Spring 2008, MET 415 - FEA Applications I

Prof. Dave Johnson, dhj1@psu.edu, Penn State - Erie, The Behrend College

Sample Problem for Exam 2


The 0.6 m. x 0.2 m. x 0.025 m. plate shown is made of steel and has a hole in the center and circular notches directly above and below the hole. All three circular features have a radius of 0.015 m.

The plate is loaded parallel to its longest dimension with a traction surface load, P.

Use SI units in solving this problem.

THIS PROBLEM COULD BE SOLVED as a 2D model, but for Exam 2 practice, use 3D and 1/8 symmetry

Use the ANSYS material library for the properties of structural steel (E = 2.0E11 Pa = 2.0E05 MPa).

Add nonlinear, bilinear, kinematic hardening material properties with a yield stress of 300,000,000 Pa (300 MPa) and a tangent modulus of 0.0 (i.e., perfectly plastic). Use only one temperature (0) for the model.

What is the volume of your model ?

        From WB, Model > Geometry, Details Area, Properties: Volume = 370,580 cu. mm. (model is 1/8 symmetry)

What element type and element options did you use ? 
        My 1/8 symmetry model had 7568 SOLID186, plane stress w/thickness, and 100 SURF154 for load application

What is the total horizontal reaction force (SFx in N) on the model
        281,250 N (This is for the 1/8 model with loaded end area = 12.5 mm x 100 mm)

What is the maximum deflection (mm.) for the entire part ? 
        2*(0.3574 mm.) = 0.715 m. (consider only the horizontal stretch of the full part)
Note: 0.3574 mm is from Total Deformation.  The max. Directional Deformation, X is 0.356 mm

What is the maximum vonMises stress (in Pa) ? 
        303.4 MPa (can vary depending on mesh refinement near holes)

Did yielding occur on this model ? 
        Inspect the plot of equivalent plastic strain - if non-zero regions of plastic strain are visible on the model, then: Yes, yielding did occur.

How many TOTAL iterations (cumulative iterations) were needed to solve this model
(LOOK in the Solution Information Output -OR- Force Convergence).
        13 (can vary depending on your assignment of automatic time stepping: initial/min/max substeps)

Should you include large deformation effects in this analysis ? WHY
    NO, 0.36 mm deflection is not large wrt. model dimensions
Also (to prove it), with Large Deflection Effects, ON; gradual loading, automatic time stepping, etc.: max. total deformation = 0.35767 mm., and the max. vonMises stress is 303.6 M Pa, which show very small impact of large deformation effects. Sometimes you have to try it to see if the volume change of the elements effects the stiffness, deflection, and/or stresses.