Spring 2007, MET 415 - FEA Applications I

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

Homework 4B:  3D Solid Modeling

Concepts:

• 3D Modeling
• SI Units
• Symmetry (and Loads that lie on the Symmetry Plane)
• Solid BRICK and TETRAHEDRAL elements
• Listing Data: Keypoint locations, Edges of areas, Faces of Volumes
• MAPPED Meshing
• Singularity:  Stress under a point load
  

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A steel triangular plate represents an idealization^[1] of a leaf spring (above).

• The plate is 90 cm. long, 25 cm. wide, and 2.5 cm. thick.
• A 4500 N load acts on each tip of the plate.
• At the center, the plate rests on a knife edge support.
• Elastic Modulus = 211x10⁹ Pa, Poisson's Ratio = 0.3
• SOLVE using two different TETRAHEDRAL element types (two solutions) - SOLID185 and SOLID187. (Clear the mesh, change the element type, and re-mesh for each case).  Try to achieve about the same number of elements for each case.
• SOLVE using two different BRICK element types (two solutions) - SOLID185 and SOLID186. (Clear the mesh, change the element type, and re-mesh for each case).  Try to achieve about the same number of elements for each case.
  • Use a "mapped" mesh of this structure with all of the brick shaped elements.

^[1]  R. C. Juvinall & K. M. Marshek, Fundamental of Machine Component Design, 2nd ed. Wiley & Sons, 1991, pp. 454-6.

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Turn in:

• TWO element plots showing your meshes, both a tetrahedral and a brick mesh.  Label the element type and element shape on these plots.
• ONE LINE plot showing the loads and constraints
• A hand calculation of the maximum tip deflection and the bending stress on the top face, directly above the support.  Use the hand calc. to verify the FEA model.
• A table comparing the solution which lists:
  • the different element types/shapes used,
  • the number of nodes and elements, 
  • total reaction force, 
  • actual maximum deflection, 
  • interpreted SEPC*, 
  • maximum normal stress*.  
  • Include comments on the level of error at the location where the max. stress occurs.
  • Include the hand. calc. results in this table.
• Contour plots of the solution results WHICH SHOWS THE ACTUAL MAXIMUM NORMAL STRESS* for ALL models
• Deformed shape plots which show the ACTUAL tip deflection for ALL models
   * Hint: To find the maximum deflection, the entire model should be selected.  Then, since a point load is applied to this model, there will be a high stress (and high error spot) directly under the load. UN-select the nodes and elements near the tip of the beam to find the maximum stress and the relevant error (SEPC) for this model.  Singularity is also present around the knife-edge support and effects the compressive stress levels.  (Don't draw any conclusions about the maximum compressive stress.)
• Include a session log file of the initial modeling and the first solution, to which you have added comments describing the process of modeling and loading.