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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.
Anti-symmetry
P
Rotational Symmetry
Using Symmetry
Using symmetry reduces problem size (also modeling time) and can simplify boundary conditions.
Symmetryb.c.
p
p
Symmetryb.c.
p
Symmetryb.c.
Or
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
ESIZE,0.0025,0,MSHKEY,0CM,_Y,AREAASEL, , , , 2CM,_Y1,AREACHKMSH,'AREA'CMSEL,S,_Y!*AMESH,_Y1!*CMDELE,_YCMDELE,_Y1CMDELE,_Y2!*FLST,2,2,4,ORDE,2FITEM,2,2FITEM,2,10!*/GODL,P51X, ,ALL,FLST,2,1,4,ORDE,1FITEM,2,3/GO!*SFL,P51X,PRES,.2e6,FINISH/SOL/STATUS,SOLUSOLVEFINISH/POST1!*PLESOL, S,EQV, 0,1.0
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