Example 711: Material parameters of 2D membrane under biaxial stretch

The corner of a single 2D finite elastic membrane element, with a zero fibre distribution and pole-zero material behaviour, is displaced outwardly. The fibre and sheet axis coefficients of the material law are optimised wrt the difference between the calculated nodal forces and the experimentally determined forces (which in this case come from the solution of the boundary value problem).

The comfile run by this example is as follows:

#Example_711:  Find material parameters of 2D membrane under biaxial stretch
# by optimisation (Note that this example generates the nodal forces from the
# fem solution rather than reading in a deformed geometry and a set of forces)

fem de node;r;membrane;example    #4 nodes
fem de base;r;;example            #bilinear
fem de elem;r;;example            #1 element
fem de fibr;r;;example            #zero fibre angles
fem de elem;r;;example fibre      #fibre elements
fem de wind
fem draw lines
fem draw nodes                    #note bdry conditions
fem de equa;r;;example lock       #finite elastic membrane
fem de mate;r;;example            #pole-zero with default params
fem de init;r;;example            #pull on top right corner
fem de solv;r;;example
fem solve
fem draw lines deformed dotted
fem draw strain rgb=blue          #principal strains
fem draw stress rgb=green         #principal stresses
#                        !note that principle stress dir.n not same as strain
fem list strain xi 1 points 5 
fem list stress xi 1 points 5 
fem draw reactions           #nodal forces
fem de optimise;r;;example   #find 2 axis coeffs of pole-zero law
#                            !minimise sum of squared residuals
#                            !parameters initially zero, range 0 - 10
fem eval residuals wrt mat_params with 1.937,0.028 #true params give zero resids
fem eval residuals wrt mat_params #current (zero) params give non-zero resids
optimise                     #should return exact material parameters
fem list optimise            #list optimised material parameters
fem list material            #list the original material params and check that
#                            !optimised params agree with orig params 1 and 4

Additional testing commands:

fem list initial
fem list optim

Files used by this example are:

Name                 Modified     Size

example_711.com 10-Apr-2000 1.7k membrane.ipbase 10-Apr-2000 1.1k membrane.ipelem 10-Apr-2000 1.1k membrane.ipelfb 10-Apr-2000 245 membrane.ipequa 02-May-2004 1.7k membrane.ipfibr 30-Jan-2001 770 membrane.ipinit 12-Dec-2002 1.2k membrane.ipmate 12-Dec-2002 5.9k membrane.ipnode 10-Apr-2000 2.2k membrane.ipopti 16-Sep-2001 1.3k membrane.ipsolv 16-Aug-2010 2.3k membrane.ipsolv.old 13-Apr-2007 2.2k test_output.com 10-Apr-2000 32

Download the entire example:

Name                      Modified     Size

examples_7_71_711.tar.gz 17-Aug-2010 7.0k

Testing status by version:

StatusTestedReal time (s)
cmSuccessSun Mar 6 00:02:03 20160
cm-debugSuccessSat Mar 5 00:02:23 20161
cmSuccessSun Aug 19 01:26:11 20074
cm-debugSuccessWed Aug 15 01:25:04 20076
cm-debug-clear-mallocSuccessSat Aug 18 01:26:46 200710
cm-debug-clear-malloc7SuccessMon Aug 20 01:24:22 200710
cm64SuccessSun Aug 19 01:27:19 20073
cm64-debugSuccessTue Aug 21 01:21:54 20076
cm64-debug-clear-mallocSuccessThu Apr 1 10:40:54 20043
cmSuccessWed Mar 4 01:07:29 20090
cm-debugSuccessMon Mar 2 01:06:24 20091
cm64SuccessWed Mar 4 01:07:29 20090
cm64-debugSuccessTue Mar 3 01:11:55 20091
cmSuccessSun Mar 6 00:01:03 20160
cm-debugSuccessSat Mar 5 00:01:14 20160

Testing status by file:

Html last generated: Sun Mar 6 05:50:30 2016

Input last modified: Mon Aug 16 11:21:47 2010

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