MET 425 - FEA Applications II

Nonlinear Analysis and Bolt Preload

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

(REVIEW) Nonlinear Analysis:

Nonlinear Analysis is required when a useful answer cannot be determined by    LINEAR    methods.

• yielding/plasticity (beyond Hooke's law: s = Ee)
  [Requires: material property definition: s-e curve model]
• changing contact or interference between parts of an assembly
  [Requires: contact/target elements on surfaces which may change contact, plus settings and properties for the contact surface]
• large displacement, large rotation, large strain, stress stiffening
  (fishing pole, guitar string, drum head),   SMALL ANGLES   approximation: sin(q)=q, tan(q)=0, and cos(q) = 1
  [Requires: activate large deformation "switch," NLGEOM,ON]
• manufacturing processes (mold filling, forging, rolling, stamping, welding, coating).  [May require several nonlinear effects (plasticity, contact, large deformation) and birth & death of elements feature]
• specialty: hyperelastic (elastomer), viscoelastic, creep, etc.
  [Requires: unique material property definition]

New Material Reading:  ANSYS Help > Mechanical Applications > Mechanical Applications User's Guide > Features > Analysis Settings > Steps and Step Controls for Static and Transient Analyses

 Procedure:  Apply Loads GRADUALLY (incremental solution):

• Load steps:    USER   selected points which describe the load history (convenient to the analyst). 
  TIME: even though we are doing a static analysis, time is used simply as a  PROGRESS COUNTER  during the solution.  If the analyst doesn't set the value for time, ANSYS increases time by one for each load step (i.e. time always increases during a solution).
• Substeps: incremental solutions within a load step (for stability and accuracy); too small = long runs; too big = error or divergence.
  Ramped loading (KBC,0) increases the load linearly from the previous step's level to the current load step's final value (default).  The opposite of ramped loading is "stepped" loading (KBC,1).
• Equilibrium iterations: solutions without increment in loading, just correction of imbalance caused by nonlinear behavior.  To establish a "stable" solution (equilibrium) before additional loading is introduced.
  NON-Linear Analysis CONVERGENCE: A nonlinear solution is a series of successive linear (solution) steps, i.e., substeps, along a path that is not   A STRAIGHT LINE  .  Each small step must converge, i.e., must be in equilibrium, before the load is increased.

 General guidelines:

• The first analysis (sub) step should not cause yielding
• Take small steps at an abrupt transition.
• "Mildly" nonlinear problems can take larger steps
• Let the FEA program adjust the time stepping process.  Better to get a solution with less of your time spent trying to control it.  ANSYS does a fairly good job. (Activate automatic time stepping: AUTOTS,ON plus initial/min/max stepping)

 Control Output to Results File

Why ? 

• More results available for nonlinear, iterative solution

• May need   MORE   for debugging (output of intermediate load steps and substeps)

• May need   LESS   to conserve disk space

MESH ERROR ?

Mesh error energy calculations (SERR, SEPC) are invalid for NONLINEAR solutions. 
Structural mesh error calculations should be linear elastic and may use solid elements having only structural degrees of freedom and 3D shell elements.

[ANSYS Commands Reference Guide, PRERR command]

How do we evaluate mesh quality for a nonlinear solution ?

• Qualitative measure: look for jagged contours
• Quantitative measure: refine, re-solve, see if answers change - repeat if needed

Reference Reading:  ANSYS Help > Mechanical APDL > Structural Analysis Guide,  Chapter 8.1 – 8.6

New Material Reading:  ANSYS Help > Mechanical Applications > Mechanical Applications User's Guide > Features > Applying Boundary Conditions > Types of Loads > Bolt Pretension

 Available for 3-D simulations only.  Applies to a cylindrical face, to a straight edge of a line body, to a single or to multiple bodies (requires a local Coordinate System)

 The bolt load may be applied as:

• Load: Applies a force as a preload.

• Adjustment: Applies a length as a pre-adjustment. 

• Lock: Fixes all displacements (on the pretension section through the cyl. body). You can set this state for any step except the first step.

• Open: leaves the Bolt Pretension load open so that the load has no effect on the applied step. You can set this state for any step.