCh manyinteresting features is described by Gabrielson(151. :t is based onthe definition of multi-connected four sided regions (i,j grids), inwhich intermediate points are computed by linear interpolation. Itaccepts input alphanumerically via the terminal, in the form of datacards, digitizer output or directly from a larger geometric data baseintended for commuter aided manufacturing. The generated meshes can beused for either heat transfer or stress analysis.

Gordon and Rall(12] address the problem of domain mappings in thecontext of finite element analysis and present a heuristic method.Nielson and Wixom(13] discuss different techniques for surfacedefinition from boundary curves. Extensions to the method of Gordonare presented. A mesh generator based on 3-spline curverepresentation [41 uses a command language for the generation ofpoints, lines, circles, and various other curve and'surface ty pes. Ithas the ability to calculate surface intersections.

An early example of mesh generators for solid analysis is describedin (191. There, the finite element isoparametric formulation is usedas a basis for surface representation and discretization as well asvolume discretization. Cook (20,21] develops and uses the concept of"natural coordinates" to generate surface and volume grids. Anothereffort based on the same concept is -resented by Aral(221. A orocessfor checking solid models by means of computing and displaying theintersections of the alements of :he model with a series of planes isdescribed in (23].

}6Some authors oresent attempts at developing a language to be used

as a means :or inout description. For example, the SAIL languag_(24],developed by Boeing is a FORT.RN-1i.e structUral input language, whichgenera:es input data for many finite element programs, aarticular.yNASTRAN and SAMES. Silvester(25] describes %he MAG NET language, wnichis a tool for the description of finite element models. :t allowsgeometrical and topological changes, unions of separate models as wellas addition and removal of model constituents. :nput may be through akeyboard or graphics cursor. . is designed particularly forrepetitive structures.

:n most programs a bandwidth or wa,7efront optimizer is necessary toreduce subsequent solution times, and sometimes to avoid exceedingprogram limitations. A method for renumbering elements in order toachieve improved storage in prepaation for a frontal solution, ando ther methods no requiring a stiffness assembly, is given o Y3vkat(25]. 1: reoresents a modification of ta utai ll-McKe*algori:hm[27], and :equires a reasonable choie- of the first element.

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Gray et al.[28 describe two methods for automatic :enumbering ofnodes for water network analysis. The method can be extended to finiteelement programs. It is aimed at t inimization of matrix fillduring the solution process.

Other special efforts deserve attention. An example is an algorithmby Preiss[29I, which checks topological consistency of plate and solidmodels. tt is oart of an in-house NCNSAP preprocessor, n problemswhere model geome-ry changes due :o chemical reactions or physicalphase changes, such as models with abelating b1oundaries, tie problemof automatic model generation 1s turther complicated. Weeks andCost[301 propose an algorithm for tracking such boundaris, -Inconjunction with an automatic mesh generator, and a finite elementprogram for the calculation of transient thermal or stress analysis ofsuch sructures.

Model generation programris may be written as general purposepackages or as special purpose programs. A general purpose meshgenerator is more versatile, being able to handle a wide variety ofproblems, and respond well to new and unforseen situations. On theother hand, it will, by necessity, be more comolex and will require acertain amount of training before it can be used effectively. A truelygeneral purpose program should Lm.ose no rest rictions on problem size,or type. if required to run interactively, it will typically berestricted to a small amount of core. This combination of requirementsmay result in extensive disk usage and computer overhead to oerformthe necessary 7_/0 operations. The other alternative is that of aspecial purpose mesh generator, subject to certain restrictionsregarding problem type and perhaps size. This option is particularlyattractive in situations Where a certain type of st:ucture isrepeatedly analyzed with different geometric parameters. In such acase it is often oossible to produce an optimized grid based on theoverall characteristics of the structure in mind, and thereby relievethe user of deta-iled decisions and input detail. .t is often possible,and indeed most desireable, to use an approach combining the two:ossibilities Ito best advantage. :n this case a truely general purposemesh generator is coupled with several special "pre-preprocessors",whose functions would be to provide approp-ia-e instructions for thegeneration of sceci-fic struc-ural models of known configuration usingthe general purpose generator and a minimum of input.

An excellent example of a special purose mesh generation prog:amis that develoced by eick and ?ot-in['l]. A special purpose analysisprogram was written to handle 0 joints such as T,YK and T'Kjoints, prevalent in offsnore tubular structures. The associated meshgenerator oroduces a fine grid near st:ess concentration areas and acourse one away from z.nem. The grid characteristics are defined in

terms of a few parameters.

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Available Mesh Gene.ation Software

In general mesh generators may be developed for specific hardware,or may be intended to be hardware independent. Hardware dependentpackages are usually associated with turnkey systems, including forexample refresh type graphics. in the same mariner, pre- andpostprocessors may be tailored -o a scecdfic analysis program, or maybe intaended for use by a number o dif4ferent ccograms. There araadvantages and disadvantages to system dependent pac.Kages and systemindecenden: ones. Whether the package is dependent on hardware oranalysis program or both, it is usually well maintained by theoriginators. Should the hardware or analysis program change, tneauxiliaryv software is automatically changed and tested. Furthermore,the pre- and postprocesso r programs would cater well to theideosynchronacies of the analysis program, and would utilize specialhardware features most effectively. On the other hand, the user'sdependence on a single source hampers his freedom of action. Should aparticular type of hacdwar- be drooced by the manufacturer, or provesto be ineffective, the required change over to another system iusually costly in both lost ?roduction time and manpower. Furthermore,if the auxiliary software is analysis program ,dependent, and the userhas several in-house programs, the personnel t:raining problems maybecome exessive. En the case of general zur:ose auxiliary software,the training may be more demanding, but need only be done once for allprograms. A maximum flexibility of action is guaranteed. Cn the otherhand, it is more time consuming to maintain a hardware a nd analysisprogram indepcent pr ogram. Any change In h ardware or analysisprogram characte-is tis has to b e car ef s tudied as to ..s !feCton the pra- and ostpcrocessor sofE,'ace. The group pe:rormLig tihemaintainanze Ias to have continuous access to ;l aJw're ndso f twain ein question. This is only possil3!e for i x t r a.mely largeorganizations. it may also be accomothrup a wel organizusers group. A survey of available pre- and postprocessor softwa:e isgiven by Napolitano et al.[32

T-urning to specific softwar-e reported in the literature, it isoerhaps aorooria: to start bv mentioning those oackages supcorti.ooular nalvs'.s so:wa-e. "4e start by sur zvin ; auxiliacy sof _wa -soeuifia,- aim=e at carticula. analysis arogram. Following t-a t, wesnall consider analysis rogram independent softwa:e.

Of all commercial programs, oerhans the one most used in zracticeis NAST.RAN. An early survey of NASTRAN pre- and 2ostprocessors sgiven in ref[17].The :a;er "ists a number of model generation andSandw id-:n node resequencing -rog rams available through variousorganizations.

As men :ioned earlier, it is impor .tant to ?c .'! sa ....? Ili II est-ene-:'on geme t:y ai lo, *izo 1. ater us:. in in: i;'put of 1o=id a

'oounda:y :oni :ions. A pi oneering effort to thwas conducted

b yoo<-3 , who used sp ine :I.r.sen-a-ion of cu:';.s and surfa fo,;eomet:r i3.r-IaI:on. The rsultinq or-prcc-assor was inten.d f.or na.

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NJASTRAN program. A general pur-o se postprocesso: for NASTR.AN, whichoperates in both the batch and time-snarLng evir~ments is desc:4-tedin ref.(331. A modelling system designed for NASTRAN -is described, in

34I. it is based on -a hierarchial representation of gemoetry, herecalled "cons trucci on- in-contex t" , and h as parametric represertation ofcurves,sur-Faces and volumes. IGFES(35) is an in:eractize NASTRAN ore-and costprocessing sys-en, operational on 131%-360 and ?pa-ll

copters. It is modular and uses storage tube craphics as well asmechanical plotters. 7-t includes both, two and three d imerns onal s hellmesh generators and mode, edi tors. Amongst Mesn zenera:i.on actions .1re

Laplaian, inear intercaolation between ooas ie sie he CallI eddirect ray) , Coons blending and isocaramecric macoping. it hascontouring capabilities.

Several auxiliary software packages have been designed witlh the;ocular SAP program in mind. One of the preprocessors is due toKaidjian(361. It'is interactive, efficient but has somewhat limitedcapabilities. FEPSAP[37] is an optinnized version of the SAP program

orCDC comouters. :I has smecialized two c~imensional and solidsPrecrocessors. These orearocessors may also be used t-o generate loadsand boundary cniis.Crinse LydJ1 created a sy stern orfprograms buil t around the SAD-V prgam. A1mong :ne available programsis an automatic mesh generator call.ed GLGEN..

Two other progcrms, partic-ularly popular in Furope are SESAM-59(39]and As:A(40] . Slaugerud(4l]1 describes a solids preprocessor written forSESAM-69. :6 is based on the creation of a to~o logical arrangement ofthree dimensional grids, which can then be distorted to fit :thephysical geometry of thne object being analyzed. Automatic nodenumbering, definition of physical properties and spec-ificat:.4ons ofloads are possible. Afurtner development of the SESAM-69 program is amodular s ys tem (4 21 ,whi-ch includes a finite element Ore- andepost~rocessor utility nackage, CASA(431. OASA has amcroximatelvi 30,00Statements and 200 subrouzines. it required 4 toa 5 man years toad'evelop. tallows the user to 4molement soecial a nd general paurpcoseadata generators, using its subroutines as building blocks. it 'IS basedon the conceot of t e I'me sh, w h ich i s de fined by a s y stem ofo rthogo nal surfaces, wh nich may assume p riJsmaa t i c, cyl ind erc ca! orspherical shnames . The generated model may be modified later to0introduce local de-a 4'1 "'he system also allows for automatic mesharefinemean:, as well1 as load and b ounda rv condition generation.

Uerkvitz[44] a nd Grieger(43,45] describe a geometr-:icall>'niera-rchial mnesn, generation prog ram, called INGA, aim-Ied at tn e f i a teelemnent orcgra.m ASKA. It, uses finite element interco-alation functionsas a basis :or i :s nesh (generator , and 'Is interactive in nat-4re, usingprimarily a :e resh graphics stand-alone system.

Moving on toa pogrqam indecenden: a uxiliry software, an ear>lexamplie is given bmy thAe work o f 3ousque t and Yaces [79j Te reviinand model ed iti4-ng so ftwa re wdas inte n ded a s an analys is cr:c -amindependent package, and operated On storage tu1b e terminals , IhuSpo in t4-ng t.- waayV toa ,nn,. subs ecq-,e nt dav e lacm en -,s . A nUmb er ofcommerciall.Iy ava ilable packageas ex istz, as w4e11 as others in the publIic

.. ... ... .- - .. ... ....... _

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domain. The UNISTRUC{47] package uses the so called "drag me hcd" ;norder to develop three dimensional node and element arrangements :romtwo dimensional ones, and two dimensional ones from One c mensiOnalstrings. The FASTDRAW program(48] has been developed byMcDonnell-Douglas and serves as a preorocessor for STRUDL, NASTRAN andANSYS. Tektronix has developed a software package for its line ofgraphics hardware devices, called FEM. It is designed for a standalone intelligent device such as the Tektronix FEM-l1l system. It hasextensive interactive editting capabilities, and a new mesh generationmodule has been announced.

Several packages of ?re- and postprocessing software have beendeveloced in a University environment as a byproduct of researchefforts, or out of necessity to facilitate access to available finiteelement software. The GIFTS system[5@1 is one example. !t has two andthree dimensional model, load and boundary condition generationcapabilities. It is designed to run in minimum core space. t'sposcprocessor handles all but solid models ac present. t is supoortedby a users group, and is distributed out of the University of Arizona.Interfaces exist with the SAP-:V and ANSYS programs, an; others areunder develooment. Apart from ore- and pos-processing mcdules, GIFTSis also caoable of static and dynamic analysis on both a number ofmainframes and minicomouters. A finite element precrocessor,FEMGENfSl,56] , has been under development at .he Universtv of Lund r.Sweden. since 1974. I is intended to support analysis programs suc- asASKA, NASTAN, STRUDL, SAP-1V and ADINA. FEMG N uses storage tubeterminals, drum olotters and line printers. Straight lines andcircular arcs may be defined in terms or geometric po ints, or as theintersections of standard mathematical surfaces, such as planes,cylinders and cones. The program runs in 25K words on a UNVA,.-.!.30,and has been conver-ed to :3C, 3M and ?P-!l computers.

Many other efforts are underway. For example, the SUP RN FTprogram(52] is being developed in the German Federal Republic by BraunBoveri (BBC). The program supports line, surface and solid elements,and follows a geometric n'erarchv. Interfaces are being written foranalysis programs such as ASKA, NASTRAN, MARC, TCPAS and ANSYS.SUPERNET may be run in batch, or in an interactive mode. :n the Ja "=case a Computer Vision CAD system is used. A pre- and postprocesso:package called FEMALE[531 is intended as a general purpose package.aowever it seems that its mesh generation capamidlities are stil. at anearly stage. From tne current descripcion it anoears to be More c: amodel pre-viawer rather than a preprocessor. An interactive threedimensional shell mesh g.nerator is described in ref(541. t usesrefresh scope graphics, light pen and <eyboard. In itial input,defining the outlines of surface pahznes is introduced via cards. Theuser may view the outlines and perform certain operations. Afterwards,th e mesn zene.ator may be invoked, and results displayed and editted.A bandwidth otimizer Ls included, and output may be in the form ofpunched cards, zermanent files or magnetic tape outpu:. Crawfordr53z

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is in the process of developing a pre- and postprocessor package,which uses a geometrical hierarchy.

Some programs have an integrated Pre- and postprocessingcapability, which may often be important in special purpose codes, inwhich the processes of model generation and of computation areinterweaved. An interresting example is the TOTAL program reported :vBeaubien(571. It is a two dimensional analysis program designed tosimulate the failure mechanisms in layered orthotropic comoosi:es. Ithas a built in pre- and postprocesso: which heips keep ::ack of tneprogress of cracks.

Qualitative evaluation of interactive versus batch computations arehard to find in the literature. Measurements are bound to be systemdependent, and often represent personal opinions and experiences. itis nevertheless interesting to mention figures extracted from apromotional publication[84l. It is cla-imed there that an interactivesolution costs only 45% of the cost of a similar computation performedin the batch mode. Out of 100 dollars spent in a batch computation, 73are spent on model generation, !a on computer processing and 20 onresult interoretation. In the interactive so uion, 45 dollars arespent on the commutation, 20 of which are spent on model generation,15 on computer processing and la on result interpretation. 7t is notclear whether these figures are typical of the program in question orare generally valid.

Postprocessing and display techniques.

Although postprocessing 4s often directly related to tne meshg.eneration process, special display techniques are often employedthis stage, so that it is appropriate to recort on postprocessorsystems and such techniques under the same heading.

Contouring of stress and deflection results is a useful and Pcoularpostbrocessing operation. Ref.[53], for examole, gives a FCRT.ANprogram wh nich admits several subregions, each divided ino ri ra r,g.I a. ror quadrilateral finite eemen:s. The oroblem of cont3uring w!dh, .higher order elemen: boundar ies is mathematical!y ntr 1u vng. AnSinitial " eor- has been -onduc:ed bv Akin and -rav[59 , in which theylay out the fundamental relationshis and .rov.i some numericalexamples. A follow up papering] utilizes a predictr-correct,: metno-to trace Sucn contours accurately. Similarly, Meek and Ber[51]d escr ibe a method for tracing deflactions across '-i=her orde:elements. It is based on a process involving averaging ncdal "'a.s,followed 'y eemenc suodivision and local linearization. Resu!-s are

given for -:iangular and quadrilateral elements.

I ..

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Akin and Stoddart([21 present aln algori-hm for plottingintersections of isoparametric solid elements with an a:bitrary plane,and tne subsequent .Lots of stress or displacement contours on theresulting mesh. The plots are generated zoint by soint 1n a randomorder, and are suitable for graphics terminals or elec-rostatiCpnotters. Fcay a l. [531 describe a me thod for calculating theintersection of a plane "with second order isocarametric solid brickelements.

A paper describing an alorithm for clipping and capping solidpolyhedron (4 4 z di: actl> a::l i:ae to the dispay of th.eedimensional models. oroduces an input, file for the " well d is t riu-dhidden line progcam, '401VZE-3Y1'Tj .. version of cne program foc l-bit minicomruters, cal1ed - is also available[35]. A twoand three dimensional half-tone and color program for the output offinite element results is described by Murai and Tateishi[66]. :t hassome mesh generation capabilities, is capable of solving the hiddenline and surface problems and contouring. Furthermore it usesinexpensive hardware.

Mesh Optimization

Among the most interesting areas of current research inpreprocessing is that of mesh optimization. Here the stress is ondevising the optimum mesh configuration for a particular element typeand an approximate number of degrees of freedom in order to obtain anoptimum solution for the croblem at hand. It is obvious that a cleardefinition of what constitutes an optimum solution is necessary. 'twill be found, for example that high accuracy in a peak stress value,achieved by an optimized grid may be associated with poor deflectionresults. : is also obvious that a grid may be optimum for onespecific loading case, but far from it for another.

Several authors have been actwie in this area, as is evident fromeref.[67,8,-,6,7'3,71]. A paper by Turke and McNeice(72] introduces the

node coordinates of the mesh as independent unknowns in the finiteelement variationa! formulation. T.he solution, w ich is based on aminimization of tie potential energy of the system, provides bothdisplacement values as well as new node coordinates. Certain

* constraints have to be imposed on the node relocation to ensuremeaningful results. Carroll72] extends grid optimization to t'Ie areaof vibrational mode computation. He shows that a dif-f.,erent optimum-rid is associated witn each mode.

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Turke and McNeice[741 and Melosh and Killian(7 ] s.ow thesuperiority of an optimized mesh over one obtained by uniformrefinement. The introduction of additional freedoms and elements wasallowed in (751, based on local solutions to study the effect ofelement subdivision. Denayer[76] generalized some algorithms given in(81 for the generation of topologically uniform grids. The mappingprocess from a parent grid to the area under consideration is chosenso as to achieve-certain optimal conditions, which translate into avariational formulation lending itself to a finite element solution.Carey(77] presents a method for selective refinement of a finiteelement mesh near in area of interest. Lagrangian constraints are usedto maintain continuity with the rest of the model. Results show goodconvergence in the solution of the Poisson equation with a singularityin two dimensions.

tnteractive Software Design

Associated with interactive software, special problems in 'designmethodology, software reliability, portability and resting arise. Someof the surveyed work is being directed to this specific area.Requirements for developing general purpose pre- and postprocessingsystems are formulated by Tischler and Bernier[79], and discussed byHerness and Tocher. :n (831 it is claimed that 7,3% to 99% of the costof a finite element analysis is typically attributed to manpowercosts, the cest being computer charges. The concept of a modularprogram library, in which the pre- and postprocessors interact withthe analysis programs via a standard data base is well represented bythe GIFTS package(81]. The design of interactive are- andpostprocessor systems is described in (821, which discusses proceduresfor program design, testing, overlaying, data handling and commandlanguage design. The problem of program portability is more complexfor graphics software than it is for standard batch analysis programs.Foley(33] discusses the design of device independent basic software.

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Conclusion

The paper reviews the ;rincipal components of finite element Pre-and postnprocessing (so-called "auxiliary finite element software"). :?tprovides an assesment of the current state of the art and a literaturesurvey.

Ac knowl edgemen ts

The author would like to acknowledge the support of the Office of INaval Research under contract number N00014-75-C-3837, and that of theNational Science Foundation under contract number ENG77-17313. MissMaria Pinedo helped in typing the manuscript.

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