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:

Testing status by file:

• cmiss_test.log
  

  i686-linux
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.
  mips-irix
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.
  Success	cm-debug-clear-malloc:	cmiss_test.log.retain.
  Success	cm-debug-clear-malloc7:	cmiss_test.log.retain.
  Success	cm64:	cmiss_test.log.retain.
  Success	cm64-debug:	cmiss_test.log.retain.
  Success	cm64-debug-clear-malloc:	cmiss_test.log.retain.
  rs6000-aix
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.
  Success	cm64:	cmiss_test.log.retain.
  Success	cm64-debug:	cmiss_test.log.retain.
  x86_64-linux
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.

  
  
• cmiss_test.out
  

  i686-linux
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.
  mips-irix
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.
  Success	cm-debug-clear-malloc:	ndiff test: no significant differences with generic answer.
  Success	cm-debug-clear-malloc7:	ndiff test: no significant differences with generic answer.
  Success	cm64:	ndiff test: no significant differences with generic answer.
  Success	cm64-debug:	ndiff test: no significant differences with generic answer.
  Success	cm64-debug-clear-malloc:	ndiff test: no significant differences with generic answer.
  rs6000-aix
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.
  Success	cm64:	ndiff test: no significant differences with generic answer.
  Success	cm64-debug:	ndiff test: no significant differences with generic answer.
  x86_64-linux
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.

  
  

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

Input last modified: Wed Jul 22 08:51:17 2009