MappingasetofnodesfromonecoordinatesystemtoanotherYoucanmapasetofnodesfromonecoordinatesystemtoanother.Youcanalsorotate,translate,orscalethenodesinasetbyusingamoredirectmethodinsteadofcoordinatesystemmapping.Thesecapabilitiesareusefulformanygeometricsituations:ameshcanbegeneratedquiteeasilyinalocalcoordinatesystem(forexample,onthesurfaceofacylinder)usingothermethodsandthencanbemappedintotheglobal(X,Y,Z)system.Inothercasessomepartsofyourmodelneedtobetranslatedorrotatedalongagivenaxisorscaledwithrespecttoonepoint.Themappingcapabilitycannotbeusedinamodeldefinedintermsofanassemblyofpartinstances.Thefollowingdifferentmappingsareprovided:asimplescaling;asimpleshiftand/orrotation;skewedCartesian;cylindrical;spherical;toroidal;and,inAbaqus/Standardonly,blendedquadratic.ThefirstfiveofthesemappingsareshowninFigure2.1.1–13.Figure2.1.1–13Coordinatesystems;anglesareindegrees.BlendedquadraticmappingisshowninFigure2.1.1–14.Figure2.1.1–14Useofblendedquadraticmappingtodevelopasolidmeshontoacurvedblock.Inallcasesthecoordinatesofthenodesinthesetareassumedtobedefinedinthelocalsystem:theselocalcoordinatesateachnodearereplacedwiththeglobalCartesian(X,Y,Z)coordinatesdefinedbythemapping.Allangularcoordinatesshouldbegivenindegrees.Youcanuseeithercoordinatesornodenumberstodefinethenewcoordinatesystem,theaxisofrotationandtranslation,orthereferencepointusedforscaling.Themappingcapabilitycanbeusedseveraltimesinsuccessiononthesamenodes,ifrequired.ScalingthelocalcoordinatesbeforetheyaremappedForallmappingsexcepttheblendedquadraticmapping,youcanspecifyascalingfactortobeappliedtothelocalcoordinatesbeforetheyaremapped.Thisfacilityisusefulfor“stretching”someofthecoordinatesthataregiven.Forexample,incaseswherethelocalsystemusessomeangularcoordinatesandsomedistancecoordinates(cylindrical,spherical,etc.),itmaybepreferabletogeneratethemeshinasystemthatusesdistancemeasuresintheangulardirectionsandthenscaleontotheangularcoordinatesystemforthemapping.Twodifferentscalingmethodsareavailable.SpecifyingthescalingfactorsdirectlyAfirstmethodofscalingthenodeswithrespecttotheoriginofthelocalsystemistospecifythescalefactorsdirectly.Inthiscasethescalingisdoneatthesametimeasthemappingfromonecoordinatesystemtoanother.InputFileUsage:*NMAP,NSET=namefirstdatalineseconddatalinescalefactorforfirstlocalcoord,scalefactorforsecondlocalcoord,scalefactorforthirdlocalcoordSpecifyingthescalingwithrespecttoareferencepointAlternatively,youcanscalewithrespecttoapointotherthantheorigin.Thereferencepointwithrespecttowhichthescalingisdonecanbedefinedbyusingeitheritscoordinatesortheusernodenumber.InputFileUsage:Usethefollowingoptiontodefinethescalingreferencepointbyusingitscoordinates(default):*NMAP,TYPE=SCALE,DEFINITION=COORDINATESX-coordinateofreferencepoint,Y-coordinateofreferencepoint,Z-coordinateofreferencepointscalefactorforfirstlocalcoord,scalefactorforsecondlocalcoord,scalefactorforthirdlocalcoordUsethefollowingoptiontodefinethescalingreferencepointbyusingitsnodenumber:*NMAP,TYPE=SCALE,DEFINITION=NODESLocalnodenumberofthereferencepointscalefactorforfirstlocalcoord,scalefactorforsecondlocalcoord,scalefactorforthirdlocalcoordIntroducingasimpleshiftand/orrotationbymappingfromonecoordinatesystemtoanotherInthecaseofasimpleshiftand/orrotation,pointainFigure2.1.1–13definestheoriginofthelocalrectangularcoordinatesystemdefiningthemap.Thelocal-axisisdefinedbythelinejoiningpointsaandb.Thelocal–planeisdefinedbytheplanepassingthroughpointsa,b,andc.InputFileUsage:*NMAP,NSET=name,TYPE=RECTANGULARIntroducingapureshiftbyspecifyingtheaxisandmagnitudeofthetranslationYoucandefineapuretranslation(orshift)tomoveasetofnodesbyaprescribedvaluealongadesiredaxis.Youmustspecifytheaxisoftranslationbyprovidingeitherthecoordinatesorthetwonodenumbersdefiningthisaxis,andyoumustprescribethemagnitudeofthetranslation.InputFileUsage:Usethefollowingoptiontospecifytheaxisoftranslationusingcoordinates(default):*NMAP,NSET=name,TYPE=TRANSLATION,DEFINITION=COORDINATESUsethefollowingoptiontospecifytheaxisoftranslationusingnodenumbers:*NMAP,NSET=name,TYPE=TRANSLATION,DEFINITION=NODESIntroducingapurerotationbyspecifyingtheaxis,origin,andangleoftherotationYoucandefinearotationofasetofnodesbyprovidingtheaxisofrotation,theoriginofrotation,andthemagnitudeoftherotation.Youmustspecifytheaxisofrotationbyprovidingeitherthecoordinatesorthetwonodenumbersdefiningthisaxis.Youmustspecifytheoriginoftherotationbyprovidingeitherthecoordinatesorthenodenumberattheoriginofrotation.Finally,youmustspecifytheangleoftherotationindegrees.InputFileUsage:Usethefollowingoptiontospecifytheaxisofrotationusingcoordinates(default):*NMAP,NSET=name,TYPE=ROTATION,DEFINITION=COORDINATESUsethefollowingoptiontospecifytheaxisofrotationusingnodenumbers:*NMAP,NSET=name,TYPE=ROTATION,DEFINITION=NODESMappingfromcylindricalcoordinatesFormappingfromcylindricalcoordinates,pointainFigure2.1.1–13definestheoriginofthelocalcylindricalcoordinatesystemdefiningthemap.Thelinegoingthroughpointaandpointbdefinesthe-axisofthelocalcylindricalcoordinatesystem.Thelocal–plane