Spring 2008, MET 415 - FEA Applications I

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

Homework Assignment 8A

Concepts:

• 3D Element Types
• Surface Patch for Loading (or Assembly)
• Solution Steps: Load, then Unload
• NON-Linear Solution:
  • small or large deformations ?
  • gradual load application (substeps)
  • automatic time stepping
  • iterative solution, (equilibrium) convergence
  • results controls
• Postprocessing (at different time/load step points)

An allen wrench has a hexagonal cross-section with each external flat edge 1/8 in.  The long segment (H1) is 3 in., the shorter segment (V2) is 1.25 in., and the radius of the bend (R3) is 0.25 in.  Construct the 3D solid geometry with any CAD program.

Import the 3D solid geometry to ANSYS Workbench DesignModeler.

The shorter end of the wrench is inserted 1/4" into the socket of a seized screw.  A downward force is applied to the top face, last 3/4" of the longer segment.  
For each of these load "patches," create a New Sketch on an appropriate sketch plane - draw a single line to cut the wrench body, then Extrude that line; use "Imprint Faces"; Direction: Both, Symmetric; Through All; Thin: Yes, with 0 thickness - in and out

Import the modified 3D solid geometry to ANSYS Workbench Simulation.

Define properties of structural steel (E = 29E06 psi. Poisson's ratio = 0.3) and include a nonlinear stress-strain material model (Multi-linear, Kinematic Hardening)

Perform a static structural simulation

Apply a downward force of 23.5 # distributed over the last 3/4" of the top face of the longer segment. 
Use gradual loading, with automatic time stepping (initial, max. & min. substeps).  Weak springs should be unnecessary.

At the end of the shorter segment:

• on the 6 faces representing the 1/4" socket, use a "Compression Only" Support.  This support acts normal to each face, but only resists compression.  
  This is another nonlinear behavior and requires an iterative solution.
  A "Compression Only" Support can be used to model flexible body to rigid ground contact.  
  It uses contact/target regions.
• the flat face on the end is constrained with a frictionless support to keep the wrench  fully inserted in the socket.

Run the analysis for TWO Load Steps: apply the force, then remove it (ramp up, then back to zero)

GRADUAL Loading: Analysis Settings > Automatic Time Stepping: ON; Substeps (Initial >>1, min ≤ initial, max >> initial)

Turn in:

• A plot showing the mesh. (Document the number of nodes and elements used. Report the volume/mass of the model)
• An "environment" plot showing ALL the loads and constraints on the model
• A plot showing the total deformation that occurs on the model at the end of the loading step (TIME=1).
• A plot showing the vonMises stress that occurs on the model at the end of the loading step (TIME=1).
• A plot showing the equivalent plastic strain that occurs on the model at the end of the loading step (TIME=1).
• A plot showing the total deformation that occurs on the model at the end of the UN-loading step (TIME=2).
• A plot showing the vonMises stress that occurs on the model at the end of the UN-loading step (TIME=2).
• A plot showing the normal bending stress the top face of the longer segment at the end of the loading step (TIME=1), compared to a hand calculation of the expected bending stress on that face of the wrench body.
• Are large deformation effects needed in this analysis ? [Include a plot to support your answer - compare results with and without large deflection effects]