Example 431: A plane strain analysis of a plate under uniform normal tension

This problem investigates a square plate with sides of length 2 centered at the origin under plane strain. Uniform normal tensile stresses of sigma_x in the x-direction and sigma_y in the y-direction. There are no shear stresses. As the problem is symmetric only a quarter of the plate is modelled. The analytic strains for this case are e_x = (1+nu)(1-nu).sigma_x/E - nu(1+nu).sigma_y/E and e_y = (1+nu)(1-nu).sigma_y/E - nu(1+nu).sigma_x/E where nu is Poisson's ratio and E is Young's modulus. For this case E=200 GPa, nu=0.3, the stress in the x-direction is 10 kPa and the stress in the y-direction is 5 kPa. This gives analytic displacements of 0.03575 micrometers in the x-direction and 0.000325 micrometers in the y-direction. Compare this with the equivalent plane stress example in example_422.

The comfile run by this example is as follows:

#Example_431 A square plate under plane strain uniform normal stress
fem                            #set up the FEM environment
fem define nodes;r;planestrainplate;example #read in the nodes to define the plate
#                              !  Due to symmetry only model the top-right
#                              !  quarter of the plate
fem define window;c            #Calculate the size of the window
fem define bases;r;;example        #define a bilinear basis function
fem define elements;r;;example     #defines the elements of the plate
fem draw nodes                 #Show the nodes
fem draw lines                 #Show the lines
fem define fibre;d             #Default fibre angle
fem define element;r;;example fibre
fem define equation;r;;example     #define a static linear elastic problem with
#                              !  plane strain elements
fem list equation              #List the equation
fem define material;r;;example     #define the material parameters. Young's modulus
#                              !  is 200 GPa and Poison's ratio is 0.3
fem list material              #List the material
fem define initial;r;;example      #Define the boundary conditions. Due to symmetry
#                              !  the left edge of the plate cannot move in
#                              !  the x-direction and the bottom edge of the
#                              !  plate cannot move in the y-direction. A
#                              !  uniform normal stress of 10 kPa is applied
#                              !  in the x-direction on the right edge of the
#                              !  plate and a uniform normal stress of 5 kPa
#                              !  is applied in the y-directon on the top
#                              !  edge of the plate.
fem list initial               #List the initial
fem draw nodes                 #make the node numbers visible (note the fixed
#                              !  nodal boundary conditions)
fem define solve;r;;example        #Define the solver used.
fem solve                      #solves the boundary value problem
fem draw line deformed dotted scale 3 #draws (scaled) deformed body with
#                              !  dotted lines
fem list node solution         #list the nodal displacements
fem list node reaction         #list the nodal reactions (forces)
fem draw stress scale 0.05     #draw (scaled) principal stress vectors
fem draw reaction scale 0.05   #draw (scaled) reaction (force) vectors

Additional testing commands:

fem list node solution
fem list node reaction
fem list stress full
#fem list strain !This does not work for FE40 problems

Files used by this example are:

Name                     Modified     Size

example_431.com 10-Apr-2000 2.4k planestrainplate.ipbase 10-Apr-2000 1.1k planestrainplate.ipelem 10-Apr-2000 1.1k planestrainplate.ipelfb 10-Apr-2000 640 planestrainplate.ipequa 26-May-2003 1.7k planestrainplate.ipinit 10-Apr-2000 860 planestrainplate.ipmate 10-Apr-2000 1.4k planestrainplate.ipnode 10-Apr-2000 1.5k planestrainplate.ipsolv 13-Apr-2007 1.1k test_output.com 13-Dec-2002 123

Download the entire example:

Name                      Modified     Size

examples_4_43_431.tar.gz 23-Jul-2009 6.2k

Testing status by version:

StatusTestedReal time (s)
cmSuccessSun Mar 6 00:01:55 20160
cm-debugSuccessSat Mar 5 00:02:11 20160
cmSuccessSun Aug 19 01:27:34 20073
cm-debugSuccessWed Aug 15 01:23:27 20076
cm-debug-clear-mallocSuccessSat Aug 18 01:25:56 200710
cm-debug-clear-malloc7SuccessMon Aug 20 01:23:36 20079
cm64SuccessSun Aug 19 01:28:23 20073
cm64-debugSuccessTue Aug 21 01:21:48 20076
cm64-debug-clear-mallocSuccessThu Apr 1 10:13:53 20044
cmSuccessWed Mar 4 01:07:15 20090
cm-debugSuccessMon Mar 2 01:06:56 20091
cm64SuccessWed Mar 4 01:07:15 20090
cm64-debugSuccessTue Mar 3 01:11:41 20091
cmSuccessSun Mar 6 00:01:02 20160
cm-debugSuccessSat Mar 5 00:01:13 20160

Testing status by file:

Html last generated: Sun Mar 6 05:50:20 2016

Input last modified: Wed Jul 22 08:51:18 2009

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