add script and demo of element solution

Author: mkraska

Linear/Separate/README.md

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+# Plane beams - element solution
+Tested with CGX/CCX 2.11
+
++ Linear static solution
++ Plane stress model
++ Test of element separation to avoid nodal averaging of results (AKA element solution in ANSYS)
+
+File                    | Contents    
+ :-------------         | :-------------
+ [pre.fbd](pre.fbd)     | Pre-processing script for CGX     
+ [post-e.fbd](post-e.fbd)   | Post-processing script for CGX, no nodal averaging
+ [post-n.fbd](post-n.fbd)   | Post-processing script for CGX, nodal averaging
+ [nodal.inp](nodal.inp)| CCX input with non-separated mesh (nodal averaging)
+ [element.inp](element.inp)| CCX input with non-separated mesh (nodal averaging)
+
+## Preprocessing
+```
+> cgx -b pre.fbd
+```
+There are four beams, fixed at the left end and loaded by a pressure on the top faces. Each beam is meshed with a different element type:
+
+Disk |CGX | CCX
+:-- |:-- | :--
+1 (upper)|tr6s |CPS6
+2|tr3s | CPS3
+3|qu8s | CPS8R
+4 (lower)|qu4s | CPS4
+
+<img src="mesh.png" width="400" title="Beams with different element types">
+
+The pre-processing script calls `separate.py`, which separates the elements into disjoint meshes to avoid nodal averaging of the element results (stress). See the [Helper Scripts](../../Scripts) page for details.
+
+## Solving
+Because of the different meshes, both versions with and without nodal averaging require different input input files and therefore, different simulation runs.
+```
+> ccx nodal
+> ccx element
+```
+
+## Postprocessing
+
+The difference between connected and disjoint meshes is shown by the CGX function `seta ! all`, which plots disjoint meshes in different colours.
+
+### Nodal averaging (nodal solution)
+```
+> cgx -b post-n.fbd
+```
+<img src="nodal-mesh.png" width="400" title="Elements are connected by sharing nodes"> <img src="nodal-sx.png" width="400" title="Longitudinal stress, averaged at the nodes">
+
+### No nodal averaging (element solution)
+```
+> cgx -b post-e.fbd
+```
+<img src="element-mesh.png" width="400" title="Elements don't share nodes, nodes are connected by equations"> <img src="element-sx.png" width="400" title="Longitudinal stress, not averaged at the nodes">

Linear/Separate/element-mesh.png

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+*include,input=separate-nod.inc
+*include,input=separate-ele.inc
+*include,input=separate-eqn.inc
+*include, input=fix.nam
+*boundary
+Nfix,1,2
+*MATERIAL,NAME=steel
+*ELASTIC
+210000,.3
+*solid SECTION,ELSET=EALL,MATERIAL=steel
+*STEP
+*STATIC
+*dload
+*include,input=load.dlo
+*el file
+S
+*node file
+U
+*end step

Linear/Separate/element-sx.png

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+*include,input=all.msh
+*include, input=fix.nam
+*boundary
+Nfix,1,2
+*MATERIAL,NAME=steel
+*ELASTIC
+210000,.3
+*solid SECTION,ELSET=Eall,MATERIAL=steel
+*STEP
+*STATIC
+*dload
+*include,input=load.dlo
+*el file
+S
+*node file
+U
+*end step

Linear/Separate/element.inp

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+read element.frd new
+rot -z
+view elem
+view edge off
+seta ! all
+hcpy png
+sys mv hcpy_1.png element-mesh.png
+
+ds -0 e 1
+view disp
+scal d 500
+frame
+plot fv all
+hcpy png
+sys mv hcpy_2.png element-sx.png

Linear/Separate/mesh.png

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+read nodal.frd
+rot -z
+view elem
+seta ! all
+hcpy png
+sys mv hcpy_1.png nodal-mesh.png
+
+ds -0 e 1
+view disp
+scal d 500
+frame
+plot fv all
+hcpy png
+sys mv hcpy_2.png nodal-sx.png