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Beam Elements - University of Wisconsin–Madison

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1) Structural Symmetry2)BookshelfProblem
Jake BlanchardFall2009
Making Use of Problem Symmetry
Reflective or mirror symmetry exists if there is symmetry of geometry, loads, and properties with respect to a plane.Other symmetry types exist, but are less commonAnother type –Axisymmetryuses special element formulations rather than boundary conditions and will be studied later in the course.
Rotational Symmetry
Using Symmetry
Using symmetry reduces problem size (also modeling time) and can simplify boundary conditions.
Ux= 0Rotz= 0
E=200 GPa=0.3Thickness=3 mmPlane StressFillet radius is 2 cmp=0.2 MPaFind max VonMisesstress
10 cm
20 cm
2 cm
To easily vary fillet radius…
File/Write db log file…Choose write essential commands onlyEdit file and change radiusFile/Clear and Start NewFile/Read input from…
My Log File Listing
/PREP7!*ET,1,PLANE82!*KEYOPT,1,3,3KEYOPT,1,5,0KEYOPT,1,6,0!*!*R,1,.003,!*!*MPTEMP,,,,,,,,MPTEMP,1,0MPDATA,EX,1,,200e9MPDATA,PRXY,1,,0.3BLC4,0,0,.2,.02BLC4,.2,0,-.02,-.08FLST,2,2,5,ORDE,2FITEM,2,1FITEM,2,-2AADD,P51X!*LFILLT,9,8,.02, ,FLST,2,3,4FITEM,2,6FITEM,2,7FITEM,2,1AL,P51XFLST,2,2,5,ORDE,2FITEM,2,1FITEM,2,3AADD,P51X
Edited and Annotated Version
/PREP7 ! enter preprocessorET,1,PLANE82 ! specify plane82 as element typeKEYOPT,1,3,3 ! with thickness optionR,1,.003, ! real constant for 3mm thicknessMP,EX,1,200e9 ! define elastic modulusMP,PRXY,1,0.3 ! definepoisson'sratioBLC4,0,0,.2,.02 ! make a 20cm by 2cm block with bottom left edge at originBLC4,.2,0,-.02,-.08 ! make a -2cm by -8cm block with bottom left edge at 20cm,0cmAADD,1,2 ! add areas 1 and 2LFILLT,9,8,.02, , ! make a .02 cm fillet between lines 9 and 8AL,6,7,1 ! make an area from lines 6,7 and 2 (fillet region)AADD,1,3 ! add areas 1 and 3ESIZE,0.0025,0, ! setdefaultelement edge length to 2.5 mmMSHKEY,0 ! specify free meshingAMESH,all! mesh all areasLSEL,s,loc,x,0.2 ! select all lines withcentroidat x=20 cmDL,all, ,ALL, ! constrain these lines in all directionsLSEL,s,loc,y,0.02 ! select all lines withcentroidat y=2 cmSFL,all,PRES,.2e6, ! apply pressure on this lineallsel,all! select everything/SOL ! enter solution processorSOLVE ! solve problem/POST1 ! enter post processorPLESOL, S,EQV, 0,1.0 ! plot equivalent stress
Using Variables in Input Files
Plate with an offset hole
/PREP7 ! enter the preprocessorlen= 3 ! define full strip dimensionswid=1rad= .1 ! define hole radius and center coordinatesxc= 0yc= .25ET,1,PLANE42 ! define element type as plane42KEYOPT,1,3,3 ! specify constant thicknessoptionMP,EX,1,10e6 ! Elastic modulusMP,PRXY,1,.3 ! Poisson's RatioR,.1!Set real constant for thickness/PNUM,KP,1 ! Turnkeypoint, line, and area numbering on/PNUM,LINE,1/PNUM,AREA,1BLC4,0,-wid/2,len/2,wid!Create RectangleCYL4,xc,yc,rad ! Create CircleASBA,1,2! Subtract area2 from area1SMRTSIZE,1 ! Setsmartsizecontrol to 1MSHKEY,0 ! free meshingAMESH,all! mesh all areaslsel,s,loc,x,0! select all lines on symmetry planeDL,all, ,symm, ! apply symmetry constraintnsel,s,loc,x,0! select nodes at x=0nsel,r,loc,y,-wid/2 ! select from selected set nodes at y=-widd,all,uy,0! fix selected node inuyto prevent rigid body motionlsel,s,loc,x,len/2! select lines on free edgeSFL,all,PRES,-1000, ! apply pressure on linesallsel,all! selectleverything/SOL!enter solution processorSOLVE ! solve/POST1 ! enter general postprocessorPLNSOL, S,X, 0,1.0 ! plot x direction stressesFINISH





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Beam Elements - University of Wisconsin–Madison