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mkraskamkraska
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3-point bending example added
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‎NonLinear/3PB/Biegung.inp

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*include, input=all.msh
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*include, input=xsym.nam
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*include, input=ysym.nam
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*include, input=load.nam
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*include, input=support.nam
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*include, input=part1.nam
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*include, input=part2.nam
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*include, input=part3.nam
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*boundary
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Nxsym,1
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Nysym,2
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Nsupport,3
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**surface definitions
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*include, input=c1a.sur
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*include, input=c1s.sur
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*include, input=c2a.sur
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*include, input=c2s.sur
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*material, name=alu
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*elastic
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72000,0.3
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*plastic
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160,0
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215,0.04
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500,0.3
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*material, name=steel
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*elastic
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210000,0.3
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** material assignment to bodies
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*solid section, elset=Epart1, material=alu
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*solid section, elset=Epart2, material=steel
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*solid section, elset=Epart3, material=steel
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** contact definitions
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*surface interaction, name=tool
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*surface behavior, pressure-overclosure=linear
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100000,1,1
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***friction
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**0.1,1e7
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*contact pair, interaction=tool, type=surface to surface
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Sc1a,Sc1s
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Sc2a,Sc2s
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*step,nlgeom
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*static
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0.01,1,0.00001,0.02
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*boundary
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Nload,3,3,-20
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*node file
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U
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*el file
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S,PE
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*node print, nset=Nload, totals=only
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RF
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*end step

‎NonLinear/3PB/Biegung.png

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‎NonLinear/3PB/README.md

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# Three-point bending test pf a hollow profile
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Tested with CGX/CCX 2.10
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+ Non-linear static analysis
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+ Plasticity
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+ Penalty contact
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+ Symmetry reduction
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File | Contents
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:------------- | :-------------
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[par.pre.fbl](par.pre.fbl) | CGX script, pre-processing, parametrized with `param.py`
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[post.fbl](post.fbl) | CGX script, post-processing
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[Biegung.inp](Biegung.inp) | CCX input
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[df.gpl](df.gpl) | Gnuplot control file for the force-displacement plot
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The model represents a three point bending test on a elasto-plastic beam with a hollow box section. The simulation
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domain is reduced to a quarter due to symmetry.
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## Pre-Processing
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You may adjust the parameter values in the file [par.pre.fbl](par.pre.fbl) and then run
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```
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> ../../Scripts/param.py par.pre.fbl
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> cgx -b pre.fbl
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```
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<img src="Refs/parts.png" width="400" title="Parts: Specimen, indenter and support">
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<img src="Refs/groups.png" width="400" title="Node groups for constraint application">
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<img src="Refs/pairs.png" width="400" title="Contact pairs">
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The load application cylinders are controlled by imposed displacements to the nodes in the y=0 plane.
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## Solving
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The time step has to be limited for stable contact. Initially, the number of contact
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elements grows with increasing indentation, but then shrinks due to local buckling below the indenter.
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```
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> ccx Biegung
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> ../../Scripts/monitor.py Biegung
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```
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<img src="Biegung.png" title="Convergence plot">
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## Post-Processing
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A movie showing the contact details:
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```
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> cgx -b cpost.fbl
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```
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<img src="movie.gif" title="contact zone">
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```
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> cgx -b post.fbl
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```
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The plastic strain is displayed, the color bar is restricted to 0...4%.
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<img src="Refs/PE.png" title="Equivalent strain">
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<img src="Refs/PEexpanded.png" title="Equivalent strain, expanded model">
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<img src="Refs/PEexpanded_y.png" width="400" title="Equivalent strain, expanded model"><img src="Refs/PEexpanded_yx.png" width="400" title="Equivalent strain, expanded model">
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A force-displacement-curve is generated:
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<img src="Refs/df.png" title="Force-Displacement Curve">

‎NonLinear/3PB/Refs/PE.png

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‎NonLinear/3PB/Refs/PEexpanded.png

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‎NonLinear/3PB/Refs/PEexpanded_y.png

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‎NonLinear/3PB/Refs/PEexpanded_yx.png

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‎NonLinear/3PB/Refs/df.png

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‎NonLinear/3PB/Refs/groups.png

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‎NonLinear/3PB/Refs/pairs.png

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‎NonLinear/3PB/Refs/parts.png

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‎NonLinear/3PB/cpost.fbl

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read Biegung.frd
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view disp
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view elem
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rot x
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rot c 90
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rot l 10
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zoom 4
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plot f all n
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max 0.04
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min 0
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anim real on
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movi frames auto
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ds 1 ah

‎NonLinear/3PB/df.gpl

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set term png
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set grid
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set xlabel "Displacement in mm"
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set ylabel "Force in kN"
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#set yrange [-100:100]
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#set nokey
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#set key top left
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set out "Refs/df.png"
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set parametric
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set dummy t
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set trange [0:1]
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set samples 2
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plot 1.85*t, 46*t title "Theoretical elastic range" w lp,\
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"total force fx,fy,fz_NLOAD.txt" using ($1*20):(-4*$4/1000) title "FEA simulation" w l
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set out #

‎NonLinear/3PB/par.pre.fbl

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# <th=4>
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# <wi=200>
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# <he=50>
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# <le=250>
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# <l2=40>
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# <lr=wi+2*th> lenthe of the indenter
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# <ro=20> radius of the intenter
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# <ra=6>
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# <cs=10> width of contact region
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# part
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pnt py 0 <wi/2> 0
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swep all new tra 0 <-th> 0 2
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swep all new1 tra 0 0 <he/2-ra> 6
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pnt pr 0 <wi/2-ra> <he/2-ra>
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swep new1 new2 rot pr x 90 6
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swep new2 new3 tra 0 <-wi/2+ra> 0 10
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seta bl l L00A L009
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bia bl 5
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copy all new mir z
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swep all new4 tra <cs> 0 0 4
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swep new4 new5 tra <le-2*cs> 0 0 20
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swep new5 new6 tra <2*cs> 0 0 4
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swep new6 new7 tra <l2-cs> 0 0 4
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seta part1 se all
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# center indenter
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seto part2
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pnt p1 0 0 <he/2>
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pnt p2 <ro> 0 <he/2+ro>
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pnt pc 0 0 <he/2+ro>
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line l12 p1 p2 pc 6
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line lc1 pc p1
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line l2c p2 pc
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surf s1 l12 l2c lc1
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swep part2 new tra 0 <lr/2> 0
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copy part2 ind1 rot pc y -90
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setc
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# support part
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seto part3
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copy part2 sup1 tra 0 0 0
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copy part3 sup2 mir x
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move part3 tra <le> 0 <-he-2*ro>
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setc
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# meshing
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#div part1 auto
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elty all he8i
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mesh all
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merg n part1
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merg n part2
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merg n part3
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# boundary conditions
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seta nodes n all
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enq nodes ysym rec _ 0 _ 0.1
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enq nodes xsym rec 0 _ _ 0.1
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# enq nodes load rec 0 _ <he/2> 0.1
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# enq nodes support rec <le> _ <-he/2>
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# enq nodes tmp rec 0 _ 0 15
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# enq tmp side rec 0 _ _ 1
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seta npart2 n part2
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enq npart2 load rec _ 0 _ 0.1
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seta npart3 n part3
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enq npart3 support rec _ 0 _ 0.1
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send all abq
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send all abq nam
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# contact surfacess
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seta c1a s A00L A00I
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comp c1a do
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comp c1a do
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send c1a abq sur
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seta c1s s A034
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comp c1s do
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comp c1s do
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send c1s abq sur
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seta c2a s A02B A028
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comp c2a do
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comp c2a do
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send c2a abq sur
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seta c2s s A03J A03T
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comp c2s do
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comp c2s do
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send c2s abq sur
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#seta ! all
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view elem
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seta ! all
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view elem
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rot -x
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rot c 90
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rot r 30
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rot u 30
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frame
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zoom 1.5
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text Parts
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seta ! all
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hcpy png
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sys mv hcpy_1.png Refs/parts.png
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text Node groups
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plot n ysym r
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plus n xsym r
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plus n load b
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plus n support k
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hcpy png
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sys mv hcpy_2.png Refs/groups.png
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view back
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text Contact pairs
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plot f c1a
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plus f c1s n
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plus f c2a
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plus f c2s n
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hcpy png
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sys mv hcpy_3.png Refs/pairs.png

‎NonLinear/3PB/post.fbl

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read Biegung.frd
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read part1.nam inp
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comp Npart1 do
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# todo: parametrize the theoretical solution
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sys ../../Scripts/dat2txt.py Biegung
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sys gnuplot df.gpl
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view disp
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view elem
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rot y
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frame
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rot l 70
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rot u 10
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zoom 1.5
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# plastic strain
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ds -0 e 1
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plot fv Npart1
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min 0 f
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max 0.04 f
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text Plastic strain
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hcpy png
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sys mv hcpy_1.png Refs/PE.png
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view elem off
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copy all new mir x
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copy new new1 mir y
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plot fv Npart1
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plus e new n
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plus e new1 n
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rot y
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rot r 80
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rot u 10
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frame
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zoom 2
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max 0.04
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min 0
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hcpy png
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sys mv hcpy_2.png Refs/PEexpanded.png
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rot y
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frame
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hcpy png
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sys mv hcpy_3.png Refs/PEexpanded_y.png
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frame
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zoom 4
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rot y
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rot r 20
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rot u 10
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hcpy png
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sys mv hcpy_4.png Refs/PEexpanded_yx.png

‎README.md

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src="Linear/ShearCenter/Refs/Sxz.png"
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width="200"
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title="Thin-walled profiles to illustrate the shear center">
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](Linear/ShearCenter/)
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](NonLinear/3PB/)
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[<img
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src="Linear/ShearCenter/Refs/PEexpanded_yx.png"
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width="200"
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title="Three-point bending of a hollow profile, elastic-plastic">
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](NonLinear/3PB/)

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