Example 422: A plane stress 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 stress. 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 = sigma_x/E - nu.sigma_y/E and e_y = sigma_y/E - 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 0.0425 micrometers in the x-direction and 0.010 micrometers in the y-direction. Compare this with the equivalent plane strain example in example_431.

The comfile run by this example is as follows:

#Example_442 A square plate under plane stress uniform normal stress
fem                              #set up the FEM environment
fem define nodes;r;planestressplate;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 stress 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 boundary conditions
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_422.com 10-Apr-2000 2.6k planestressplate.ipbase 10-Apr-2000 1.1k planestressplate.ipelem 10-Apr-2000 1.1k planestressplate.ipelfb 10-Apr-2000 640 planestressplate.ipequa 26-May-2003 1.7k planestressplate.ipinit 10-Apr-2000 860 planestressplate.ipmate 10-Apr-2000 1.4k planestressplate.ipnode 10-Apr-2000 1.5k planestressplate.ipsolv 13-Apr-2007 1.1k test_output.com 13-Dec-2002 122

Download the entire example:

Name                      Modified     Size

examples_4_42_422.tar.gz 23-Jul-2009 6.2k

Testing status by version:

StatusTestedReal time (s)
cmSuccessSun Mar 6 00:01:54 20161
cm-debugSuccessSat Mar 5 00:02:10 20160
cmSuccessSun Aug 19 01:29:21 20074
cm-debugSuccessWed Aug 15 01:23:54 20075
cm-debug-clear-mallocSuccessSat Aug 18 01:27:11 200710
cm-debug-clear-malloc7SuccessMon Aug 20 01:23:36 200710
cm64SuccessSun Aug 19 01:29:38 20073
cm64-debugSuccessTue Aug 21 01:21:05 20076
cm64-debug-clear-mallocSuccessThu Apr 1 10:13:51 20043
cmSuccessWed Mar 4 01:07:14 20090
cm-debugSuccessMon Mar 2 01:06:18 20091
cm64SuccessWed Mar 4 01:07:14 20090
cm64-debugSuccessTue Mar 3 01:11:40 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 08:51:17 2009

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