Concepts:

Contact finite elements/Impact
Full Transient Dynamic Analysis Damping Options
Time Integration Initial Conditions
Time History Postprocessor
Animation, Over Time

A solid ball, of 3 in. radius, is dropped from 100 in. above a flexible base.  The ball is released from rest at a position which is off-center with respect to the base.

Treat this as a 2D system (Geometry file - ParaSolid, available):

• Use 2D plane stress elements (unit thickness) to model the ball (obviously, we are not concerned with the stresses developed in the ball).  Mapped Face Mesh, quads; face sizing w 0.5" element size. (We want a coarse mesh for better solution speed).

• Use 2D plane stress elements to model the 100 in. long base.  The base is 1.0 in high, unit depth (or thickness) and fixed at both ends.  Mesh the base: Mapped Face Mesh, quads; edge sizing 2 elements through the 1" dimension.

• The both bodies are the same material.  Modulus, 1,000,000 psi; Poisson's ratio, 0.40; and density of 0.20 lbm/cu.in

Hand calculations:

• Predict the time of impact based on free-fall behavior
• Transverse (or bending) natural frequencies of  the "clamped-clamped" beam (handout)

Solution:

• LOAD STEP 1:
  • Gravity load acts on both bodies
  • Ball constrained by a "Displacement" Support: UX = UY = 0
  • Base is fixed at Both Ends - use 2 separate Fixed Supports
  • Starting from rest (static), no initial velocity
  • Step, end time: 0.001 sec (WHY such a small value for TIME ?)
  • Auto Time Stepping: OFF
  • Define By: Substeps
  • No. of Substeps: 2     (WHY two substeps ?)
  • Time Integration: OFF   (WHY turn off time integration ?)
  • Weak Springs: OFF
  • Large Deflection: ON
  • Output Controls, Calculate Results At:  Last Time Point
  • Analysis Data Management: Where are the solution files being written ?
• LOAD STEP 2:
  • Step, end time: 3.0 sec
  • Auto Time Stepping: ON
  • Define By: TIME
  • Initial Time Step: 0.001 s
  • Minimum Time Step: 0.000001 s
  • Maximum Time Step: 0.2 s
  • Time Integration: ON
  • Weak Springs: OFF
  • Large Deflection: ON
  • Output Controls: Calculate Results At, Equally Spaced Time Points
  • Number of Time Points: 50
  • RELEASE the ball part so it can drop (In the "Tabular Data" table, right-mouse on the Displacement condition for the ball for load Step 2 and select the toggle, "Activate/Deactivate At This Step," to release the displacement condition)

Turn In:

• the hand calculations: time of impact and natural frequencies of clamped-clamped beam
• Answers to the 3 (bolded) questions embedded in the procedure, above
• plots illustrating the model environment
• plot which shows the contact region
• time history plots (displacement probe or reaction probe) of:
  • the vertical motion of the center of the base, 
  • the vertical motion of the ball
  • of the vertical reaction forces at EACH end of the base, separately
• time history plots* of solution summary items:
  • the integration time step size,
  • the number of equilibrium iterations for each substep, 
  • the response frequency of the system
  • Write an description of what each of these solution summary item plots shows
•   What frequencies do you see responding in the time history plot of vertical motion of the center of the base ?
• Describe the vibration of the base that is observed in the animation (Is it 1st mode bending or higher modes ?).  Compare to the calculated natural frequencies of the base.  Does this response match the hand calculations ?  which frequency ?
• show a results animation to your instructor

* A command object for Time History Postprocessor (POST26):

/SHOW,PNG ! send plots to PNG file
/GFILE,400 ! plot file resolution
/RGB,INDEX,100,100,100,0 ! switch the
/RGB,INDEX,0,0,0,15 ! B/W colors
/VIEW,1,0,0,1 ! set the viewing direction
/POST26
SOLU,2,DTIME,,ITS
SOLU,3,EQIT,,NoEqIt
SOLU,4,RESFRQ,,RespFreq
PLVAR,2
PLVAR,3
PLVAR,4
FINISH