Example 534: Pressure inflation and axial extension of a cylinder with fibres & free theta

A trilinear cylinder (r interpolation) of incompressible transversely isotropic material (exponential law), with fibres at 75 degrees wrt the horizontal on the inside and -45 degrees wrt the horizontal on the outside, is axially stretched (by 0.111), left free to twist in theta and inflated to 1.67kPa.

The comfile run by this example is as follows:

#Example_534  Inflation and 10% axial extension of a cylinder with
#             fibres and free theta
fem define coordinate;r;cylfib2;example #Defines cylindrical polar coords.
fem define node;r;;example         #Defines nodes.
fem define base;r;;example         #Defines basis functions.
fem define element;r;;example      #Defines elements.
fem define fibre;r;;example        #Defines fibre distribution.
fem define element;r;;example fibre #Defines fibre elements.
fem define window;r;;example       #Defines 2D window coordinates.
fem draw lines                 #Make line segments visible on window.
fem define equation;r;;example     #Defines equation.
fem define material;r;;example     #Defines material information.
fem define initial;r;;example      #Similar to the previous cylinder/fibre
#                              !  problem except that for equation 2
#                              !  (theta-direction), make nodes 2,4 free
#                              !  to move (do not prescribe a
#                              !  displacement).
fem define solve;r;;example        #Defines solution information.
fem solve increment 0.5 error 1.0D-10 #Solve the problem with 50% of
#                              !  the prescribed conditions.
fem solve increment 0.5 error 1.0D-10 #Solve the problem for the last
#                              !  increment.
fem list strain ref            #List strain information wrt reference
#                              !  coordinates.
fem list stress ref            #List stress information wrt reference
#                              !  coordinates.
fem draw lines deformed dotted #Draw deformed mesh on window.
              #The presence of fibres in different orientations across
              #  the wall of the cylinder leads to a twisting of the
              #  cylinder (deformed theta coordinates of nodes 2,4 are
              #  now displacing).  Although the amount of q displacement
              #  resulting from the fibre distribution is somewhat
              #  different from the previous problem in which
              #  displacement of nodes 2,4 were prescribed, the strains
              #  and stresses are quite similar, especially at the 3rd
              #  Gauss point near where the experimental strains were
              #  measured and optimized parameters were obtained.

Additional testing commands:

fem list stress ref
fem list strain ref

Files used by this example are:

Name                Modified     Size

example_534.com 10-Apr-2000 2.3k cylfib2.ipbase 09-Jul-2001 4.2k cylfib2.ipcoor 10-Apr-2000 647 cylfib2.ipelem 10-Apr-2000 409 cylfib2.ipelfb 10-Apr-2000 237 cylfib2.ipequa 02-May-2004 2.1k cylfib2.ipfibr 30-Jan-2001 720 cylfib2.ipinit 05-Dec-2002 2.2k cylfib2.ipmate 13-Oct-2003 3.0k cylfib2.ipnode 10-Apr-2000 1.1k cylfib2.ipsolv 16-Aug-2010 2.3k cylfib2.ipsolv.old 13-Apr-2007 2.2k cylfib2.ipwind 10-Apr-2000 262 test_output.com 10-Apr-2000 40

Download the entire example:

Name                      Modified     Size

examples_5_53_534.tar.gz 14-Aug-2014 7.9k

Testing status by version:

StatusTestedReal time (s)
cmSuccessSun Mar 6 00:02:00 20161
cm-debugSuccessSat Mar 5 00:02:18 20161
cmSuccessSun Aug 19 01:27:46 20074
cm-debugSuccessWed Aug 15 01:27:55 20079
cm-debug-clear-mallocSuccessSat Aug 18 01:30:57 200713
cm-debug-clear-malloc7SuccessMon Aug 20 01:28:12 200713
cm64SuccessSun Aug 19 01:29:08 20074
cm64-debugSuccessTue Aug 21 01:24:06 20079
cm64-debug-clear-mallocSuccessTue Feb 1 09:44:53 20054
cmSuccessWed Mar 4 01:07:24 20090
cm-debugSuccessMon Mar 2 01:07:20 20093
cm64SuccessWed Mar 4 01:07:24 20090
cm64-debugSuccessTue Mar 3 01:12:13 20093
cmSuccessSun Mar 6 00:01:03 20160
cm-debugSuccessSat Mar 5 00:01:14 20161

Testing status by file:

Html last generated: Sun Mar 6 05:50:23 2016

Input last modified: Thu Aug 14 10:03:14 2014

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