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:

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 08:51:18 2009