Significance of Epsilon

Epsilon is a measure of the error.

• If Epsilon value is less than 10e-9 it indicates a numerically stable problem.
• On other hand a large value of epsilon is evidence of numerical ill-conditioning.
• In OptiStruct Epsilon value will be shown in .out file for Linear static and Nonlinear static (small displacement).

It is ratio of work done by Residual Loads to the work done by actual loads when acts through displacement{D}.

It can be calculated as follows:

ε =

Where,

• {D}= Calculated displacement vector
• R= Applied load
• ΔR= Residual load vector
      ΔR= R-{K}{D}
• K=Stiffness Matrix

Examples:

In above examples we an observe epsilon value less than 10e-9 which shows Numerically stable problem. Non linear with large displacement can be seen blank.